![\"Note:](\"../images/qiskit_header.png\")
Trusted Notebook\" align=\"middle\">"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Qiskit Tutorials\n",
+ "\n",
+ "***\n",
+ "\n",
+ "\n",
+ "Welcome Qiskitters.\n",
+ "\n",
+ "\n",
+ "These tutorials aim to explain how to use Qiskit. We assume you have installed Qiskit; if not, please look at [qiskit.org](http://www.qiskit.org) or the install [documentation](https://qiskit.org/documentation/install.html). \n",
+ "\n",
+ "\n",
+ "We've collected a core reference set of notebooks in this section outlining the features of Qiskit. We will be keeping them up to date with the latest Qiskit version, currently 0.12. The focus of these notebooks is not on learning quantum computing. Instead we will be focused on how to use Qiskit, and will go into details only when needed. For those interested in learning about quantum computing we recommend the awesome [educational material](https://quantum-computing.ibm.com/support) we and the community have put together.\n",
+ "\n",
+ "\n",
+ "Qiskit is made up of four elements: Terra, Aer, Ignis, and Aqua. Each element has its own goal, and together they make the full Qiskit framework. \n",
+ "\n",
+ "## Getting started with Qiskit\n",
+ "\n",
+ "This section gives you the tools to make your first circuits, run them on real quantum systems and simulators, and view the data.\n",
+ "\n",
+ "1. [Getting started with Qiskit](fundamentals/1_getting_started_with_qiskit.ipynb) - How to use Qiskit.\n",
+ "\n",
+ "2. [Plotting data in Qiskit](fundamentals/2_plotting_data_in_qiskit.ipynb) - Illustrates the different ways of plotting data in Qiskit.\n",
+ " \n",
+ "3. [The IBM Q Account](fundamentals/3_the_ibmq_account.ipynb) - Understanding the IBM Q account.\n",
+ "\n",
+ "4. [Circuit Properties](fundamentals/4_quantum_circuit_properties.ipynb) - Important properties of quantum circuits.\n",
+ " \n",
+ "5. [Using the Transpiler](fundamentals/5_using_the_transpiler.ipynb) - Mapping and optimizing circuits using the Qiskit transpiler.\n",
+ "\n",
+ "6. [Jupyter Tools](fundamentals/6_qiskit_jupyter_tools.ipynb) - Qiskit functionality for Jupyter notebooks.\n",
+ "\n",
+ "7. [Summary of quantum operations](fundamentals/7_summary_of_quantum_operations.ipynb) - List of quantum operations (gates, reset, measurements) in Qiskit Terra\n",
+ " \n",
+ " \n",
+ "## 2 Qiskit Terra\n",
+ "\n",
+ "Terra, the ‘earth’ element, is the foundation on which the rest of the software lies. Terra provides a bedrock for composing quantum programs at the level of circuits and pulses, to optimize them for the constraints of a particular device, and to manage the execution of batches of experiments on remote-access devices. Terra defines the interfaces for a desirable end-user experience, as well as the efficient handling of layers of optimization, pulse scheduling and backend communication.\n",
+ "\n",
+ "1. [Advanced circuits](advanced/terra/1_advanced_circuits.ipynb) - Circuit building tools added including registerless declarations, composite gate updates and parameterized circuits.\n",
+ "2. [Operators overview](advanced/terra/2_operators_overview.ipynb) - Gives a summary of the features and uses of the Operator class.\n",
+ "3. [Advanced circuit visualization](advanced/terra/3_advanced_circuit_visualization.ipynb) - Details on drawing your quantum circuits.\n",
+ "4. [Transpiler passes and passmanager](advanced/terra/4_transpiler_passes_and_passmanager.ipynb) - How to use the transpiler passes, passmanger, and extend the transpiler with a new pass.\n",
+ "5. [Pulse schedules](advanced/terra/5_pulse_schedules.ipynb) - An introduction to working with pulse schedules.\n",
+ "6. [Creating a new provider](advanced/terra/6_creating_a_provider.ipynb) - A guide to integration of a new provider with Qiskit structures and interfaces\n",
+ "\n",
+ "\n",
+ "\n",
+ "## 3 Qiskit Aer\n",
+ "\n",
+ "Aer, the ‘air’ element, permeates all Qiskit elements. To really speed up development of quantum computers, we need better simulators with the ability to model realistic noise processes that occur during computation on actual devices. Aer provides a high-performance simulator framework for studying quantum computing algorithms and applications in the noisy intermediate-scale quantum regime. \n",
+ "1. [Aer provider](advanced/aer/1_aer_provider.ipynb) - Gives a summary of the Qiskit Aer provider containing the Qasm, statevector, and unitary simulator\n",
+ "2. [Device noise simulation](advanced/aer/2_device_noise_simulation.ipynb) - Shows how to use the Qiskit Aer noise module to automatically generate a basic noise model for simulating hardware backends\n",
+ "3. [Building noise models](advanced/aer/3_building_noise_models.ipynb) - Shows how to use Qiskit Aer noise module to construct custom noise models for noisy simulations\n",
+ "4. [Custom gate noise](advanced/aer/4_custom_gate_noise.ipynb) - Shows to implement simulations using custom noisy gates.\n",
+ "5. [Noise transformations](advanced/aer/5_noise_transformation.ipynb) - Demonstrates the noise approximation utility functions to construct approximate Clifford noise models out of a general noise model\n",
+ "6. [Extended stabilizer tutorial](advanced/aer/6_extended_stabilizer_tutorial.ipynb) - Gives an overview of the *extended stabilizer* Qasm Simulator method\n",
+ "7. [Matrix Product State simulator](advanced/aer/7_matrix_product_state_method.ipynb) - Gives an overview of the *matrix product state* Simulator method\n",
+ " \n",
+ "## 4 Qiskit Ignis\n",
+ "Ignis, the ‘fire’ element, is dedicated to fighting noise and errors and to forging a new path. This includes better characterization of errors, improving gates, and computing in the presence of noise. Ignis is meant for those who want to design quantum error correction codes, or who wish to study ways to characterize errors through methods such as tomography and randomized benchmarking, or even to find a better way for using gates by exploring dynamical decoupling and optimal control. Ignis tutorials are found [here](advanced/ignis/) and include:\n",
+ " 1. [Calibrating a qubit](advanced/ignis/1_calibrating_a_qubit.ipynb) - Using pulse to calibrate a \"pi-pulse\" gate by fitting a Rabi oscillation on a qubit. Using the \"pi-pulse\" measure the single-shot analog voltages that are returned by an experiment.\n",
+ " 2. [Hamiltonian and gate characterizations](advanced/ignis/2_hamiltonian_and_gate_characterization.ipynb) - Sequences to measure ZZ rates between qubits and to measure rotation and angle errors in the gates.\n",
+ " 3. [Relaxation and decoherence](advanced/ignis/3_relaxation_and_decoherence.ipynb) - How to measure coherence times on the real quantum hardware\n",
+ " 4. [Measurement error mitigation](advanced/ignis/4_measurement_error_mitigation.ipynb) - How to peform calibration experiments for measurement errors and fed those calibrations into a \"filter\" that can be utilized to mitigate errors in subsequent experiments.\n",
+ " 5. Randomized Benchmarking:\n",
+ " * a. [Randomized benchmarking](advanced/ignis/5a_randomized_benchmarking.ipynb) - Randomized benchmarking (RB) is a technique used to measure the average gate error by measuring the outcomes of random Clifford circuits. This is used internally to report gate errors on our systems. \n",
+ " * b. [Interleaved RB](advanced/ignis/5b_interleaved_rb.ipynb) - A variant of RB used to measure the error of a specific gate.\n",
+ " * c. [Purity RB](advanced/ignis/5c_purity_rb.ipynb) - A variant of RB used to measure the *incoherent* error per gate.\n",
+ " 6. Tomography:\n",
+ " * a. [Quantum state tomography](advanced/ignis/6a_state_tomography.ipynb) - How to identify a quantum state using state tomography, in which the state is prepared repeatedly and measured in different bases. \n",
+ " * b. [Quantum process tomography](advanced/ignis/6b_process_tomography.ipynb) - A method to reconstruct the quantum process matrix by preparing certain states, applying a gate, and then measuring the outcome in different bases. \n",
+ " 7. [Quantum volume](advanced/ignis/7_quantum_volume.ipynb) - How to run quantum volume measurements on the quantum hardware.\n",
+ " 8. [Repetition Code](advanced/ignis/8_repetition_code.ipynb) - How to run a simple error correction code, known as the repetition code. This can be used to characterize bit flip errors in the hardware.\n",
+ " 9. [Logging](advanced/ignis/9_ignis_logging.ipynb) - An introduction to some of the logging features in Ignis, intended to be used to track characterization parameters.\n",
+ " \n",
+ "\n",
+ "## 5 Qiskit Aqua\n",
+ "Aqua, the ‘water’ element, is the element of life. To make quantum computing live up to its expectations, we need to find real-world applications. Aqua is where algorithms for NISQ computers are built. These algorithms can be used to build applications for quantum computing.\n",
+ " * [Amplitude Estimation](advanced/aqua/amplitude_estimation.ipynb) - Illustrates amplitude estimation, for a simple case, where the (assumed to be unknown) success probability *p* of a Bernoulli random variable is estimated\n",
+ " * [HHL](advanced/aqua/linear_systems_of_equations.ipynb) - Solving linear systems of equations with the HHL algorithm\n",
+ " * [Creating an Aqua algorithm](advanced/aqua/Aqua_how_to_build_a_pluggable_algorithm_components.ipynb) - Building an algorithm within the framework of Aqua\n",
+ "\n",
+ "Aqua is accessible to domain experts in *Artificial Intelligence*, *Chemistry*, *Finance* or *Optimization*, who want to explore the benefits of using quantum computers as accelerators for specific computational tasks, without needing to worry about how to translate the problem into the language of quantum machines:\n",
+ "\n",
+ "### 5.1 Qiskit Artificial Intelligence\n",
+ "[Qiskit AI](advanced/aqua/artificial_intelligence/index.ipynb) demonstates using quantum computers to tackle problems in the artificial intelliegence domain. These include using a quantum-enhanced support vector machine to experiment with classification problems on a quantum computer\n",
+ "\n",
+ "### 5.2 Qiskit Chemistry\n",
+ "[Qiskit Chemistry](advanced/aqua/chemistry/index.ipynb) - applications in the domain of quantum chemistry on quantum computers, including ground state energy, dipole moments and dissociation plots\n",
+ "\n",
+ "### 5.3 Qiskit Finance\n",
+ "[Qiskit Finance](advanced/aqua/finance/index.ipynb) - provides a collection of applications of quantum algorithms to use cases relevant in finance. This includes use cases like portfolio management, derivative pricing, or credit risk analysis.\n",
+ " \n",
+ "### 5.4 Qiskit Optimization\n",
+ "[Qiskit Optimization](advanced/aqua/optimization/index.ipynb) - using VQE (Variational Quantum Eigensolver) to experiment with optimization problems (max-cut and traveling salesman problem) on a quantum computer. Includes optimization problem modelling, using docplex, which can be automatically translated to input suitable for VQE.\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-09T15:31:26.743124Z",
+ "start_time": "2019-08-09T15:31:26.732618Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "This code is a part of Qiskit
© Copyright IBM 2017, 2019.
This code is licensed under the Apache License, Version 2.0. You may
obtain a copy of this license in the LICENSE.txt file in the root directory
of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
Any modifications or derivative works of this code must retain this
copyright notice, and modified files need to carry a notice indicating
that they have been altered from the originals.
![\"Note:](\"../../../images/qiskit_header.png\")
Trusted Notebook\" align=\"middle\">"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Terra 0.8 - Circuit API Updates"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "In this tutorial, we'll introduce three new components of the Terra circuit-building API added in the Terra 0.8 release. Their purpose is to facilitate circuit construction, reduce boilerplate, and aid reuse through composition and parameterization. These three new components are:\n",
+ "\n",
+ " 1. [Optional register declarations](#1.-Optional-register-declarations)\n",
+ " 2. [Portable `Instruction`s and `CompositeGate` replacement](#2.-Portable-Instructions-and-CompositeGate-replacement)\n",
+ " 3. [Parameterized Circuit](#3.-Parameterized-circuits)\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:00:47.649701Z",
+ "start_time": "2019-08-21T09:00:45.301727Z"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister\n",
+ "import matplotlib.pyplot as plt\n",
+ "%matplotlib inline"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## 1. Optional registers\n",
+ "\n",
+ "For circuits that require only a single register, register declarations can amount to unneeded overhead.\n",
+ "Terra 0.8 adds more concise syntax to create and build circuits without explicit register declaration."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Registerless `QuantumCircuit` declaration"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "An alternate constructor has been added to `QuantumCircuit` that accepts one or two integers: the number of qubits (required), and the number of classical bits (optional)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:00:47.654546Z",
+ "start_time": "2019-08-21T09:00:47.651707Z"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "qc = QuantumCircuit(3, 2)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "This will create a quantum circuit equivalent to the following (still valid) circuit declaration:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:00:47.661925Z",
+ "start_time": "2019-08-21T09:00:47.656456Z"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "qr = QuantumRegister(3, name='q')\n",
+ "cr = ClassicalRegister(2, name='c')\n",
+ "qc = QuantumCircuit(qr, cr)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Registers are created automatically and can be accessed through the circuit as needed."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:00:47.667125Z",
+ "start_time": "2019-08-21T09:00:47.663431Z"
+ }
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[QuantumRegister(3, 'q')]\n",
+ "[ClassicalRegister(2, 'c')]\n"
+ ]
+ }
+ ],
+ "source": [
+ "print(qc.qregs)\n",
+ "print(qc.cregs)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Quantum/classical bit index-based addressing"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "In the spirit of register-less circuits, qubits and classical bits (clbits) can now be addressed directly by index, without a need for referencing a register.\n",
+ "In the following example, `bell.h(0)` attaches a Hadamard gate to the first quantum bit."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:00:47.677660Z",
+ "start_time": "2019-08-21T09:00:47.668843Z"
+ },
+ "scrolled": true
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
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┌───┐ \n", + "q2_0: |0>┤ H ├──────\n", + " ├───┤┌─┐┌─┐\n", + "q1_0: |0>┤ H ├┤M├┤M├\n", + " └───┘└╥┘└╥┘\n", + " c_0: 0 ══════╩══╬═\n", + " ║ \n", + " c_1: 0 ═════════╩═\n", + "" + ], + "text/plain": [ + "
┌──────────┐ \n", + "q_0: |0>┤0 ├────────────\n", + " │ my_gate │┌──────────┐\n", + "q_1: |0>┤1 ├┤0 ├\n", + " └──────────┘│ my_gate │\n", + "q_2: |0>────────────┤1 ├\n", + " └──────────┘" + ], + "text/plain": [ + "
┌───┐ \n", + "q_0: |0>┤ H ├──■────────────────────\n", + " └───┘┌─┴─┐ ┌───────────┐\n", + "q_1: |0>─────┤ X ├──■──┤0 ├\n", + " └───┘┌─┴─┐│ sub_circ │\n", + "q_2: |0>──────────┤ X ├┤1 ├\n", + " └───┘└───────────┘" + ], + "text/plain": [ + "
┌──────────┐ \n", + "q_0: |0>┤ U2(0,pi) ├──■──────────────────────────────────────\n", + " └──────────┘┌─┴─┐ ┌───┐ ░ ┌────────────┐\n", + "q_1: |0>────────────┤ X ├──■──┤ H ├────■─────░─┤ U3(1,2,-2) ├\n", + " └───┘┌─┴─┐└───┘┌───┴───┐ ░ └───┬────┬───┘\n", + "q_2: |0>─────────────────┤ X ├─────┤ Rz(1) ├─░─────┤ Id ├────\n", + " └───┘ └───────┘ ░ └────┘" + ], + "text/plain": [ + "
┌───┐ ░ ┌───────┐ ░ ┌───┐┌─┐\n", + "q_0: |0>┤ H ├──■──────────────────░─┤ Rz(θ) ├─░──────────────────■──┤ H ├┤M├\n", + " └───┘┌─┴─┐ ░ ├───────┤ ░ ┌─┴─┐└───┘└╥┘\n", + "q_1: |0>─────┤ X ├──■─────────────░─┤ Rz(θ) ├─░─────────────■──┤ X ├──────╫─\n", + " └───┘┌─┴─┐ ░ ├───────┤ ░ ┌─┴─┐└───┘ ║ \n", + "q_2: |0>──────────┤ X ├──■────────░─┤ Rz(θ) ├─░────────■──┤ X ├───────────╫─\n", + " └───┘┌─┴─┐ ░ ├───────┤ ░ ┌─┴─┐└───┘ ║ \n", + "q_3: |0>───────────────┤ X ├──■───░─┤ Rz(θ) ├─░───■──┤ X ├────────────────╫─\n", + " └───┘┌─┴─┐ ░ ├───────┤ ░ ┌─┴─┐└───┘ ║ \n", + "q_4: |0>────────────────────┤ X ├─░─┤ Rz(θ) ├─░─┤ X ├─────────────────────╫─\n", + " └───┘ ░ └───────┘ ░ └───┘ ║ \n", + " c_0: 0 ══════════════════════════════════════════════════════════════════╩═\n", + "" + ], + "text/plain": [ + "
"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "fig = plt.figure(figsize=(8,6))\n",
+ "ax = fig.add_subplot(111)\n",
+ "\n",
+ "ax.plot(theta_range, list(map(lambda c: c.get('0', 0), counts)), '.-', label='0')\n",
+ "ax.plot(theta_range, list(map(lambda c: c.get('1', 0), counts)), '.-', label='1') \n",
+ "\n",
+ "ax.set_xticks([i * np.pi / 2 for i in range(5)])\n",
+ "ax.set_xticklabels(['0', r'$\\frac{\\pi}{2}$', r'$\\pi$', r'$\\frac{3\\pi}{2}$', r'$2\\pi$'], fontsize=14)\n",
+ "ax.set_xlabel('θ')\n",
+ "ax.legend()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-04-24T14:50:01.020312Z",
+ "start_time": "2019-04-24T14:49:58.618Z"
+ }
+ },
+ "source": [
+ "### Reducing compilation cost"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Compiling over a parameterized circuit prior to binding can, in some cases, significantly reduce compilation time as compared to compiling over a set of bound circuits."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:01:22.016899Z",
+ "start_time": "2019-08-21T09:01:04.252823Z"
+ }
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Time compiling over set of bound circuits: 17.536379098892212\n"
+ ]
+ }
+ ],
+ "source": [
+ "import time\n",
+ "from itertools import combinations\n",
+ "from qiskit.compiler import transpile, assemble\n",
+ "from qiskit.test.mock import FakeTokyo\n",
+ "\n",
+ "start = time.time()\n",
+ "qcs = []\n",
+ "\n",
+ "theta_range = np.linspace(0, 2*np.pi, 32)\n",
+ "\n",
+ "for n in theta_range:\n",
+ " qc = QuantumCircuit(5)\n",
+ "\n",
+ " for k in range(8):\n",
+ " for i,j in combinations(range(5), 2):\n",
+ " qc.cx(i,j)\n",
+ " qc.rz(n, range(5))\n",
+ " for i,j in combinations(range(5), 2):\n",
+ " qc.cx(i,j)\n",
+ "\n",
+ " qcs.append(qc)\n",
+ " \n",
+ "compiled_circuits = transpile(qcs, backend=FakeTokyo())\n",
+ "qobj = assemble(compiled_circuits, backend=FakeTokyo())\n",
+ "\n",
+ "end = time.time()\n",
+ "print('Time compiling over set of bound circuits: ', end-start)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:01:24.863414Z",
+ "start_time": "2019-08-21T09:01:22.698533Z"
+ }
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Time compiling over parameterized circuit, then binding: 2.1587467193603516\n"
+ ]
+ }
+ ],
+ "source": [
+ "start = time.time()\n",
+ "qc = QuantumCircuit(5)\n",
+ "theta = Parameter('theta')\n",
+ "\n",
+ "for k in range(8):\n",
+ " for i,j in combinations(range(5), 2):\n",
+ " qc.cx(i,j)\n",
+ " qc.rz(theta, range(5))\n",
+ " for i,j in combinations(range(5), 2):\n",
+ " qc.cx(i,j)\n",
+ "\n",
+ "transpiled_qc = transpile(qc, backend=FakeTokyo())\n",
+ "qobj = assemble([transpiled_qc.bind_parameters({theta: n})\n",
+ " for n in theta_range], backend=FakeTokyo())\n",
+ "end = time.time()\n",
+ "print('Time compiling over parameterized circuit, then binding: ', end-start)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Composition"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Parameterized circuits can be composed like standard `QuantumCircuit`s.\n",
+ "Generally, when composing two parameterized circuits, the resulting circuit will be parameterized by the union of the parameters of the input circuits."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-05-08T15:07:47.268889Z",
+ "start_time": "2019-05-08T15:07:47.262971Z"
+ }
+ },
+ "source": [
+ "However, parameter names must be unique within a given circuit.\n",
+ "When attempting to add a parameter whose name is already present in the target circuit:\n",
+ " - if the source and target share the same `Parameter` instance, the parameters will be assumed to be the same and combined\n",
+ " - if the source and target have different `Parameter` instances, an error will be raised\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:01:50.115060Z",
+ "start_time": "2019-08-21T09:01:50.103768Z"
+ }
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " ┌────────────┐┌────────────┐\n",
+ "q_0: |0>┤0 ├┤0 ├\n",
+ " │ sc_1(phi) ││ sc_2(phi) │\n",
+ "q_1: |0>┤1 ├┤1 ├\n",
+ " ├────────────┤└────────────┘\n",
+ "q_2: |0>┤0 ├──────────────\n",
+ " │ sc_2(phi) │ \n",
+ "q_3: |0>┤1 ├──────────────\n",
+ " └────────────┘ \n"
+ ]
+ }
+ ],
+ "source": [
+ "phi = Parameter('phi')\n",
+ "\n",
+ "sub_circ1 = QuantumCircuit(2, name='sc_1')\n",
+ "sub_circ1.rz(phi, 0)\n",
+ "sub_circ1.rx(phi, 1)\n",
+ "\n",
+ "sub_circ2 = QuantumCircuit(2, name='sc_2')\n",
+ "sub_circ2.rx(phi, 0)\n",
+ "sub_circ2.rz(phi, 1)\n",
+ "\n",
+ "qc = QuantumCircuit(4)\n",
+ "qr = qc.qregs[0]\n",
+ "\n",
+ "qc.append(sub_circ1.to_instruction(), [qr[0], qr[1]])\n",
+ "qc.append(sub_circ2.to_instruction(), [qr[0], qr[1]])\n",
+ "\n",
+ "qc.append(sub_circ2.to_instruction(), [qr[2], qr[3]])\n",
+ "\n",
+ "print(qc.draw())\n",
+ "\n",
+ "# The following raises an error: \"QiskitError: 'Name conflict on adding parameter: phi'\"\n",
+ "# phi2 = Parameter('phi')\n",
+ "# qc.u3(0.1, phi2, 0.3, 0)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "To insert a subcircuit under a different parameterization, the `to_instruction` method accepts an optional argument (`parameter_map`) which, when present, will generate instructions with the source parameter replaced by a new parameter."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:01:52.116713Z",
+ "start_time": "2019-08-21T09:01:52.098869Z"
+ }
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " ┌────────────────┐\n",
+ "q1_0: |0>┤0 ├\n",
+ " │ │\n",
+ "q1_1: |0>┤1 oracle(theta) ├\n",
+ " │ │\n",
+ "q1_2: |0>┤2 ├\n",
+ " └┬──────────────┬┘\n",
+ "q1_3: |0>─┤0 ├─\n",
+ " │ │ \n",
+ "q1_4: |0>─┤1 oracle(phi) ├─\n",
+ " │ │ \n",
+ "q1_5: |0>─┤2 ├─\n",
+ " ┌┴──────────────┴┐\n",
+ "q1_6: |0>┤0 ├\n",
+ " │ │\n",
+ "q1_7: |0>┤1 oracle(gamma) ├\n",
+ " │ │\n",
+ "q1_8: |0>┤2 ├\n",
+ " └────────────────┘\n",
+ " ┌───────────┐ \n",
+ "q1_0: |0>┤ Rz(theta) ├──■─────────────────────────────────\n",
+ " └───────────┘┌─┴─┐┌───────────┐ \n",
+ "q1_1: |0>─────────────┤ X ├┤ Rz(theta) ├──■───────────────\n",
+ " └───┘└───────────┘┌─┴─┐┌───────────┐\n",
+ "q1_2: |0>───────────────────────────────┤ X ├┤ Rz(theta) ├\n",
+ " ┌─────────┐ └───┘└───────────┘\n",
+ "q1_3: |0>─┤ Rz(phi) ├───■─────────────────────────────────\n",
+ " └─────────┘ ┌─┴─┐ ┌─────────┐ \n",
+ "q1_4: |0>─────────────┤ X ├─┤ Rz(phi) ├───■───────────────\n",
+ " └───┘ └─────────┘ ┌─┴─┐ ┌─────────┐ \n",
+ "q1_5: |0>───────────────────────────────┤ X ├─┤ Rz(phi) ├─\n",
+ " ┌───────────┐ └───┘ └─────────┘ \n",
+ "q1_6: |0>┤ Rz(gamma) ├──■─────────────────────────────────\n",
+ " └───────────┘┌─┴─┐┌───────────┐ \n",
+ "q1_7: |0>─────────────┤ X ├┤ Rz(gamma) ├──■───────────────\n",
+ " └───┘└───────────┘┌─┴─┐┌───────────┐\n",
+ "q1_8: |0>───────────────────────────────┤ X ├┤ Rz(gamma) ├\n",
+ " └───┘└───────────┘\n"
+ ]
+ }
+ ],
+ "source": [
+ "p = Parameter('p')\n",
+ "qc = QuantumCircuit(3, name='oracle')\n",
+ "qc.rz(p, 0)\n",
+ "qc.cx(0, 1)\n",
+ "qc.rz(p, 1)\n",
+ "qc.cx(1, 2)\n",
+ "qc.rz(p, 2)\n",
+ "\n",
+ "theta = Parameter('theta')\n",
+ "phi = Parameter('phi')\n",
+ "gamma = Parameter('gamma')\n",
+ "\n",
+ "qr = QuantumRegister(9)\n",
+ "larger_qc = QuantumCircuit(qr)\n",
+ "larger_qc.append(qc.to_instruction({p: theta}), qr[0:3])\n",
+ "larger_qc.append(qc.to_instruction({p: phi}), qr[3:6])\n",
+ "larger_qc.append(qc.to_instruction({p: gamma}), qr[6:9])\n",
+ "print(larger_qc.draw())\n",
+ "\n",
+ "print(larger_qc.decompose().draw())"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 21,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:02:11.062428Z",
+ "start_time": "2019-08-21T09:02:11.054317Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "
"
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/html": [
+ ""
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "import qiskit.tools.jupyter\n",
+ "%qiskit_version_table\n",
+ "%qiskit_copyright"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.7.4"
+ },
+ "varInspector": {
+ "cols": {
+ "lenName": 16,
+ "lenType": 16,
+ "lenVar": 40
+ },
+ "kernels_config": {
+ "python": {
+ "delete_cmd_postfix": "",
+ "delete_cmd_prefix": "del ",
+ "library": "var_list.py",
+ "varRefreshCmd": "print(var_dic_list())"
+ },
+ "r": {
+ "delete_cmd_postfix": ") ",
+ "delete_cmd_prefix": "rm(",
+ "library": "var_list.r",
+ "varRefreshCmd": "cat(var_dic_list()) "
+ }
+ },
+ "types_to_exclude": [
+ "module",
+ "function",
+ "builtin_function_or_method",
+ "instance",
+ "_Feature"
+ ],
+ "window_display": false
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/qiskit/advanced/terra/operators_overview.ipynb b/qiskit/advanced/terra/2_operators_overview.ipynb
similarity index 77%
rename from qiskit/advanced/terra/operators_overview.ipynb
rename to qiskit/advanced/terra/2_operators_overview.ipynb
index deb610a35..3de5bc625 100644
--- a/qiskit/advanced/terra/operators_overview.ipynb
+++ b/qiskit/advanced/terra/2_operators_overview.ipynb
@@ -7,15 +7,6 @@
" Trusted Notebook\" align=\"middle\">"
]
},
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "# Operators Overview\n",
- "\n",
- "The latest version of this notebook is available on https://github.com/Qiskit/qiskit-tutorial."
- ]
- },
{
"cell_type": "markdown",
"metadata": {},
@@ -30,8 +21,8 @@
"execution_count": 1,
"metadata": {
"ExecuteTime": {
- "end_time": "2018-09-29T00:15:24.371649Z",
- "start_time": "2018-09-29T00:15:22.358409Z"
+ "end_time": "2019-08-21T09:02:56.554914Z",
+ "start_time": "2019-08-21T09:02:54.249612Z"
}
},
"outputs": [],
@@ -63,7 +54,12 @@
{
"cell_type": "code",
"execution_count": 2,
- "metadata": {},
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:02:56.572857Z",
+ "start_time": "2019-08-21T09:02:56.566140Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -99,7 +95,12 @@
{
"cell_type": "code",
"execution_count": 3,
- "metadata": {},
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:02:56.589962Z",
+ "start_time": "2019-08-21T09:02:56.585681Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -122,7 +123,12 @@
{
"cell_type": "code",
"execution_count": 4,
- "metadata": {},
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:02:56.615497Z",
+ "start_time": "2019-08-21T09:02:56.611146Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -154,7 +160,12 @@
{
"cell_type": "code",
"execution_count": 5,
- "metadata": {},
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:02:56.804167Z",
+ "start_time": "2019-08-21T09:02:56.798857Z"
+ }
+ },
"outputs": [
{
"name": "stdout",
@@ -181,7 +192,12 @@
{
"cell_type": "code",
"execution_count": 6,
- "metadata": {},
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:02:57.764881Z",
+ "start_time": "2019-08-21T09:02:57.760401Z"
+ }
+ },
"outputs": [
{
"name": "stdout",
@@ -208,7 +224,12 @@
{
"cell_type": "code",
"execution_count": 7,
- "metadata": {},
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:02:58.292849Z",
+ "start_time": "2019-08-21T09:02:58.287354Z"
+ }
+ },
"outputs": [
{
"name": "stdout",
@@ -229,7 +250,12 @@
{
"cell_type": "code",
"execution_count": 8,
- "metadata": {},
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:02:58.779572Z",
+ "start_time": "2019-08-21T09:02:58.774878Z"
+ }
+ },
"outputs": [
{
"name": "stdout",
@@ -258,7 +284,12 @@
{
"cell_type": "code",
"execution_count": 9,
- "metadata": {},
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:03:02.187313Z",
+ "start_time": "2019-08-21T09:03:02.183719Z"
+ }
+ },
"outputs": [
{
"name": "stdout",
@@ -292,7 +323,12 @@
{
"cell_type": "code",
"execution_count": 10,
- "metadata": {},
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:03:02.854419Z",
+ "start_time": "2019-08-21T09:03:02.842387Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -318,7 +354,12 @@
{
"cell_type": "code",
"execution_count": 11,
- "metadata": {},
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:03:03.064145Z",
+ "start_time": "2019-08-21T09:03:03.058953Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -342,7 +383,12 @@
{
"cell_type": "code",
"execution_count": 12,
- "metadata": {},
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:03:03.353613Z",
+ "start_time": "2019-08-21T09:03:03.345462Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -363,8 +409,13 @@
},
{
"cell_type": "code",
- "execution_count": 13,
- "metadata": {},
+ "execution_count": 15,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:03:47.550069Z",
+ "start_time": "2019-08-21T09:03:47.408126Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -384,18 +435,17 @@
" 0. +0.j 0. +0.j]], input_dims=(2, 2, 2, 2, 2, 2, 2, 2, 2, 2), output_dims=(2, 2, 2, 2, 2, 2, 2, 2, 2, 2))"
]
},
- "execution_count": 13,
+ "execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Create an operator from a QuantumCircuit object\n",
- "qr = QuantumRegister(10)\n",
- "circ = QuantumCircuit(qr)\n",
- "circ.h(qr[0])\n",
+ "circ = QuantumCircuit(10)\n",
+ "circ.h(0)\n",
"for j in range(1, 10):\n",
- " circ.cx(qr[j-1], qr[j])\n",
+ " circ.cx(j-1, j)\n",
"\n",
"# Convert circuit to an operator by implicit unitary simulation\n",
"Operator(circ)"
@@ -414,23 +464,28 @@
},
{
"cell_type": "code",
- "execution_count": 14,
- "metadata": {},
+ "execution_count": 16,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:03:49.196556Z",
+ "start_time": "2019-08-21T09:03:49.161398Z"
+ }
+ },
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Operatator is unitary: True\n",
- " ┌──────────┐┌─┐ \n",
- "q1_0: |0>┤0 ├┤M├───\n",
- " │ unitary │└╥┘┌─┐\n",
- "q1_1: |0>┤1 ├─╫─┤M├\n",
- " └──────────┘ ║ └╥┘\n",
- " c0_0: 0 ═════════════╩══╬═\n",
- " ║ \n",
- " c0_1: 0 ════════════════╩═\n",
- " \n"
+ " ┌──────────┐┌─┐ \n",
+ "q_0: |0>┤0 ├┤M├───\n",
+ " │ unitary │└╥┘┌─┐\n",
+ "q_1: |0>┤1 ├─╫─┤M├\n",
+ " └──────────┘ ║ └╥┘\n",
+ " c_0: 0 ═════════════╩══╬═\n",
+ " ║ \n",
+ " c_1: 0 ════════════════╩═\n",
+ " \n"
]
},
{
@@ -439,7 +494,7 @@
"{'11': 1024}"
]
},
- "execution_count": 14,
+ "execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
@@ -452,11 +507,9 @@
"print('Operatator is unitary:', XX.is_unitary())\n",
"\n",
"# Add to a circuit\n",
- "qr = QuantumRegister(2)\n",
- "cr = ClassicalRegister(2)\n",
- "circ = QuantumCircuit(qr, cr)\n",
- "circ.append(XX, [qr[0], qr[1]])\n",
- "circ.measure(qr, cr)\n",
+ "circ = QuantumCircuit(2, 2)\n",
+ "circ.append(XX, [0, 1])\n",
+ "circ.measure([0,1], [0,1])\n",
"print(circ)\n",
"\n",
"backend = BasicAer.get_backend('qasm_simulator')\n",
@@ -473,22 +526,27 @@
},
{
"cell_type": "code",
- "execution_count": 15,
- "metadata": {},
+ "execution_count": 18,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:04:12.017240Z",
+ "start_time": "2019-08-21T09:04:11.989825Z"
+ }
+ },
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
- " ┌───────────┐┌─┐ \n",
- "q1_0: |0>┤0 ├┤M├───\n",
- " │ Pauli:XX │└╥┘┌─┐\n",
- "q1_1: |0>┤1 ├─╫─┤M├\n",
- " └───────────┘ ║ └╥┘\n",
- " c0_0: 0 ══════════════╩══╬═\n",
- " ║ \n",
- " c0_1: 0 ═════════════════╩═\n",
- " \n"
+ " ┌───────────┐┌─┐ \n",
+ "q_0: |0>┤0 ├┤M├───\n",
+ " │ Pauli:XX │└╥┘┌─┐\n",
+ "q_1: |0>┤1 ├─╫─┤M├\n",
+ " └───────────┘ ║ └╥┘\n",
+ " c_0: 0 ══════════════╩══╬═\n",
+ " ║ \n",
+ " c_1: 0 ═════════════════╩═\n",
+ " \n"
]
},
{
@@ -497,16 +555,16 @@
"{'11': 1024}"
]
},
- "execution_count": 15,
+ "execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Add to a circuit\n",
- "circ2 = QuantumCircuit(qr, cr)\n",
- "circ2.append(Pauli(label='XX'), [qr[0], qr[1]])\n",
- "circ2.measure(qr, cr)\n",
+ "circ2 = QuantumCircuit(2, 2)\n",
+ "circ2.append(Pauli(label='XX'), [0, 1])\n",
+ "circ2.measure([0,1], [0,1])\n",
"print(circ2)\n",
"\n",
"# Simulate\n",
@@ -529,8 +587,13 @@
},
{
"cell_type": "code",
- "execution_count": 16,
- "metadata": {},
+ "execution_count": 19,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:04:14.208734Z",
+ "start_time": "2019-08-21T09:04:14.201058Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -541,7 +604,7 @@
" [ 0.+0.j -1.+0.j 0.+0.j -0.+0.j]], input_dims=(2, 2), output_dims=(2, 2))"
]
},
- "execution_count": 16,
+ "execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
@@ -563,8 +626,13 @@
},
{
"cell_type": "code",
- "execution_count": 17,
- "metadata": {},
+ "execution_count": 20,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:04:14.899024Z",
+ "start_time": "2019-08-21T09:04:14.891072Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -575,7 +643,7 @@
" [ 0.+0.j 0.+0.j -1.+0.j -0.+0.j]], input_dims=(2, 2), output_dims=(2, 2))"
]
},
- "execution_count": 17,
+ "execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
@@ -597,8 +665,13 @@
},
{
"cell_type": "code",
- "execution_count": 18,
- "metadata": {},
+ "execution_count": 21,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:04:15.655155Z",
+ "start_time": "2019-08-21T09:04:15.648295Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -607,7 +680,7 @@
" [-1.+0.j 0.+0.j]], input_dims=(2,), output_dims=(2,))"
]
},
- "execution_count": 18,
+ "execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
@@ -627,8 +700,13 @@
},
{
"cell_type": "code",
- "execution_count": 19,
- "metadata": {},
+ "execution_count": 22,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:04:16.460560Z",
+ "start_time": "2019-08-21T09:04:16.452319Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -637,7 +715,7 @@
" [ 1.+0.j 0.+0.j]], input_dims=(2,), output_dims=(2,))"
]
},
- "execution_count": 19,
+ "execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
@@ -663,8 +741,13 @@
},
{
"cell_type": "code",
- "execution_count": 20,
- "metadata": {},
+ "execution_count": 23,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:04:17.113510Z",
+ "start_time": "2019-08-21T09:04:17.105398Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -679,7 +762,7 @@
" [ 0.+0.j 0.+0.j 0.+0.j -1.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j]], input_dims=(2, 2, 2), output_dims=(2, 2, 2))"
]
},
- "execution_count": 20,
+ "execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
@@ -693,8 +776,13 @@
},
{
"cell_type": "code",
- "execution_count": 21,
- "metadata": {},
+ "execution_count": 24,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:04:17.324353Z",
+ "start_time": "2019-08-21T09:04:17.315952Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -709,7 +797,7 @@
" [ 0.+0.j 0.+0.j 0.+0.j -1.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j]], input_dims=(2, 2, 2), output_dims=(2, 2, 2))"
]
},
- "execution_count": 21,
+ "execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
@@ -732,8 +820,13 @@
},
{
"cell_type": "code",
- "execution_count": 22,
- "metadata": {},
+ "execution_count": 25,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:04:18.829988Z",
+ "start_time": "2019-08-21T09:04:18.812834Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -744,7 +837,7 @@
" [ 0. +0.j 0. +0.j 0. +0.j -1.5+0.j]], input_dims=(2, 2), output_dims=(2, 2))"
]
},
- "execution_count": 22,
+ "execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
@@ -767,8 +860,13 @@
},
{
"cell_type": "code",
- "execution_count": 23,
- "metadata": {},
+ "execution_count": 26,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:04:19.151814Z",
+ "start_time": "2019-08-21T09:04:19.147497Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -776,7 +874,7 @@
"False"
]
},
- "execution_count": 23,
+ "execution_count": 26,
"metadata": {},
"output_type": "execute_result"
}
@@ -796,8 +894,13 @@
},
{
"cell_type": "code",
- "execution_count": 24,
- "metadata": {},
+ "execution_count": 27,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:04:20.045005Z",
+ "start_time": "2019-08-21T09:04:20.039841Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -806,7 +909,7 @@
" [1.+0.j 0.+0.j]], input_dims=(2,), output_dims=(2,))"
]
},
- "execution_count": 24,
+ "execution_count": 27,
"metadata": {},
"output_type": "execute_result"
}
@@ -827,8 +930,13 @@
},
{
"cell_type": "code",
- "execution_count": 25,
- "metadata": {},
+ "execution_count": 28,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:04:20.821642Z",
+ "start_time": "2019-08-21T09:04:20.815611Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -836,7 +944,7 @@
"True"
]
},
- "execution_count": 25,
+ "execution_count": 28,
"metadata": {},
"output_type": "execute_result"
}
@@ -854,8 +962,13 @@
},
{
"cell_type": "code",
- "execution_count": 26,
- "metadata": {},
+ "execution_count": 29,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:04:21.146256Z",
+ "start_time": "2019-08-21T09:04:21.141242Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -863,7 +976,7 @@
"False"
]
},
- "execution_count": 26,
+ "execution_count": 29,
"metadata": {},
"output_type": "execute_result"
}
@@ -883,8 +996,13 @@
},
{
"cell_type": "code",
- "execution_count": 27,
- "metadata": {},
+ "execution_count": 30,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:04:22.171481Z",
+ "start_time": "2019-08-21T09:04:22.147477Z"
+ }
+ },
"outputs": [
{
"name": "stdout",
@@ -910,6 +1028,55 @@
"source": [
"Note that process fidelity is generally only a valid measure of closeness if the input operators are unitary (or CP in the case of quantum channels), and an exception will be raised if the inputs are not CP."
]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 32,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:04:44.743744Z",
+ "start_time": "2019-08-21T09:04:44.734826Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "
"
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/html": [
+ ""
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "import qiskit.tools.jupyter\n",
+ "%qiskit_version_table\n",
+ "%qiskit_copyright"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
}
],
"metadata": {
@@ -929,7 +1096,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
- "version": "3.7.3"
+ "version": "3.7.4"
},
"varInspector": {
"cols": {
diff --git a/qiskit/advanced/terra/3_advanced_circuit_visualization.ipynb b/qiskit/advanced/terra/3_advanced_circuit_visualization.ipynb
new file mode 100644
index 000000000..40db77ea6
--- /dev/null
+++ b/qiskit/advanced/terra/3_advanced_circuit_visualization.ipynb
@@ -0,0 +1,808 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ " Trusted Notebook\" align=\"middle\">"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Visualizing a Quantum Circuit"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:07:19.545078Z",
+ "start_time": "2019-08-21T09:07:19.541701Z"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Drawing a Quantum Circuit\n",
+ "\n",
+ "When building a quantum circuit, it often helps to draw the circuit. This is supported natively by a `QuantumCircuit` object. You can either call `print()` on the circuit, or call the `draw()` method on the object. This will render a [ASCII art version](https://en.wikipedia.org/wiki/ASCII_art) of the circuit diagram."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:07:20.108439Z",
+ "start_time": "2019-08-21T09:07:20.103752Z"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "# Build a quantum circuit\n",
+ "circuit = QuantumCircuit(3, 3)\n",
+ "\n",
+ "circuit.x(1)\n",
+ "circuit.h(range(3))\n",
+ "circuit.cx(0, 1)\n",
+ "circuit.measure(range(3), range(3));"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:07:20.325315Z",
+ "start_time": "2019-08-21T09:07:20.317485Z"
+ }
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " ┌───┐ ┌─┐ \n",
+ "q_0: |0>┤ H ├───────■──┤M├───\n",
+ " ├───┤┌───┐┌─┴─┐└╥┘┌─┐\n",
+ "q_1: |0>┤ X ├┤ H ├┤ X ├─╫─┤M├\n",
+ " ├───┤└┬─┬┘└───┘ ║ └╥┘\n",
+ "q_2: |0>┤ H ├─┤M├───────╫──╫─\n",
+ " └───┘ └╥┘ ║ ║ \n",
+ " c_0: 0 ═══════╬════════╩══╬═\n",
+ " ║ ║ \n",
+ " c_1: 0 ═══════╬═══════════╩═\n",
+ " ║ \n",
+ " c_2: 0 ═══════╩═════════════\n",
+ " \n"
+ ]
+ }
+ ],
+ "source": [
+ "print(circuit)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:07:20.500036Z",
+ "start_time": "2019-08-21T09:07:20.491928Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ ""
+ ]
+ },
+ "execution_count": 11,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "circuit.draw()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Alternative Renderers for Circuits\n",
+ "\n",
+ "A text output is useful for quickly seeing the output while developing a circuit, but it doesn't provide the most flexibility in its output. There are two alternative output renderers for the quantum circuit. One uses [matplotlib](https://matplotlib.org/), and the other uses [LaTeX](https://www.latex-project.org/), which leverages the [qcircuit package](https://github.com/CQuIC/qcircuit). These can be specified by using `mpl` and `latex` values for the `output` kwarg on the draw() method."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:07:21.031200Z",
+ "start_time": "2019-08-21T09:07:20.821727Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "
Version Information
| Qiskit Software | Version |
|---|---|
| Qiskit | None |
| Terra | 0.9.0 |
| Aer | 0.3.0 |
| Ignis | 0.2.0 |
| Aqua | 0.5.6 |
| IBM Q Provider | 0.3.2rc1 |
| System information | |
| Python | 3.7.4 (default, Aug 13 2019, 15:17:50) \n", + "[Clang 4.0.1 (tags/RELEASE_401/final)] |
| OS | Darwin |
| CPUs | 4 |
| Memory (Gb) | 16.0 |
| Wed Aug 21 05:02:11 2019 EDT | |
This code is a part of Qiskit
© Copyright IBM 2017, 2019.
This code is licensed under the Apache License, Version 2.0. You may
obtain a copy of this license in the LICENSE.txt file in the root directory
of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
Any modifications or derivative works of this code must retain this
copyright notice, and modified files need to carry a notice indicating
that they have been altered from the originals.
Trusted Notebook\" align=\"middle\">"
]
},
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "# Operators Overview\n",
- "\n",
- "The latest version of this notebook is available on https://github.com/Qiskit/qiskit-tutorial."
- ]
- },
{
"cell_type": "markdown",
"metadata": {},
@@ -30,8 +21,8 @@
"execution_count": 1,
"metadata": {
"ExecuteTime": {
- "end_time": "2018-09-29T00:15:24.371649Z",
- "start_time": "2018-09-29T00:15:22.358409Z"
+ "end_time": "2019-08-21T09:02:56.554914Z",
+ "start_time": "2019-08-21T09:02:54.249612Z"
}
},
"outputs": [],
@@ -63,7 +54,12 @@
{
"cell_type": "code",
"execution_count": 2,
- "metadata": {},
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:02:56.572857Z",
+ "start_time": "2019-08-21T09:02:56.566140Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -99,7 +95,12 @@
{
"cell_type": "code",
"execution_count": 3,
- "metadata": {},
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:02:56.589962Z",
+ "start_time": "2019-08-21T09:02:56.585681Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -122,7 +123,12 @@
{
"cell_type": "code",
"execution_count": 4,
- "metadata": {},
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:02:56.615497Z",
+ "start_time": "2019-08-21T09:02:56.611146Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -154,7 +160,12 @@
{
"cell_type": "code",
"execution_count": 5,
- "metadata": {},
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:02:56.804167Z",
+ "start_time": "2019-08-21T09:02:56.798857Z"
+ }
+ },
"outputs": [
{
"name": "stdout",
@@ -181,7 +192,12 @@
{
"cell_type": "code",
"execution_count": 6,
- "metadata": {},
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:02:57.764881Z",
+ "start_time": "2019-08-21T09:02:57.760401Z"
+ }
+ },
"outputs": [
{
"name": "stdout",
@@ -208,7 +224,12 @@
{
"cell_type": "code",
"execution_count": 7,
- "metadata": {},
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:02:58.292849Z",
+ "start_time": "2019-08-21T09:02:58.287354Z"
+ }
+ },
"outputs": [
{
"name": "stdout",
@@ -229,7 +250,12 @@
{
"cell_type": "code",
"execution_count": 8,
- "metadata": {},
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:02:58.779572Z",
+ "start_time": "2019-08-21T09:02:58.774878Z"
+ }
+ },
"outputs": [
{
"name": "stdout",
@@ -258,7 +284,12 @@
{
"cell_type": "code",
"execution_count": 9,
- "metadata": {},
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:03:02.187313Z",
+ "start_time": "2019-08-21T09:03:02.183719Z"
+ }
+ },
"outputs": [
{
"name": "stdout",
@@ -292,7 +323,12 @@
{
"cell_type": "code",
"execution_count": 10,
- "metadata": {},
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:03:02.854419Z",
+ "start_time": "2019-08-21T09:03:02.842387Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -318,7 +354,12 @@
{
"cell_type": "code",
"execution_count": 11,
- "metadata": {},
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:03:03.064145Z",
+ "start_time": "2019-08-21T09:03:03.058953Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -342,7 +383,12 @@
{
"cell_type": "code",
"execution_count": 12,
- "metadata": {},
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:03:03.353613Z",
+ "start_time": "2019-08-21T09:03:03.345462Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -363,8 +409,13 @@
},
{
"cell_type": "code",
- "execution_count": 13,
- "metadata": {},
+ "execution_count": 15,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:03:47.550069Z",
+ "start_time": "2019-08-21T09:03:47.408126Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -384,18 +435,17 @@
" 0. +0.j 0. +0.j]], input_dims=(2, 2, 2, 2, 2, 2, 2, 2, 2, 2), output_dims=(2, 2, 2, 2, 2, 2, 2, 2, 2, 2))"
]
},
- "execution_count": 13,
+ "execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Create an operator from a QuantumCircuit object\n",
- "qr = QuantumRegister(10)\n",
- "circ = QuantumCircuit(qr)\n",
- "circ.h(qr[0])\n",
+ "circ = QuantumCircuit(10)\n",
+ "circ.h(0)\n",
"for j in range(1, 10):\n",
- " circ.cx(qr[j-1], qr[j])\n",
+ " circ.cx(j-1, j)\n",
"\n",
"# Convert circuit to an operator by implicit unitary simulation\n",
"Operator(circ)"
@@ -414,23 +464,28 @@
},
{
"cell_type": "code",
- "execution_count": 14,
- "metadata": {},
+ "execution_count": 16,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:03:49.196556Z",
+ "start_time": "2019-08-21T09:03:49.161398Z"
+ }
+ },
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Operatator is unitary: True\n",
- " ┌──────────┐┌─┐ \n",
- "q1_0: |0>┤0 ├┤M├───\n",
- " │ unitary │└╥┘┌─┐\n",
- "q1_1: |0>┤1 ├─╫─┤M├\n",
- " └──────────┘ ║ └╥┘\n",
- " c0_0: 0 ═════════════╩══╬═\n",
- " ║ \n",
- " c0_1: 0 ════════════════╩═\n",
- " \n"
+ " ┌──────────┐┌─┐ \n",
+ "q_0: |0>┤0 ├┤M├───\n",
+ " │ unitary │└╥┘┌─┐\n",
+ "q_1: |0>┤1 ├─╫─┤M├\n",
+ " └──────────┘ ║ └╥┘\n",
+ " c_0: 0 ═════════════╩══╬═\n",
+ " ║ \n",
+ " c_1: 0 ════════════════╩═\n",
+ " \n"
]
},
{
@@ -439,7 +494,7 @@
"{'11': 1024}"
]
},
- "execution_count": 14,
+ "execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
@@ -452,11 +507,9 @@
"print('Operatator is unitary:', XX.is_unitary())\n",
"\n",
"# Add to a circuit\n",
- "qr = QuantumRegister(2)\n",
- "cr = ClassicalRegister(2)\n",
- "circ = QuantumCircuit(qr, cr)\n",
- "circ.append(XX, [qr[0], qr[1]])\n",
- "circ.measure(qr, cr)\n",
+ "circ = QuantumCircuit(2, 2)\n",
+ "circ.append(XX, [0, 1])\n",
+ "circ.measure([0,1], [0,1])\n",
"print(circ)\n",
"\n",
"backend = BasicAer.get_backend('qasm_simulator')\n",
@@ -473,22 +526,27 @@
},
{
"cell_type": "code",
- "execution_count": 15,
- "metadata": {},
+ "execution_count": 18,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:04:12.017240Z",
+ "start_time": "2019-08-21T09:04:11.989825Z"
+ }
+ },
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
- " ┌───────────┐┌─┐ \n",
- "q1_0: |0>┤0 ├┤M├───\n",
- " │ Pauli:XX │└╥┘┌─┐\n",
- "q1_1: |0>┤1 ├─╫─┤M├\n",
- " └───────────┘ ║ └╥┘\n",
- " c0_0: 0 ══════════════╩══╬═\n",
- " ║ \n",
- " c0_1: 0 ═════════════════╩═\n",
- " \n"
+ " ┌───────────┐┌─┐ \n",
+ "q_0: |0>┤0 ├┤M├───\n",
+ " │ Pauli:XX │└╥┘┌─┐\n",
+ "q_1: |0>┤1 ├─╫─┤M├\n",
+ " └───────────┘ ║ └╥┘\n",
+ " c_0: 0 ══════════════╩══╬═\n",
+ " ║ \n",
+ " c_1: 0 ═════════════════╩═\n",
+ " \n"
]
},
{
@@ -497,16 +555,16 @@
"{'11': 1024}"
]
},
- "execution_count": 15,
+ "execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Add to a circuit\n",
- "circ2 = QuantumCircuit(qr, cr)\n",
- "circ2.append(Pauli(label='XX'), [qr[0], qr[1]])\n",
- "circ2.measure(qr, cr)\n",
+ "circ2 = QuantumCircuit(2, 2)\n",
+ "circ2.append(Pauli(label='XX'), [0, 1])\n",
+ "circ2.measure([0,1], [0,1])\n",
"print(circ2)\n",
"\n",
"# Simulate\n",
@@ -529,8 +587,13 @@
},
{
"cell_type": "code",
- "execution_count": 16,
- "metadata": {},
+ "execution_count": 19,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:04:14.208734Z",
+ "start_time": "2019-08-21T09:04:14.201058Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -541,7 +604,7 @@
" [ 0.+0.j -1.+0.j 0.+0.j -0.+0.j]], input_dims=(2, 2), output_dims=(2, 2))"
]
},
- "execution_count": 16,
+ "execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
@@ -563,8 +626,13 @@
},
{
"cell_type": "code",
- "execution_count": 17,
- "metadata": {},
+ "execution_count": 20,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:04:14.899024Z",
+ "start_time": "2019-08-21T09:04:14.891072Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -575,7 +643,7 @@
" [ 0.+0.j 0.+0.j -1.+0.j -0.+0.j]], input_dims=(2, 2), output_dims=(2, 2))"
]
},
- "execution_count": 17,
+ "execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
@@ -597,8 +665,13 @@
},
{
"cell_type": "code",
- "execution_count": 18,
- "metadata": {},
+ "execution_count": 21,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:04:15.655155Z",
+ "start_time": "2019-08-21T09:04:15.648295Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -607,7 +680,7 @@
" [-1.+0.j 0.+0.j]], input_dims=(2,), output_dims=(2,))"
]
},
- "execution_count": 18,
+ "execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
@@ -627,8 +700,13 @@
},
{
"cell_type": "code",
- "execution_count": 19,
- "metadata": {},
+ "execution_count": 22,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:04:16.460560Z",
+ "start_time": "2019-08-21T09:04:16.452319Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -637,7 +715,7 @@
" [ 1.+0.j 0.+0.j]], input_dims=(2,), output_dims=(2,))"
]
},
- "execution_count": 19,
+ "execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
@@ -663,8 +741,13 @@
},
{
"cell_type": "code",
- "execution_count": 20,
- "metadata": {},
+ "execution_count": 23,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:04:17.113510Z",
+ "start_time": "2019-08-21T09:04:17.105398Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -679,7 +762,7 @@
" [ 0.+0.j 0.+0.j 0.+0.j -1.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j]], input_dims=(2, 2, 2), output_dims=(2, 2, 2))"
]
},
- "execution_count": 20,
+ "execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
@@ -693,8 +776,13 @@
},
{
"cell_type": "code",
- "execution_count": 21,
- "metadata": {},
+ "execution_count": 24,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:04:17.324353Z",
+ "start_time": "2019-08-21T09:04:17.315952Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -709,7 +797,7 @@
" [ 0.+0.j 0.+0.j 0.+0.j -1.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j]], input_dims=(2, 2, 2), output_dims=(2, 2, 2))"
]
},
- "execution_count": 21,
+ "execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
@@ -732,8 +820,13 @@
},
{
"cell_type": "code",
- "execution_count": 22,
- "metadata": {},
+ "execution_count": 25,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:04:18.829988Z",
+ "start_time": "2019-08-21T09:04:18.812834Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -744,7 +837,7 @@
" [ 0. +0.j 0. +0.j 0. +0.j -1.5+0.j]], input_dims=(2, 2), output_dims=(2, 2))"
]
},
- "execution_count": 22,
+ "execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
@@ -767,8 +860,13 @@
},
{
"cell_type": "code",
- "execution_count": 23,
- "metadata": {},
+ "execution_count": 26,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:04:19.151814Z",
+ "start_time": "2019-08-21T09:04:19.147497Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -776,7 +874,7 @@
"False"
]
},
- "execution_count": 23,
+ "execution_count": 26,
"metadata": {},
"output_type": "execute_result"
}
@@ -796,8 +894,13 @@
},
{
"cell_type": "code",
- "execution_count": 24,
- "metadata": {},
+ "execution_count": 27,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:04:20.045005Z",
+ "start_time": "2019-08-21T09:04:20.039841Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -806,7 +909,7 @@
" [1.+0.j 0.+0.j]], input_dims=(2,), output_dims=(2,))"
]
},
- "execution_count": 24,
+ "execution_count": 27,
"metadata": {},
"output_type": "execute_result"
}
@@ -827,8 +930,13 @@
},
{
"cell_type": "code",
- "execution_count": 25,
- "metadata": {},
+ "execution_count": 28,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:04:20.821642Z",
+ "start_time": "2019-08-21T09:04:20.815611Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -836,7 +944,7 @@
"True"
]
},
- "execution_count": 25,
+ "execution_count": 28,
"metadata": {},
"output_type": "execute_result"
}
@@ -854,8 +962,13 @@
},
{
"cell_type": "code",
- "execution_count": 26,
- "metadata": {},
+ "execution_count": 29,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:04:21.146256Z",
+ "start_time": "2019-08-21T09:04:21.141242Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -863,7 +976,7 @@
"False"
]
},
- "execution_count": 26,
+ "execution_count": 29,
"metadata": {},
"output_type": "execute_result"
}
@@ -883,8 +996,13 @@
},
{
"cell_type": "code",
- "execution_count": 27,
- "metadata": {},
+ "execution_count": 30,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:04:22.171481Z",
+ "start_time": "2019-08-21T09:04:22.147477Z"
+ }
+ },
"outputs": [
{
"name": "stdout",
@@ -910,6 +1028,55 @@
"source": [
"Note that process fidelity is generally only a valid measure of closeness if the input operators are unitary (or CP in the case of quantum channels), and an exception will be raised if the inputs are not CP."
]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 32,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:04:44.743744Z",
+ "start_time": "2019-08-21T09:04:44.734826Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "Version Information
| Qiskit Software | Version |
|---|---|
| Qiskit | None |
| Terra | 0.9.0 |
| Aer | 0.3.0 |
| Ignis | 0.2.0 |
| Aqua | 0.5.6 |
| IBM Q Provider | 0.3.2rc1 |
| System information | |
| Python | 3.7.4 (default, Aug 13 2019, 15:17:50) \n", + "[Clang 4.0.1 (tags/RELEASE_401/final)] |
| OS | Darwin |
| CPUs | 4 |
| Memory (Gb) | 16.0 |
| Wed Aug 21 05:04:44 2019 EDT | |
This code is a part of Qiskit
© Copyright IBM 2017, 2019.
This code is licensed under the Apache License, Version 2.0. You may
obtain a copy of this license in the LICENSE.txt file in the root directory
of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
Any modifications or derivative works of this code must retain this
copyright notice, and modified files need to carry a notice indicating
that they have been altered from the originals.
Trusted Notebook\" align=\"middle\">"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Visualizing a Quantum Circuit"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:07:19.545078Z",
+ "start_time": "2019-08-21T09:07:19.541701Z"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Drawing a Quantum Circuit\n",
+ "\n",
+ "When building a quantum circuit, it often helps to draw the circuit. This is supported natively by a `QuantumCircuit` object. You can either call `print()` on the circuit, or call the `draw()` method on the object. This will render a [ASCII art version](https://en.wikipedia.org/wiki/ASCII_art) of the circuit diagram."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:07:20.108439Z",
+ "start_time": "2019-08-21T09:07:20.103752Z"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "# Build a quantum circuit\n",
+ "circuit = QuantumCircuit(3, 3)\n",
+ "\n",
+ "circuit.x(1)\n",
+ "circuit.h(range(3))\n",
+ "circuit.cx(0, 1)\n",
+ "circuit.measure(range(3), range(3));"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:07:20.325315Z",
+ "start_time": "2019-08-21T09:07:20.317485Z"
+ }
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " ┌───┐ ┌─┐ \n",
+ "q_0: |0>┤ H ├───────■──┤M├───\n",
+ " ├───┤┌───┐┌─┴─┐└╥┘┌─┐\n",
+ "q_1: |0>┤ X ├┤ H ├┤ X ├─╫─┤M├\n",
+ " ├───┤└┬─┬┘└───┘ ║ └╥┘\n",
+ "q_2: |0>┤ H ├─┤M├───────╫──╫─\n",
+ " └───┘ └╥┘ ║ ║ \n",
+ " c_0: 0 ═══════╬════════╩══╬═\n",
+ " ║ ║ \n",
+ " c_1: 0 ═══════╬═══════════╩═\n",
+ " ║ \n",
+ " c_2: 0 ═══════╩═════════════\n",
+ " \n"
+ ]
+ }
+ ],
+ "source": [
+ "print(circuit)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:07:20.500036Z",
+ "start_time": "2019-08-21T09:07:20.491928Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "┌───┐ ┌─┐ \n", + "q_0: |0>┤ H ├───────■──┤M├───\n", + " ├───┤┌───┐┌─┴─┐└╥┘┌─┐\n", + "q_1: |0>┤ X ├┤ H ├┤ X ├─╫─┤M├\n", + " ├───┤└┬─┬┘└───┘ ║ └╥┘\n", + "q_2: |0>┤ H ├─┤M├───────╫──╫─\n", + " └───┘ └╥┘ ║ ║ \n", + " c_0: 0 ═══════╬════════╩══╬═\n", + " ║ ║ \n", + " c_1: 0 ═══════╬═══════════╩═\n", + " ║ \n", + " c_2: 0 ═══════╩═════════════\n", + "" + ], + "text/plain": [ + "
"
+ ]
+ },
+ "execution_count": 12,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "# Matplotlib Drawing\n",
+ "circuit.draw(output='mpl')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:07:22.142678Z",
+ "start_time": "2019-08-21T09:07:21.046746Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 13,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "# Latex Drawing\n",
+ "circuit.draw(output='latex')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Controlling output from circuit.draw()\n",
+ "\n",
+ "By default, the draw method returns the rendered image as an object and does not output anything. The exact class returned depends on the output specified: `'text'`(the default) returns a `TextDrawer` object, `'mpl'` returns a `matplotlib.Figure` object, and `latex` returns a `PIL.Image` object. Having the return types enables modifying or directly interacting with the rendered output from the drawers. Jupyter notebooks understand these return types and render them for us in this tutorial, but when running outside of Jupyter, you do not have this feature automatically. However, the `draw()` method has optional arguments to display or save the output. When specified, the `filename` kwarg takes a path to which it saves the rendered output. Alternatively, if you're using the `mpl` or `latex` outputs, you can leverage the `interactive` kwarg to open the image in a new window (this will not always work from within a notebook but will be demonstrated anyway)."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Customizing the output\n",
+ "\n",
+ "Depending on the output, there are also options to customize the circuit diagram rendered by the circuit.\n",
+ "\n",
+ "### Disable Plot Barriers and Reversing Bit Order\n",
+ "The first two options are shared among all three backends. They allow you to configure both the bit orders and whether or not you draw barriers. These can be set by the `reverse_bits` kwarg and `plot_barriers` kwarg, respectively. The examples below will work with any output backend; `latex` is used here for brevity."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:07:22.894879Z",
+ "start_time": "2019-08-21T09:07:22.884270Z"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "# Draw a new circuit with barriers and more registers\n",
+ "\n",
+ "q_a = QuantumRegister(3, name='qa')\n",
+ "q_b = QuantumRegister(5, name='qb')\n",
+ "c_a = ClassicalRegister(3)\n",
+ "c_b = ClassicalRegister(5)\n",
+ "\n",
+ "circuit = QuantumCircuit(q_a, q_b, c_a, c_b)\n",
+ "\n",
+ "circuit.x(q_a[1])\n",
+ "circuit.x(q_b[1])\n",
+ "circuit.x(q_b[2])\n",
+ "circuit.x(q_b[4])\n",
+ "circuit.barrier()\n",
+ "circuit.h(q_a)\n",
+ "circuit.barrier(q_a)\n",
+ "circuit.h(q_b)\n",
+ "circuit.cswap(q_b[0], q_b[1], q_b[2])\n",
+ "circuit.cswap(q_b[2], q_b[3], q_b[4])\n",
+ "circuit.cswap(q_b[3], q_b[4], q_b[0])\n",
+ "circuit.barrier(q_b)\n",
+ "circuit.measure(q_a, c_a)\n",
+ "circuit.measure(q_b, c_b);"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:07:26.192606Z",
+ "start_time": "2019-08-21T09:07:23.731988Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 15,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "# Draw the circuit\n",
+ "circuit.draw(output='latex')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:07:29.055491Z",
+ "start_time": "2019-08-21T09:07:26.594527Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 16,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "# Draw the circuit with reversed bit order\n",
+ "circuit.draw(output='latex', reverse_bits=True)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:07:31.528574Z",
+ "start_time": "2019-08-21T09:07:29.102557Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 17,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "# Draw the circuit without barriers\n",
+ "circuit.draw(output='latex', plot_barriers=False)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:07:34.023384Z",
+ "start_time": "2019-08-21T09:07:31.568046Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 18,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "# Draw the circuit without barriers and reverse bit order\n",
+ "circuit.draw(output='latex', plot_barriers=False, reverse_bits=True)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Backend-specific customizations\n",
+ "\n",
+ "Some available customizing options are specific to a backend. The `line_length` kwarg for the `text` backend can be used to set a maximum width for the output. When a diagram is wider than the maximum, it will wrap the diagram below. The `mpl` backend has the `style` kwarg, which is used to customize the output. The `scale` option is used by the `mpl` and `latex` backends to scale the size of the output image with a multiplicative adjustment factor. The `style` kwarg takes in a `dict` with multiple options, providing a high level of flexibility for changing colors, changing rendered text for different types of gates, different line styles, etc. Available options are:\n",
+ "\n",
+ "- **textcolor** (str): The color code to use for text. Defaults to `'#000000'`\n",
+ "- **subtextcolor** (str): The color code to use for subtext. Defaults to `'#000000'`\n",
+ "- **linecolor** (str): The color code to use for lines. Defaults to `'#000000'`\n",
+ "- **creglinecolor** (str): The color code to use for classical register lines `'#778899'`\n",
+ "- **gatetextcolor** (str): The color code to use for gate text `'#000000'`\n",
+ "- **gatefacecolor** (str): The color code to use for gates. Defaults to `'#ffffff'`\n",
+ "- **barrierfacecolor** (str): The color code to use for barriers. Defaults to `'#bdbdbd'`\n",
+ "- **backgroundcolor** (str): The color code to use for the background. Defaults to `'#ffffff'`\n",
+ "- **fontsize** (int): The font size to use for text. Defaults to 13\n",
+ "- **subfontsize** (int): The font size to use for subtext. Defaults to 8\n",
+ "- **displaytext** (dict): A dictionary of the text to use for each element\n",
+ " type in the output visualization. The default values are:\n",
+ " \n",
+ " \n",
+ " 'id': 'id',\n",
+ " 'u0': 'U_0',\n",
+ " 'u1': 'U_1',\n",
+ " 'u2': 'U_2',\n",
+ " 'u3': 'U_3',\n",
+ " 'x': 'X',\n",
+ " 'y': 'Y',\n",
+ " 'z': 'Z',\n",
+ " 'h': 'H',\n",
+ " 's': 'S',\n",
+ " 'sdg': 'S^\\\\dagger',\n",
+ " 't': 'T',\n",
+ " 'tdg': 'T^\\\\dagger',\n",
+ " 'rx': 'R_x',\n",
+ " 'ry': 'R_y',\n",
+ " 'rz': 'R_z',\n",
+ " 'reset': '\\\\left|0\\\\right\\\\rangle'\n",
+ " \n",
+ " \n",
+ " You must specify all the necessary values if using this. There is\n",
+ " no provision for an incomplete dict passed in.\n",
+ "- **displaycolor** (dict): The color codes to use for each circuit element.\n",
+ " By default, all values default to the value of `gatefacecolor` and\n",
+ " the keys are the same as `displaytext`. Also, just like\n",
+ " `displaytext`, there is no provision for an incomplete dict passed\n",
+ " in.\n",
+ "- **latexdrawerstyle** (bool): When set to True, enable LaTeX mode, which will\n",
+ " draw gates like the `latex` output modes.\n",
+ "- **usepiformat** (bool): When set to True, use radians for output.\n",
+ "- **fold** (int): The number of circuit elements at which to fold the circuit.\n",
+ " Defaults to 20\n",
+ "- **cregbundle** (bool): If set True, bundle classical registers.\n",
+ "- **showindex** (bool): If set True, draw an index.\n",
+ "- **compress** (bool): If set True, draw a compressed circuit.\n",
+ "- **figwidth** (int): The maximum width (in inches) for the output figure.\n",
+ "- **dpi** (int): The DPI to use for the output image. Defaults to 150.\n",
+ "- **creglinestyle** (str): The style of line to use for classical registers.\n",
+ " Choices are `'solid'`, `'doublet'`, or any valid matplotlib\n",
+ " `linestyle` kwarg value. Defaults to `doublet`."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:07:34.082174Z",
+ "start_time": "2019-08-21T09:07:34.067403Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ ""
+ ]
+ },
+ "execution_count": 19,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "# Set line length to 80 for above circuit\n",
+ "circuit.draw(output='text', line_length=80)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 20,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:07:34.550463Z",
+ "start_time": "2019-08-21T09:07:34.114408Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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1ReqE15G7p7tCWhde820tsGr/hv3a/Y/dSo1PVWZqZnHb0A7XZnXqNqmroXOHassbW5xzAhXA8tCDsq7bINtXu2Xdu0+28+fl8dZf5eblaXRpDnl367tGl+CQlPgYuVncFRjaxm77+VMH5FczSNUDG9xmz8rDLH2N8vfggw9q/vz5slqtGj9+vJYvX+7Qfp988olmzpyp2rVrS5JOnTpFqAEAVLgq/6v59NPpSj6afMtZlYtJFxXcMlge3oX5btXEVVo7ba3CuoVp5IKRmvqfqfpj9B/lU91H9VtdW82n64iuavHrFvLwMW8udPP1kWX4oyqY/7ZsBw/K441X5ebvZ3RZDos/Gm90CQ5JiY9R7eDm8vCyvz8r9dQB1Qszx2yNWfoa5SsgIEDLli2TJL3wwgsOh5qie2o6duyon3/+WRcuXNC9996rcePGVWS5AABU/Rmb9DPpkqQaQTXstudezdWJPSfUul9rSdKZI2cUuy5Wj0U+ph5P9ihuF/9NvLIzsu1mbJxtWsC0Utt4br3D2aPsbLk/NkJu//eb1bJypLY7MX369BLfj4iIcKhNRZi6cqrDbVPiY5SeclxLJ9Sx256Xk6muD75YpuNWRF+X1oeSsX3tKl6YV7jy3LSAaXavjTR9+nQFBwdr165d+tvf/ubQPjcuFHDffffp7rvvVlRUlF577TX985//VG5ubnF7o88RAGAOkWmRDrWr8sHGP9BfknTu+Dm17t+6ePuOhTt0+ezl4sCSfrowAAW3CC5uU5BXoI9nFy4acP19OFWBNXqHrGuj5DZwgAo2fiy3BwbKzc3N6LKqnJSEfeo+9BW16vWk3fZVL7ZTkElmbOB6vLy89Mwzz0iS/vSnP8lms5W6z61CTWJiohITE/Xdd9+pU6dOGj58uFatWlXR5QMAXFSVDzaBjQMV0iZE0RHR8qvtp1r1ayluU5yObjsq6dq9MyFtQuTp46nNczZrwIwByrqYpZ1LdurKxStys7jpV+1+Zdg5OJJSn9vn+OdZ98ao4O+L5T7nFbk1a6b8J5+WbdeXcutzb4XUdidCTpX8rIuIiAj1GN2jxDaNZjcqz5KKJTg4OZZ+9rhysi6qUfuBqh4Yar/9SrrqlXHhgIro69L6WTK2r11FcuEVX4pMi7R77UzXz5706NFDQUFBOnLkiHbv3l3qvrcLNUWWLVumd955R4888ohdsHH2OQIAqrYqf4+NxWLRU+89peCWwVo3c51WT16tagHV1GtsL1k8LAppU/jFrlZILf1+2e91OeWyVjyxQjsX71TfyX0V1j1MQc2C5O3vbfCZlA/r4SMqeGOe3J+bIUv7dtfutVm5xlTLPI97qfJfr58SHyMPb7+bVkRL/mmPqgU2kH/NIIMqKxsz9DXKV5cuXSRJu3btKrVtaaHm+s8p+lwAACpClZ+xkaR6Tetp8qbJdttWTlipoOZB8vL1Kt7Wfkh7tR/S3q5dp0c63fR5BXkFshZYZbPaVJBfoLzsPHl4e1T6S7lsCSdV8PIrch//jCz39CzebnloSOEKabu+lNt9fUr4hMqj37B+RpdQqpT4GAWF3SWLu/3/ZsnHvzbVZWhm6GuUr+bNm0uSDh06VGI7R0KNJP3www/Kz89X48aN5eXlZXefDQAA5cUlgs2tnPrulBp3bXxH+3407SPFrImRJMV/Xbhi1Oy42QpsGFhe5VUIt7DG8lwfdfN2Hx95Rq12ej2/xIiOIxQVd/O5VCb3PvH2Lbf3ffodJ1fyy5ihr1G+li9frl27dmnv3r0ltnvyyScdevim1WrV6NGjlZeXJ6uJZoYBAObiksEmJzNHqSdS1WtMrzvaf9TiURq1eFQ5VwUAlcO+ffu0b1/pN+4tWrRI/v7+WrVqVanPqVm92ly/PAEAmI9LBhvvat6KOM/ytADwS82bN8/oEgAAkOQCiwegaup8b2ejS3AZ9DUAADADgg1MadbCWUaX4DLoawAAYAYEG5jSvGe5/MVZ6GsAAGAGBBuY0v5d+40uwWXQ1wAAwAwINgAAAABMj2ADAAAAwPQINjAlHhjpPPQ1AAAwA4INTCl6XbTRJbgM+hoAAJiBSz6gsyqa3/WY0SU41bLXlqnfsH6GHDts0AJDjmsUI/sazhOZFlmm9snLfCVJ9cddtXsNAIBRmLEBAAAAYHoEGwAAAACmR7CBKT2/4HmjS3AZ9DUAADADgg1MKbxVuNEluAz6GgAAmAHBBqY0YcAEo0twGfQ1AAAwA4INAAAAANMj2AAAAAAwPYINTKlVl1ZGl+Ay6GsAAGAGBBuY0tHYo0aX4DLoawAAYAYEGwAAAACmR7ABAAAAYHoEG5jSvNXzjC7BZdDXAADADAg2AAAAAEyPYANTmvX4LKNLcBn0NQAAMAOCDQAAAADT8zC6AMBsErZMNeS4YYMWGHJcoLKaFjDNkONGpkUaclwAQMmYsYEpDRs/zOgSXAZ9DQAAzIBgA1MaMXGE0SW4DPoaAACYAcEGpjS+/3ijS3AZ9DUAADADgg1M6WLqRaNLcBn0NQAAMAOCDQAAAADTI9jAlMJahRldgsugrwEAgBmw3DNM6c01bxpdgsugr1EVeHh4qH379urSpYsaNmwod3d3paWl6bvvvtO+fft06dKlm/apX7++li5dqgkTJujMmTMGVA0AKAuXCTZWq1U7F+/Unvf3KP10uuo1raeh84Zq7fS1atqzqR6LfEyS9NNXP+mLd79QUlySMi9kyj/AX63ub6WHX3tYvjV8DT4LFFk6Z6nGv8xN7c5AX8PM6tatq//3//6fxo0bp/r169+yTU5Ojv71r39pwYIF2rdvn6TCUPPf//5XLVq0UE5OjoYPH+7MsgEAd8Blgs2aKWv0/Sffa8DMAWrQsYES9ibog2c+UOb5TN036b7idmcOnVF493D1eLKHfKr56Oyxs9ry+hZJ0siFIw2qHjfavmG7ab5sL58coruHvaq2940p3maz2fTuMzXVf/z7anrXIwZWVzoz9TVwvZEjR+rvf/+7AgMDJUknTpzQN998o2PHjik/P18hISHq0qWLunXrpieeeEKPP/64Fi1apIULF2rLli1q0aKF4uLiNH48P/8AYAYuEWxi18UqZk2MJm+erKb3NJUkNevdTEkHknTwk4Nq0KFBcds+E/oUv7ZarWrcrbHOHDqjY7uOSZLyc/K19o9rdWznMeVk5ahBhwZ69K+PKrhFsHNPCqaQmXZaWenJqtuwg932S+filZudoaDwrgZVBlRt8+fP18yZMyVJ0dHRevXVV7Vr165btm3UqJGmTJmiqVOnaurUqRo/frx8fHwUFxen+++/X2lpac4sHQBwh1wi2ERHRKvl/S2LQ02ROuF15O7prpDWIZIka4FV+zfs1+5/7FZqfKoyUzOL24Z2CJUkFeQXqG5YXQ3+82DVCKqh7Qu26/0x7+uFr15w3gnBNFLiY+RmcVdgaBu77edPHZBfzSBVD2xwmz0B3KlXXnlFM2fOVG5urp599lktXbq0xPY///yzZs6cqc8//1yffPKJfHx8dOXKFQ0ZMoRQAwAmUuVXRUs/na7ko8nq+HDHm967mHRRwS2D5eFdmO9WTVyltdPWKqxbmEYuGKmp/5mqP0b/UT7VfVS/VeG12d7+3howc4BqhdSSxd2i3s/0VvKRZOVl5zn1vFzdu1vfNboEh6TEx6h2cHN5eNnfn5V66oDqhZljtsYsfQ1I0j333KPZs2crPz9fw4YNKzXUFKlfv74WLVokLy8v5eTkyM/PT9OnT6/gagEA5anKz9ikn0mXJNUIqmG3Pfdqrk7sOaHW/VpLks4cOaPYdbF6LPIx9XiyR3G7+G/ilZ2RXTxjc6OEvQkKaBggTx/PCjoDaVrAtAr77MqqtC8UJ06cUJMmTUpsExERUZ4lFZu6cqrDbVPiY5SeclxLJ9Sx256Xk6muD75YpuNWxM+BI1/cjOxrV/HCvMIv39MCptm9rswqY80Wi0XLly+XxWLRG2+8oc2bNzu03/ULBcTFxWnGjBn6/PPPNX36dK1cuVJxcXF27Y0+TwBwNZFpkQ61q/IzNv6B/pKkc8fP2W3fsXCHLp+9XBxY0k8XBqDr75UpyCvQx7M/liS7+3CKXEm/ovXPr9fglwZXSO24vU2bNhldgkNSEvap+9BX9PjrcXZ/PDx9FWSSGRuz9DUwcOBAtWzZUgkJCXr11Vcd2ufGUHP//fdrx44dWrJkiSwWi6ZMmVLBVQMAykuVn7EJbByokDYhio6Ill9tP9WqX0txm+J0dNtRSdfunQlpEyJPH09tnrNZA2YMUNbFLO1cslNXLl6Rm8VNv2r3K7vPzb2aq+WPL1enRzqpy7AuFXoOjqbUqiTkVEiJ70dERKjH6B4ltmk0u1F5llQsYYtj7dLPHldO1kU1aj9Q1QND7bdfSVe9Mi4cUBE/B6X1s2RsX7uK5GWF/4xMi7R7XZlVhppvnDkZO3asJGnJkiXKzc0tdf9bhZqie2oWLlyoZ599Vr/73e/07LPPKisrq3i/yv7fBgBcVZWfsbFYLHrqvacU3DJY62au0+rJq1UtoJp6je0li4dFIW0Kv9jVCqml3y/7vS6nXNaKJ1Zo5+Kd6ju5r8K6hymoWZC8/b2LP7Mgv0Dv/+F91Qmvw2wNbislPkYe3n43rYiW/NMeVQtsIP+aQQZVBlRNPXv2lCRt2LCh1LYlhRqp8BLM/fv3y9fXVx073nyPJgCg8qnyMzaSVK9pPU3eNNlu28oJKxXUPEhevl7F29oPaa/2Q9rbtev0SKebPu+jqR/JZrUVP9QTzjfupXFGl1CqlPgYBYXdJYu7/f9myce/Ns1laJI5+hoIDg5WcHCwLl68qPj4+BLblhZqisTGxqpz587q1KmTdu/eXVGlAwDKiUsEm1s59d0pNe7auMz7pSWmKWZNjDx9PPVi2LWbv1/8+kXVDq1djhWiJP2G9TO6hFLd+8Tbt9ze9+l3nFzJL2OGvgZ8fHy0d+9eJScnl9iuZs2aDoUaSTpw4IBiY2PtLkMDAFReLhlscjJzlHoiVb3G9CrzvgENAri+uhIY0XGEouKijC7DJdDXMIOTJ0+qe/fupba7dOmSPv30U129erXUh28uXrxYixcvLs8yAQAVyCWDjXc1b0WcZ3laAHBFM2bMkL+/PzMxAFDFVPnFAwAAuBGhBgCqHoINTKnzvZ2NLsFl0NcAAMAMCDYwpVkLZxldgsugrwEAgBkQbGBK856dZ3QJLoO+BgAAZkCwgSnt37Xf6BJcBn0NAADMgGADAAAAwPQINgAAAABMj2ADU+KBkc5DXwMAADNwyQd0wvyi10Wr37B+hhw7bNACQ45rFCP7GihJZFpkmfdJXuYrSao/7qrdawCA+TFjA1Na9toyo0twGfQ1AAAwA4INAAAAANMj2AAAAAAwPYINTOn5Bc8bXYLLoK8BAIAZEGxgSuGtwo0uwWXQ1wAAwAwINjClCQMmGF2Cy6CvAQCAGRBsAAAAAJgez7GBKbXq0sroEqqEMw3PlNpm4PMDHWoHwPWEnAoptU3UO1EaMXFEiW0YYwCUB2ZsYEpHY48aXYLLeGDWA0aXAMDE1i1dZ3QJAFwEwQYAAACA6RFsAAAAAJgewQamNG/1PKNLAAA4gPEagLMQbAAAAACYHsEGpjTr8VlGlwAAcADjNQBnIdgAAAAAMD2eYwOUUcKWqYYcN2zQAkOOCwBmNS1gmtOPGZkW6fRjAijEjA1Madj4YUaXAABwAOM1AGch2MCUSnuKNQCgcmC8BuAsBBuY0vj+440uAQDgAMZrAM5CsIEpXUy9aHQJAAAHMF4DcBaCDQAAAADTI9jAlMJahRldAgDAAYzXAJyFYHOdS2cvaVrANMWujzW6FJTizTVvGl0CAFQI35T6citw/K9nv+RfSbYKLOgXMtt47efnp8DAQPn7+5fatkOHDqpVq5YTqgLgCILNdRLjEiVJDTs1NLgSlGbpnKVGlwAA5a76z+EK+/RRhe4Y5FC4qRN3l8K2DFO92B5OqO7OVPbx2t3dXY888oiioqKUkJCgrKwsnT9/XpmZmfr555+1fv16DR8+XJ6ennb7de3aVTt37tS2bdtUo0YNg6oHcD2CzXUSv0uUXy0/1ValgQYAACAASURBVA2va3QpKMX2DduNLsFhyyeH6NDOFXbbbDab3hlbQ8djNhpUVenc8t1VLbGxapxoLt+U+pX6N8JAVZHnn6ECzzzVONWk1HBTJ+4uBcX2lE025dSsvDfoV+bx+tFHH9XJkye1YcMGDR8+XI0bN1Z2drbOnz+v7OxsNWzYUEOHDlVUVJR+/vlnjRw5UlJhqNm2bZtq1aqlkydP6sqVKwafCQBJ8jC6AGewWq3auXin9ry/R+mn01WvaT0NnTdUa6evVdOeTfVY5GOSpMQDiWrQsYFi18Vq+8LtSj2RqrpN6urhOQ+rxX0tDD4LmFFm2mllpSerbsMOdtsvnYtXbnaGgsK7GlRZCWxS3bhuCjzUSe65PsWbc2pc1NnuXyqzYYKBxQFVW3adVP38wAY1+mxocbhJ6rtFNnerXbvrQ83pe7fqUrMfDKrYnLy9vbVixQqNGjVKkvTDDz/o3Xff1bZt2/TDDz/IarXKYrGoefPmuv/++zVhwgS1bdtWa9as0ZgxY9S1a1fVqlVL69at0+9+9zvl5+cbfEYAJBeZsVkzZY22vrVVPUf31Pio8er424764JkPdOHkBYV2DC1ul3QgSWd/PKtvVn6jB2Y9oNHLR0uSVjyxQheTKu9vw1B5pcTHyM3irsDQNnbbz586IL+aQaoe2MCgym7DJtXf3Vf19veQJdfb7i2vyzXVcNuDqpHQ1KDiANdQFG7yvbJvOXNDqPllvLy89PHHH2vUqFHKzMzUpEmT1Lp1ay1YsEBHjhyR1VoYIq1Wq3744QctXrxY7dq109ixY5WZmal+/fqpVq1a2rhxI6EGqGSq/IxN7LpYxayJ0eTNk9X0nsIvZM16N1PSgSQd/OSgGnQo/GKZfiZdl1MuK7xHuCaunyiLe+FfInXC6mhez3k6vPWwev2hlzLOZWjlhJWK/zZedcPr6vHFjyu0fehtj4+K8e7Wd40uwSEp8TGqHdxcHl6+dttTTx1QvbDKN1vje66+An5sJ0lyk5vde26yyCab6n91vzIaJMjmUWBEiYBLuN3MTeD3XUwXairbeD1//nwNHDhQKSkp6tevnw4dOuTQfgcOHCgOPZJ04cIFQg1QyVT5GZvoiGi1vL9lcagpUie8jtw93RXSOkRS4WyNJA1+aXBxqJGk4JbBsnhYlJmaKUn618x/qV7zenr9+OvqNaaX3nvqPVkL7C8RQMWLPxpvdAkOSYmPUXrKcS2dUMfuT+wnbyoo/C6jy7tJwA/tZNPtf57d5CaPXB/VOMmsDVDRbpy5Cd/4uOlCjVS5xuvevXvr2WefVV5enoYMGeJwqCm6p6ZGjRratm2bcnJyNHbsWA0YMKCCKwZQFlV6xib9dLqSjyarz8Q+N713MemiglsGy8O7sAsS4xJVI6iGmvRoYtcu80KmrPlW1QqppeyMbB3eelj/c/h/5OXrpZ5P9dS2iG06GXNS4XeHV9h5TAuYVmGfXVlNnz69xPcjIiIcalMRpq6c6nDblIR96j70FbXq9aTd9lUvtlNQGWdsnPFzsGRqrGqFlvz7DpvNql0vx+q9/7xU4fW4ihfmFa4aNS1gmt3rysyMNUvmrLvprzopctJX8rkUKEl6a+3T2vrc+wZXVai0cVgydry+0auvvipJmjt3rvbt2+fQPtcvFFB0T83MmTM1d+5czZkzR1u3brVrX9l/ngAzikyLdKhdlZ6xST+TLkmqEWS/DGPu1Vyd2HOi+DI06VqwudH+9fvlZnFTi1+3UGp8qvwD/FUtsFrx+yGtQ5TyY0oFnQHMLP3sceVkXVSj9gNVPTC0+E9BXrZyrqSrXiVcOCCvIEc2W8nLn7m5WZRfkOekigB0a/GAvL38iv+9Z5vfysPds4Q9cCtt2rRRnz59lJGRobfeesuhfW4VavLz87VgwQKlpaWpe/fu6tKlSwVXDsBRVXrGxj+w8OFa546fU+v+rYu371i4Q5fPXlZoh2v3xiQeSFRBboHysvPk6VP4F8aV9CvavmC7ugzvotqhtZWWmCaf6j52x/Cp7qOcrJwKPQ9HU2pVEnIqpMT3IyIi1GN0yc9taDS7UXmWVCxhi2PtUuJj5OHtd9OKaMk/7VG1wAbyrxlUpuM64+egzneS2363Utv1WtRSXeq53s9lRUleVvjPyLRIu9eVmRlrlsxX9/ULBRTd93ZP299q7eqjt1wtzdlKG6slY8fr62dPBg8eLElau3atMjIySt33dqFGkq5evapVq1ZpypQpGjx4sGJjrz3YuzL/PAFVXZWesQlsHKiQNiGKjojW3o/26tgXxxQ1I0rfrvpWkoqDTfqZdGWcy5BvTV99OO5D/fjfHxW7PlYLH1go72reGjpvqCTJy89LOZn2ISY7I1ve/varR6HijXtpnNEllColPkZBYXfJ4m7/+4Pk41+X+TI0Z7nY/LCs7vm3vc/GJquu1Dmrq3WZpQQq2o2rnxW53WpplVVlGa+LZlZ2795datuSQk2Ros9hxgaoPCr/iPgLWCwWPfXeUwpuGax1M9dp9eTVqhZQTb3G9pLFw6KQNvYLB/zhwz/I3dNdK55coQ2zNijs7jA9u+VZ+dUsvASgbnhdZV7IVFZaVvExko8mK6hF2X7zjl+u37B+RpdQqnufeFvDXtp50/a+T7+jIdM2OL8gB+T7Zymx7xbZLDbZrnsiZ9HrvGqZSuq7RSp9UgfAL1DSks4lLQVdGVWW8bpJk8J7aI8cOVJiO0dCzfWfU/S5AIxXpS9Fk6R6Tetp8qbJdttWTlipoOZB8vL1kiS1faBt8dTx6BWjb/tZPtV91GZAG30+/3M9+JcHtS9qn9zc3NT4rsYVVj9ubUTHEYqKizK6jCops2GC4n+7WgGHOxYv/Zznn6mLLb7XxVbfq8An2+AKgaqttOfUOPoQz8qisozXzzzzjAICAnT06NES2z399NMOPXzzxIkT6tevn9LT0yuiXAB3oMoHm1s59d0pNe7a+I72Hf7WcH04/kP9KfxPqhNeR0+//7Td8tBAVZBTO03JvXYUB5ufRv7D4IoA11D7aDuHlnS+MdyEfNlPp+/besu2KPTdd9851G7KlCk6fPiwli1bVuJzaq5cuaLt27eXV3kAyoHLBZuczBylnkhVrzG97mj/6vWqa9LGSeVcFQAAUkajE8o+0kHn2+8r9Tk1ReGmwfYhSmv1vZMqrPqsVquWLFlidBkA7oDLBRvvat6KOO+c9fJRcTrf29noEgCg3OX7XVH8b1c7fFlZdp1UHR/2fqW9DE1ivAbgPFxDBVOatXCW0SUAQIUoa0ipzKFGYrwG4DwEG5jSvGfnGV0CAMABjNcAnIVgA1Pav2u/0SUAABzAeA3AWQg2AAAAAEyPYAMAAADA9Ag2MKXK8LA3AEDpGK8BOAvBBqYUvS7a6BIAAA5gvAbgLC73HBtUDcteW6Z+w/oZcuywQQsMOS4AmJGR43VkWmSZ2icv85Uk1R931e41AHNgxgYAAACA6RFsAAAAAJgewQam9PyC540uAQDgAMZrAM5CsIEphbcKN7oEAIADGK8BOAvBBqY0YcAEo0sAADiA8RqAsxBsAAAAAJgewQYAAACA6RFsYEqturQyugQAgAMYrwE4C8EGpnQ09qjRJQAAHMB4DcBZCDYAAAAATI9gAwAAAMD0CDYwpXmr5xldAgDAAYzXAJyFYAMAAADA9Ag2MKVZj88yugQAgAMYrwE4C8EGAAAAgOl5GF0Aysdz+5obctz5XY8ZclwjJWyZashxwwYtMOS4AADnmRYwzZDjRqZFGnJcoDwxYwNTGjZ+mNElAAAcwHgNwFkINjClERNHGF0CAMABjNcAnIVgA1Ma33+80SUAABzAeA3AWQg2MKWLqReNLgEA4ADGawDOQrABAAAAYHoEG5hSWKswo0uoemwV3B6AS2K8BuAsLPd8g0tnL+kvrf+i3//v79Xl0S5Gl4PbeHPNm0aXUKV4p9XRr77sp8S+nyqvekap7av/HKaAw52U2G+zrF55TqgQgFkxXlec+vXrq1evXurcubOCg4Nls9mUnJys2NhYffnll0pNTb1pn/79+2v27Nl66KGHlJ6ebkDVQMUh2NwgMS5RktSwU0ODK0FJls5ZqvEvc0NqeakX20O+54PUeMswnRy0rsRwU/3nMIXuGCyL1V21jrdSWuuDTqwUgNkwXpe/Hj166LnnntNDDz0kd3f3W7bJy8vT+vXrNX/+fO3fv19SYajZtGmTfHx8NHbsWL311lvOLBuocFyKdoPE7xLlV8tPdcPrGl1KhbFdvaq84SNl/fKra9tycpQ/bYby57wum9VqYHWO2b5hu9ElOGz55BAd2rnCbpvNZtM7Y2voeMxGg6qyd7rP57pSN1lemTXUeMsweWZUv2W760PN+bb7ldaKUAOgZGYarys7Pz8/LVy4UHv27NEjjzyigoICffbZZ5ozZ47GjBmjMWPG6PXXX9e2bdtksVg0cuRI7d27V3PnztXgwYOLQ82SJUv0t7/9zejTAcqdy8zYWK1W7Vy8U3ve36P00+mq17Sehs4bqrXT16ppz6Z6LPIxSVLigUQ16NhAsetitX3hdqWeSFXdJnX18JyH1eK+FgafRflw8/WVZdijKli1Rm697pGsVhW8Nlfy9JT7rOflZiHvlpfMtNPKSk9W3YYd7LZfOhev3OwMBYV3Nagye1avXP38m3+r0X9+K7/U+sUzN9e7MdSkdPtScjOoYABwMbVq1dJ//vMfde/eXXl5eZo/f74WLlyolJSUW7YPDQ3VjBkzNGXKFM2aNUsFBQVyd3fXkiVLNHnyZNls3CiJqsdlvsGumbJGW9/aqp6je2p81Hh1/G1HffDMB7pw8oJCO4YWt0s6kKSzP57VNyu/0QOzHtDo5aMlSSueWKGLSVVnyUrLQw9KF9Jk+2q3CiIXyXb+vNxfeVluXp5Gl1alpMTHyM3irsDQNnbbz586IL+aQaoe2MCgym5WFG6un7kpQqgBAON4eHho8+bN6t69uxISEtStWzf9+c9/vm2okaSkpCRNnz5df/zjH2Wz2eTu7q6ff/5ZU6ZMIdSgynKJYBO7LlYxa2I0dvVY9Z3SV816N9OAGQPUuGtjWfOtatCh8Mtl+pl0XU65rMDGgZq4fqLaDWqntg+01ZPLnlTulVwd3npYkvTZ3M809+65mh44XXEfxxl5anfMzddHluGPqmD+27IdPCiPN16Vm7+f0WU57N2t7xpdgkNS4mNUO7i5PLx87bannjqgemGVY7bmejeGmyKEGgB3yizjdWU2a9Ys9erVS0lJSerTp4/i4hz77tG/f3+9+eabcnNz09WrV9WoUSNNnDixgqsFjOMSl6JFR0Sr5f0t1fSepnbb64TXkbunu0Jah0gqnK2RpMEvDZbF/VrmC24ZLIuHRZmpmZKkuk3qaujcodryxhan1D8tYFqpbTy33mEt2dlyf2yE3GrXvqPdHantTkyfPr3E90+cOKEmTZqU2CYiIqI8Syo2deVUh9umxMcoPeW4lk6oY7c9LydTXR98sUzHrai+vhU/7xc095nP1bpRD0mSxequdV/8TUufm+m0GlzJC/OWSir8b3z968rMjDVL5q1bkrbNLxx7KlO9pY3VkrHjdVlVxp+PRo0aafbs2ZKkJ598UomJiQ7td/1CAUuWLFF0dLQ2bNigN998U2vXrtX58+ft2ht9nkBJItMiHWpX5Wds0k+nK/losjo+3PGm9y4mXVRwy2B5eBfmu8S4RNUIqqEmPewH4MwLmbLmW1UrpJYkqeuIrmrx6xby8DFvLrRG75B1bZTcBg5QwcaPTTctvWnTJqNLcEhKwj51H/qKHn89zu6Ph6evgirhjE2RKzkZ2vjltUEkK/uS/r17kYEVATArs4zXldWECRPk5eWl1atX67///a9D+9wYaiZPnqyNGzdqy5Yt8vf31x/+8IcKrhowhnm/mTso/UzhGu01gmrYbc+9mqsTe06odb/WxduKgs2N9q/fLzeLm1r82pjFAxxJqc/tc/zzrHtjVPD3xXKf84rcmjVT/pNPy7brS7n1ubdCarsTIadCSnw/IiJCPUb3KLFNo9mNyrOkYgkOTo6lnz2unKyLatR+oKoHhtpvv5KuemVcOKCi+vpWiu6p0f8tkOfvU1P/eONgqUtB484kLyv8Z2RapN3rysyMNUvmrVuS9H+LK1ameksbqyVjx+uyqgw/HzfOnIweXXiv79///neH9r9VqCn65eWiRYs0aNAgPf300/rrX/9qt19l+rkC7lSVn7HxD/SXJJ07fs5u+46FO3T57GWFdrj2hTPxQKLSTqUpL/vaAwevpF/R9gXb1WV4F9UOvbPLtSoT6+EjKnhjntyfmyFL+3bX7rVZucYUyzybSUp8jDy8/W5aES35pz2qFthA/jWDDKqsZNcvFFDEkaWgAQDlq2HDhqpfv75SU1P19ddfl9q+pFAjSdHR0crOzlbLli1Vs2bNiiwdMESVDzaBjQMV0iZE0RHR2vvRXh374piiZkTp21XfSlJxsEk/k66McxnyremrD8d9qB//+6Ni18dq4QML5V3NW0PnDTXyNMqFLeGkCl5+Re7jn5Hlnp7F2y0PDZEuXZJt15cGVlc2414aZ3QJpUqJj1FQ2F2yuNtPjCYf/7rSXoZ24+pnRW5cLY1wA8BRZhivK6sOHQp/MVb0gM2SlBZqJCk/P18HDx60+2ygKqnyl6JZLBY99d5TivpjlNbNXCe/2n7qNrKbeo3tpU9f+1QhbewXDvjDh39QdES0Vjy5Qp4+nmo/pL0GvzRYfjXNs2LY7biFNZbn+qibt/v4yDNqtdPr+SX6DetndAmluveJt2+5ve/T7zi5EsfcaknnOoc6S7r9c264LA1AacwwXldWly5d0ubNm7V79+4S23Xo0KHUUFNk69atSklJUVZWVkWUDBiqygcbSarXtJ4mb5pst23lhJUKah4kL18vSVLbB9oWX186esXoEj+vIK9A1gKrbFabCvILlJedJw9vD7m5sQaus4zoOEJRcTeHNNwZR55TQ7gBcCcYr+/crl27tGvXrlLbff/991q/fr0uXbpU6sM3i1ZYA6oilwg2t3Lqu1Nq3LXxHe370bSPFLMmRpIU/3W8JGl23GwFNgwsr/IAp6p+qolDz6m5Ptz4pgbL91x9gg0AGMxqterJJ5+UzWYz3SqnQHlyyWCTk5mj1BOp6jWm1x3tP2rxKI1aPKqcqwKMc+ae7coMOaXL4cdKffhmUbjxT/6VMholOKdAAECJrCwABLhmsPGu5q2I85XjYWC4M53v7Wx0CVWLxabLTY453NzqlUuoAeAQxmsAzlLlV0VD1TRr4SyjSwAAOIDxGoCzEGxgSvOenWd0CQAABzBeA3AWgg1Maf+u0tf0BwAYj/EagLMQbAAAAACYHsEGAAAAgOkRbGBKPOwNAMyB8RqAs7jkcs9V0fyuji/VWxVEr4tWv2H9DDl22KAFhhwXAMzIyPHajCLTIsvUPnmZrySp/rirdq8BV8SMDUxp2WvLjC4BAOAAxmsAzkKwAQAAAGB6BBsAAAAApkewgSk9v+B5o0sAADiA8RqAsxBsYErhrcKNLgEA4ADGawDOQrCBKU0YMMHoEgAADmC8BuAsBBsAAAAApkewgSm16tLK6BIAAA5gvAbgLAQbmNLR2KNGlwAAcADjNQBnIdgAAAAAMD2CDQAAAADTI9jAlOatnmd0CQAABzBeA3AWgg0AAAAA0yPYwJRmPT7L6BIAAA5gvAbgLAQbAAAAAKbnYXQBKB/P7WtuyHHndz1myHGNlLBlqiHHDRu0wJDjAgBQmmkB05x+zMi0SKcfE5UbMzYwpWHjhxldAgDAAYzXAJyFYANTGjFxhNElAAAcwHgNwFkINjCl8f3HG10CAMABjNcAnIVgA1O6mHrR6BIAAA5gvAbgLAQbAAAAAKZHsIEphbUKM7oEAIADGK8BOAvB5gaXzl7StIBpil0fa3QpKMGba940uoSqxeqmGieaSzbHmltyvVT9Z76sACgd4zVuxdPTU82aNVPbtm0VFhYmi6Xkr6SDBg1SrVq1nFQdzIpgc4PEuERJUsNODQ2uBCVZOmep0SVUKSG771eDnQ8oaG/vUsONJddLjf7zWzWIfrAwDAFACRivUSQwMFDPPfec9u7dq4yMDB07dkzff/+94uPjdenSJe3cuVNjx46Vn5+f3X6/+93vtGnTJm3btk3e3t4GVQ8zINjcIPG7RPnV8lPd8LpGl1JhbFevKm/4SFm//Oratpwc5U+bofw5r8tmtRpYnWO2b9hudAkOWz45RId2rrDbZrPZ9M7YGjoes9GgquxlNDwhq6VAdQ51LjHcFIUav9T6yquWoav1kp1baGlskv/phgo41FG1j7aT5+UaRlcEuDwzjdeoGB4eHnrppZeUlJSkv/71r7rrrrvk7e2thIQEHTp0SElJSapWrZr69Omj//3f/1VSUpKefvppSYWh5sMPP5S7u7s2b96snJwcg88GlZmH0QU4i9Vq1c7FO7Xn/T1KP52uek3raei8oVo7fa2a9myqxyIfkyQlHkhUg44NFLsuVtsXblfqiVTVbVJXD895WC3ua2HwWZQPN19fWYY9qoJVa+TW6x7JalXBa3MlT0+5z3pebqVMB8NxmWmnlZWerLoNO9htv3QuXrnZGQoK72pQZfYyGiUoqe+nCt0xWHUOdZYkpXT70q7N9aEmt9plnRy0TnnVM4wo95b8TzdUyFd95ZVZs3ibTTZlNEjQmXu3qcAn28DqAMA1BQcHa/PmzeratfDvu08//VRLly7VF198ocuXLxe3q1u3rgYOHKhJkyapR48e+sc//qFJkyapU6dOcnd311/+8hfNmTPHqNOASbjMN9g1U9Zo61tb1XN0T42PGq+Ov+2oD575QBdOXlBox9DidkkHknT2x7P6ZuU3emDWAxq9fLQkacUTK3QxqeosWWl56EHpQppsX+1WQeQi2c6fl/srL8vNy9Po0qqUlPgYuVncFRjaxm77+VMH5FczSNUDGxhU2c2Kwo3dzM3/qfSh5kyoGn3+sDwzq9ttd5ObqieGqfGWR2XJ42cbAJypXr16+uKLL9S1a1clJCSob9++GjJkiDZv3mwXaiQpNTVVK1euVM+ePTVq1ChlZmaqa9eucnd316uvvkqogUNcYsYmdl2sYtbEaPLmyWp6T1NJUrPezZR0IEkHPzmoBh0Kv1ymn0nX5ZTLCu8RronrJ8riXpj76oTV0bye83R462HdPepurf3jWh3beUw5WTlq0KGBHv3rowpuEWzY+d0JN18fWYY/qoL5b0u1a8kj8m9y8/crfcdK4t2t7xpdgkNS4mNUO7i5PLx87bannjqgemGVY7bmereauZFUqUONbFLwN30km+R2i9/VuMlNPhfrqNaPbZTWNs6AAgHXZpbxGuVv5cqVat68ueLi4tSvXz9duHDBof1sNpt8fa/9vVmzZs0SWgPXuMSMTXREtFre37I41BSpE15H7p7uCmkdIqlwtkaSBr80uDjUSFJwy2BZPCzKTM1UQX6B6obV1fRt0/XGiTfUvE9zvT/mfeedTHnLzpb7YyPkVru20ZWUSfzReKNLcEhKfIzSU45r6YQ6dn9iP3lTQeF3GV3eLV0/c1Ok0oYaSb7ng+Rzsc4tQ00Rm2wK+KGdE6sCUMQs4zXK19ixY9W/f3+dP39ev/nNbxwONdffU/Puu+8qLy9Pzz77rHr37l36znB5VX7GJv10upKPJqvPxD43vXcx6aKCWwbLw7uwGxLjElUjqIaa9Ghi1y7zQqas+VbVCqklb39vDZg5oPi93s/01qevfaq87Dx5+lTMpS7TAqaV2sZz65YyfaY1eoesa6PkNnCACjZ+LLcHBsrNza1CarsT06dPL/H9iIgIh9pUhKkrpzrcNiVhn7oPfUWtej1pt33Vi+0UVMYZm4rq69u5r8MI/fmJtZKkrKuXNP6NDkqZ+LNTa3BE306P68XHR5bYxk1uck+r7vQ+dNQL8wpXjZoWMM3udWVmxpol89YtSdvmF449lane0sZhydjxuqzM+PNRGWu2WCyaPXu2JGnKlClKSUlxaL/rQ03RPTXnzp3Tyy+/rNmzZ2vAgAF27Y0+TzhPZFqkQ+2q/IxN+pl0SVKNIPvVkXKv5urEnhPFl6FJ14LNjfav3y83i5ta/PrmxQMS9iYooGFAhYWaimDdG6OCvy+W+19my33SBCk9XbZdX5a+I8ok/exx5WRdVKP2A1U9MLT4T0FetnKupKteJVk44Fb8vKvrkd7X/sLw962p394zxcCKbi87N8uhdrl5Vyu4EgCAJA0ePFgNGzbUTz/9pLVr1zq0z61CjSS9/fbbunLlivr3769mzZpVZNmoAqr8jI1/oL8k6dzxc2rdv3Xx9h0Ld+jy2csK7XBt4YDEA4kqyC2wm325kn5F2xdsV5fhXVQ71P5yrSvpV7T++fUa/NLgCj0HR1Lqc/sc+yzr4SMqeGOe3J+bIUv7wktzLMMfVcHKNXLr3avMK6I5mqDLKuRUSInvR0REqMfoHiW2aTS7UXmWVCzBwcmxlPgYeXj73bQiWvJPe1QtsIH8awaV6bgV1dc3unGhgNQO36r+1301rM8M3ff/fl24WlrZJ/cqjCXXS9Y1ebLk3/6XCzZZldMuyWl9WFbJywr/GZkWafe6MjNjzZJ565Yk/d+q8ZWp3tLGasnY8bqszPjzUVlqvn72ZODAgZKkf/7zn7LZSn/y8+1CjSRdunRJGzdu1KhRo9S/f3/99NNPxe9V9v82cL4qP2MT2DhQIW1CFB0Rrb0f7dWxL44pakaUvl31rSQVB5v0M+nKOJch35q++nDch/rxvz8qdn2sFj6wUN7VvDV03lC7z829mqvljy9Xp0c6qcuwLk4/rzthSzipgpdfkfv4Z2S5p2fxdstDQ6RLl0w1azPuDHr1lQAAIABJREFUpXFGl1CqlPgYBYXdJYu7/e8Pko9/XebL0JzlVqufpbc8cvNqaaX/PeU0Vq9cpbX8/rbv2wpXFVBaaxYOAIxghvEa5atLl8LvRd98802pbUsKNUW+/vpru88FbqfKz9hYLBY99d5TivpjlNbNXCe/2n7qNrKbeo3tpU9f+1QhbewXDvjDh39QdES0Vjy5Qp4+nmo/pL0GvzRYfjWvrRhWkF+g9//wvuqE16nw2Zry5BbWWJ7ro27e7uMjz6jVTq/nl+g3rJ/RJZTq3ifevuX2vk+/4+RKHFPSks63fc5NJZm5Odd1t7wu11SNU01kc7PKzVb4O5vCUGPT6T5blV0n1eAqAddkhvEa5athw4aSpB9//LHEdo6Emus/p1GjyjGzh8qrygcbSarXtJ4mb5pst23lhJUKah4kL18vSVLbB9oWT2mOXjG6xM/7aOpHslltxQ/1hPON6DhCUXE3hzTcGUeeU1OZw43N3arE+z9V9VNhCjjaXtXOFP7ll9b6gNJaHVRurarzDCrAbBivXc8999wjf39/nT17tsR2AwYMcOjhm19//bVat26tS5culXepqGJcItjcyqnvTqlx18Zl3i8tMU0xa2Lk6eOpF8NeLN7+4tcv3nQPDmAWv/pioENLOt8YbvKqX1Ja64NOrvY2LDZlNI5XRuN4tVlRuHrU2R5fGFwUALiekydPOtRuzJgx+vjjj/Xvf/+7xHZZWVk6evRoOVSGqs4lg01OZo5ST6Sq15heZd43oEEAN6uhyjnX5Wt5XvFXYt9PS31OTVG4CTjcSelN+YsGAHBnrFZrqaEGKAuXDDbe1bwVcb5yrJmPO9P53s5Gl1Cl5AScV/xDHzl8WVlGowRlNEyoFJehAajcGK8BOEuVXxUNVdOshbOMLqHqKWtIIdQAcADjNQBnIdjAlOY9O8/oEgAADmC8BuAsBBuY0v5d+40uAQDgAMZrAM5CsAEAAABgegQbAAAAAKZHsIEp8bA3ADAHxmsAzuKSyz1XRfO7HjO6BKeKXhetfsP6GXLssEELDDkuAJiRkeM1nKesz/hLXuYrSao/7qrda+CXYMYGprTstWVGlwAAcADjNQBnIdgAAAAAMD2CDQAAAADTI9jAlJ5f8LzRJQAAHMB4DcBZCDYwpfBW4UaXAABwAOM1AGch2MCUJgyYYHQJAAAHMF4DcBaCDQAAAADTI9jAlFp1aWV0CQAABzBeA3AWgg1M6WjsUaNLAAA4gPEagLMQbAAAAACYHsEGAAAAgOkRbGBK81bPM7oEAIADGK8BOAvBBv+/vTsPb6pM2AZ+Z2uaLukKLd2gZactOxQQQdmLooIIAzqgg1JwUIogMq/MoIy+4uAFRRwVHGRYhAEpvPMhqLVsiuyLBVG2tlgqpRS6701yvj9CC6FtkkKTk5Pcv7m8pj15mtyJ9WnunHOeQ0REREQkeSw2JEkLJi8QOwIREVmB8zUR2QuLDRERERERSZ5S7ABEUpO5e7Yojxs5eoUoj0tEROSMEv0TRXncpPwkUR7XFXCPDUnS+ITxYkcgIiIrcL4mInthsSFJmjBzgtgRiIjICpyvicheWGxIkhKGJ4gdgYiIrMD5mojshcWGJKkgr0DsCEREZAXO10RkLyw2REREREQkeSw2JEmRnSPFjkBERFbgfE1E9sJiQ5L0/ub3xY5ADkCmlwNCE8cTkV1xviZXplKpxI7gUvhX/h5F14uQ6J+Ik8knxY5CZqxavErsCCQymU6B8NQxCDo20Kpyoyz3QNT/TYLvxS62D0dEdThfkzOIi4vD3LlzsXHjRnzzzTfYvXs3Vq1ahenTpyMysuG9krNnz8aPP/4IX19fO6d1XbxA5z2u/nQVABDRI0LkJGTOnu17kPA3rrTjyjQ3g+B5LRze2W0AALl9DwKyhscqyz3Q+utxcC8MQMC57ihsdx6QG+wXlsiFcb4mKZs6dSpee+01dO3a1ey4r7/+Gu+++y5+/PFHAMZSk5RkvBDn0KFDkZycbPOsxGJTz9XTV+Hh64EWUS3EjkJO4l+zQtBv/N8R88i0um2CIODTl3wwPGEd2vUZK2I66SoPvobsIbsRtnc0An/uBaDhcnN3qan0u4kro3aw1JBkKCo08P+1K/wuRNdta/XjENyKPo1qX642RmQr4eHh+PzzzzFs2DAAQG5uLnbs2IETJ04gOzsbCoUCHTp0QL9+/fDkk08iPj4eI0eOxMqVK5GdnY2lS5cCABISElhq7Mhlio3BYMD+f+7HoXWHUPh7IVq2a4lxS8Zhy5wtaDegHSYmTQQAXE27ivDu4Ti57ST2fLgHeel5aNG2BZ5c/CQ6PtJR5GdBUlOa/zvKCnPQIqKbyfaiGxmorixBUFRvkZI5h5LWGQ2Xm9vqlZr47dBrKsSKS9QkqmItInePh7LMy2S73/kY+F7qjKxhO1EWliVSOiLn1aFDB+zduxehoaG4efMm5s2bh02bNqGmpsZk3O7duwEA/v7+eO211/DGG29g9uzZdbcnJCRg9erVds3u6lzmHJvNr2xGygcpGDB1ABK2JqD7U92x/qX1uHXlFsK6h9WNy07LxvUL13Fk4xHEL4jH1H9NBQCseW4NCrL56Zij+DTlU7EjWCU34zhkcgUCwqJNtt/MSoOHTxC8A8JFSuY8asuNQa5H4M+9jOfc3MZSQ5IlABF7Hoey3BOy2/+rJYMMMr0cEamPQ1GhETGkdaQyXxMBxpLy3XffITQ0FAcOHECXLl2wbt26eqXmbvn5+Vi4cGHdoWcAcObMGZYaEbhEsTm57SSObz6OFze9iCGvDEH7h9tjxNwRaNO7DQw6A8K7Gd9cFl4rRHFuMQLaBGBm8kzEjo5FTHwMpqyeguryapxLOQcA2DB9AxZ2XIgFrRdg2bBlyDyWKebTc0kZv2aIHcEquRnH4RfcAUo30zcfeVlpaBnJvTXN5d5yU4ulhqTKIzcE7vktIBMa/jMtgxxyvQp+F6MbvN2RSGW+JgKAlStXIiIiAkeOHMHo0aORl5dn1c/Nnj0b8+bNAwCUlZWha9eumDZtmoWfoubmEoeipS5PRaehndDuoXYm2wOjAqFQKRDSJQSAcW8NADy28DHIFXf+mAR3CoZcKUdpXikAYPhrwzHpo0lQuilxLuUc1j6/Fot/WWyz/In+iTa7b0c1Z84cs7cvX77cqjG2MHvjbMuDbsvNOI7C3MtYNSPQZHtNVSl6j/lLkx7XFX8Pmqp/9BP42x+/hFLhBgDIzDmL198agqIXb4qczLw3lhhXjUr0TzT52pFJMTMgndwvjHoHbYYIkMkaWREDgEEwIHerDnMfFS+/pXkYEHe+biqp/H7cTYqZAcfMPWjQIEyePBllZWWYPHkyysvLrfq5uxcKSEhIQElJCTZt2oQPPvgAW7ZsQWlpqcl4sZ+nFCXlJ1keBBcoNoW/FyLn1xwMnjm43m0F2QUI7hQMpdr4Mlz96Sq0QVq07d/WZFzprVIYdAb4hhiX6wvuFAzAeAK4QqlASW4JaiproHLnWuVkKjfzBOLGvYXOA6eYbP/iL7EI4h6bZnc+6yjyS66jpa9xVcOzmd+jqMyxSw1RQ5QKNwiC+WIjl8mhUqjtmIrIuc2aNQsA8MEHHyAz07qjce4tNbWHn82cORMPP/wwnn32WaxaxSXP7cX5i821QgCANkhrsr26ohrph9LRZdida1rUFpt7nUo+BZlcho6P3lk8YMP0DUjbmQZdlQ4DXxxo01JjbUt1JiFZIWZvX758OfpP7W92TOu/tm7OSHUyd1s3rvD6ZVSVFaB115HwDggz3V5eiJZNXDjAFX8PmuLuhQJqPTHgzxgwvZ/ZpaAdQc7tw7CT8pNMvnZkUswMSCe378UukP9g/mhxAQYED/dC0mLx8luaqwFx5+umksrvx92kmBlwjNx37znx8vLC2LFjodPprD43prFSAwD//Oc/8fDDD2PKlCn1io0U/v1IldOfY+MZ4AkAuHH5hsn2vR/uRfH1YoR1u/OG82raVeRn5aOm8s4JYuWF5dizYg96PdMLfmF+ddv/uPqPeD/rfUzbOA1terex7ZOgeqYvnC52BItyM45DqfaotyJazqVD8AoIh6dPkEjJnM+9q5/VMllQwIqLeBI5iqKoi9CrqiGY+cWVQY78zmftmOr+SGG+JurRoweUSiXS0tJw7do1i+PNlRoA+Pbbb+vuV6FQNH9gapDTF5uANgEIiQ5B6vJUHPvPMVw8cBFb527F0S+OAkBdsSm8VoiSGyXQ+GiwYfoGXNh3ASeTT+LD+A+h9lJj3JJx9e5boVIgdnQs9q7cW684kW0NGz9M7AgW5WYcR1BkH8gVpjtGcy4f5mFozaihJZ1r1VstjeWGJEJQ6pDz0F7j1/f84tZ+f6tzGioDHf9vjxTma6KYmBgAwOnTpy2OtVRqAKCwsBCZmZnQaDRo375984alRjl9sZHL5Xh+7fMI7hSMbfO2YdOsTfDy98LAFwdCrpQjJNp04YA/bfgTFCoF1kxZg+0LtiOyXyRe3f0qPHw8Gn0MXbUO+Vn5dnk+ZDSh+wSxI1g06LllGL9wf73tQ174BI8nbq//A9Rklq5T0+BS0Cw3JBFFbS/g6tBdqPYuMtmud6tCbu8fcb3/fnGCNZEU5muiS5cu4bPPPkNqaqrZcaNGjbJYamqtX78eq1atQllZWbNmpcY5/Tk2ANCyXUvM+n+zTLZtnLERQR2C4KYxrp4UEx9Td8zj1DVTG72vsvwyXPr+ErqM6AK5Uo7D6w/XO6SNiGzP2otvNnoRTwc+54aoVkmbdJS0TofmRitEfWUsCBcn/wuCQi9yMiLnkpqaarHUAEBKSgo2bNiAgwcPWjwX56233mqmdGQtlyg2Dck6nXXf58Z8/9n3+M/s/0Aml6FV51aYvmU6vAK8LP8gETUbRaUGygoPq65Tc3e5URf5AYIckBnsmJboAciAiqCcum9ZaojEYzAYMGXKFMsDSRQuWWyqSquQl56HgdMGWh58D09/T7y661UbpKKm6Dmop9gRSGRV/rdwZXQydJpyqy6+WdI6A1dGJxvPSZCz1BDZC+drIrIXlyw2ai81lt90jIuB0f1Z8OECsSOQA6jyv9Wk8Xd/6k1E9sH5mojsxekXDyDntOTVJWJHICIiK3C+JiJ7YbEhSTr1/SmxIxARkRU4XxORvbDYEBERERGR5LHYEBERERGR5LHYkCRt/Wmr2BGIiMgKnK+JyF5YbEiSUrdZvogWERGJj/M1EdmLSy73TNK3+p3VGDZ+mCiPHTl6hSiPS0QkRWLO10TmJOUnNWl8zmoNAKDV9AqTr8lxcI8NERERERFJHosNERERERFJHosNSdL8FfPFjkBERFbgfE1E9sJiQ5IU1TlK7AhERGQFztdEZC8sNiRJM0bMEDsCERFZgfM1EdkLiw0REREREUkeiw0REREREUkeiw1JUudencWOQEREVuB8TUT2wmJDkvTryV/FjkBERFbgfE1E9sJiQ0REREREksdiQ0REREREksdiQ5K0ZNMSsSMQEZEVOF8Tkb2w2BARERERkeSx2JAkLZi8QOwIRERkBc7XRGQvLDZERERERCR5SrEDUPN4/UQHUR53ae+LojyumDJ3zxblcSNHrxDlcYmIiMhxJPon2v0xk/KT7P6Y94N7bEiSxieMFzsCERFZgfM1EdkLiw1J0oSZE8SOQEREVuB8TUT2wmJDkpQwPEHsCEREZAXO10RkLyw2JEkFeQViRyAiIitwviYie2GxISIiIiIiyWOxIUmK7BwpdgQiIrIC52sishcWm7sUXS9Con8iTiafFDsKWfD+5vfFjkAOwPu3KKjzA60e73c+BooKDxsmInpwfr/GQlGhsW6wQYaAsz0g0ytsG+oBcL4mEldoaCgeeeQRDB8+HHFxcfD09DQ7/s9//jN8fX3tlK55sdjc5epPVwEAET0iRE5ClqxavErsCCQyj+shCN8zGm12j7Oq3AT+1AchPw5Fm6/HAgZOfeSY/H6NRcihIWjz9TjL5cYgQ9j+UQg+NgghPwyzT8D7wPmayP66deuGVatW4fr168jOzsa+ffuQkpKCI0eOoLi4GGfOnMHcuXPh7+9v8nPvvfcePvroI+zevRsymUyk9PePf93vcvX0VXj4eqBFVAuxo9iUUFGBmmf+AMMPB+9sq6qCLnEudIvfhWAwiJjOOnu27xE7gtX+NSsEP+9fY7JNEAR88qIWl4/vECmV9FW0yEVpaBaUVRqL5Sbwpz4IOjkAAgTcjD0JyB3/d5xcU0nrdFT63oJ7QaD5cnO71PhkdoBeVYX8Lmn2DdoEUpqviaQuICAAmzZtwk8//YTp06cjKCgIBQUF+OGHH/Ddd9/h9OnT0Ov1iI2NxQcffIDffvsNM2fOhEwmw3vvvYcFCxagpqYGS5cuhSAIYj+dJnOJYmMwGLB35V680/sdzGs1D/94+B+4/ONlvNv3XWxJ3FI37mraVYR3D8fJbSfxj0H/wOuhr+Mfg/6BC/sviJi++ck0GsjHPw39F5shCAIEvR76d94DVCooFsyHTO4SvxZ2UZr/O8oKc9AiopvJ9qIbGaiuLEFQVG+RkkmfoNDj6rBdKAnLNFtu7i41vw9KQVH78yKkJbKOzqMcv8VvN19u7ik1v436P1S0vC5OYCJyGL169cLPP/+MSZMmoaysDCtWrEBMTAz8/f0xaNAgjBgxAj179oSXlxeeeOIJpKSkwMvLCx9//DEuXbpUV2omTpyIHTuk+cGrS7yD3fzKZqR8kIIBUwcgYWsCuj/VHetfWo9bV24hrHtY3bjstGxcv3AdRzYeQfyCeEz911QAwJrn1qAg27mWq5Q/MQa4lQ/h4I/QJ62EcPMmFG/9DTI3ldjRnEpuxnHI5AoEhEWbbL+ZlQYPnyB4B4SLlMw5WCo3LDUkRZbKDUsNEd2re/fu2LNnD4KDg3HgwAHExsYiMTER586dqze2uroaO3fuxMiRIzF+/HiUl5ejbdu2MBgMeO655yRbagAXKDYnt53E8c3H8eKmFzHklSFo/3B7jJg7Am16t4FBZ0B4N+Mby8JrhSjOLUZAmwDMTJ6J2NGxiImPwZTVU1BdXo1zKaa/GKe2n0KifyJ++u9PYjytBybTuEP+zNPQL10G4cwZKP/375B5Suek6k9TPhU7glVyM47DL7gDlG6mn7jmZaWhZST31jSHhspNLZYakqqGyk0tqZUaqczXRFLl4eGBL7/8Ej4+Pti2bRuGDRuGzMxMq362d+/e8PDwgCAIkMvl6NWrl43T2pbTF5vU5anoNLQT2j3UzmR7YFQgFCoFQrqEADDurQGAxxY+BrnizssS3CkYcqUcpXmldduqy6vx3bLvENwp2A7PwMYqK6GYOAEyPz+xkzRJxq8ZYkewSm7GcRTmXsaqGYEm/5z86n0ERfURO57TuLfc1G1nqSEJu7fc1JJSqQGkM18TSdXixYvRrl07nDlzBs8++yx0Op1VP3f3OTULFiyAXq/H3Llz0bu3dD94VYodwJYKfy9Ezq85GDxzcL3bCrILENwpGEq18SW4+tNVaIO0aNu/rcm40lulMOgM8A25s+xd6vJU9J3UFz9/87Ntn8Btif6JFseoUnY36T4NqXth2LIVspEjoN/xX8jiR97X6hfWZLsfc+bMMXv78uXLrRpjC7M3zrZ6bG7mCcSNewudB04x2f7FX2IR1MQ9NrZ6rZ2JSjEXq147g/CWHQEAa79+E5tff0/kVJa9scS4alSif6LJ145MipkBaeYO0L6FNa//Ak93HwDAXz9+EscTvxU5lZGleRgQd75uKin+fkgxMyDN3I6Y2dfXFy+//DIA4IUXXkB1dbVVP3d3qak9p6ZFixaYN28e5s+fjwkTJpiMF/t5JuUnWTXOqffYFF4rBABog7Qm26srqpF+KL3uMDTgTrG516nkU5DJZej4qPGN0q2sW/j5m58xaPogGya3LcOx49B/9E8oFv0VipdnAIWFEL7/QexYTqfw+mVUlRWgddeR8A4Iq/tHX1OJqvJCtOTCAc3umcHz6koNADw96DVEtooVMRHRg5HLFZgxZlldqQGAlx5fCh9P66/fRETOa+rUqdBoNPj2229x6tQpq36moVIDAMuWLUNNTQ3Gjh2L4GBpHpXk1HtsPAOMFyC6cfkGugzvUrd974d7UXy9GGHd7iwccDXtKvTVetRU1kDlbjyBvrywHHtW7EGvZ3rBL8x4qNZ/F/4Xo/9nNBQq+10MzZqW+voJ6+7LcO4X6P93CRSvz4W8q/ENn/yZp6HfuBmyhwc2eUU0axt0U4VkhZi9ffny5eg/tb/ZMa3/2ro5I9XJtHLnWG7GcSjVHvVWRMu5dAheAeHw9Alq0uPa6rV2FiYLBQz8Dj5X2sMnOxIf/+Uorozejir/m2JHbFTOauP/J+UnmXztyKSYGZBY7ntWP8t+5BsEHR+ISMRi44pfcSV+O/SaClEjWpqrAXHn66aS1O/HbVLMDEgzt6NkvnvvydChQwEA69evt+pnGys1AJCTk4PU1FTEx8dj0KBB2Lp1a91tjv7vppZT77EJaBOAkOgQpC5PxbH/HMPFAxexde5WHP3iKADUFZvCa4UouVECjY8GG6ZvwIV9F3Ay+SQ+jP8Qai81xi0xnrR58fuLqCypREx8jGjP6UEImVeg/9tbUCS8BPlDA+q2y594HCgqktRem+kLp4sdwaLcjOMIiuwDucL084Ocy4ebfBgamVdv9bOOv1q1FDSRw2pgSefSiCuWl4J2QFKYr4mkqvZk/6NHj1oca67U1Kq9H6kuIuDUe2zkcjmeX/s8tr62FdvmbYOHnwf6/qEvBr44ELve2YWQaNOFA/604U9IXZ6KNVPWQOWuQtfHu+KxhY/Bw8e4Wlj6oXRcOXEFb7Z7EwBQUVyB7LRs5GXkYfic4eI8ySaQRbaBKnlr/e3u7lBt3WT3PA9i2HjHvcp2rUHPLWtw+5AXPrFzEufW2JLOtQsKhKc+Bu/sSLTZPc7h99wQATB7nZraBQVafz2urtw4wp4bc6QwXxNJVUiI8b1sRob5RTqsKTUAcPnyZQBAaGho8wa1E6cuNgDQsl1LzPp/s0y2bZyxEUEdguCmcQMAxMTH1O1im7pmaqP39ejLj6L/H+/sTl/7wlrETY5Dz3E9bZCczJnQfQK2/lS/pJFrsXSdGpYbkhwrLr4ptXLD+ZrIdjw9PaHRaCAIQqNjZDIZwsLCrLr45rZt27Br1y6Ul5fbIq7NOfWhaI3JOp1lsnCAtdy17vAN9a37R6lWwsPPA+5adxukJCJzPK+FW3WdmnuXgo5IfRwwuOTURxIQ8HMPq65Tc+9S0CEHh9o5KRE5gvLycty6dcvsGEEQMHXqVAwcONDixTerqqpQWFho9epqjsbp99jcq6q0CnnpeRg4beAD39crO19phkREdD/KWl3FzdgTqPS7ZfE6NbXlJvT74bjVJQ2QG+yUkqhp8rukQXMzCLdiTlu8Tk1tuQk5OBQ5/ffbJyARSZLBYMCxY8fEjmFzLlds1F5qLL/pGOvl0/3rOYiH/7k8GZDb90erhwsKPbIf/caGgYgenKDUI3vI11aP13mUI2vEThsmenCcr4nIXng8BknSgg8XiB2BiIiswPmaiOyFxYYkacmrS8SOQEREVuB8TUT2wmJDknTqe+uurktEROLifE1E9sJiQ0REREREksdiQ0REREREksdiQ5LEi70REUkD52sisheXW+7ZWS3tfVHsCHaVui0Vw8YPE+WxI0evEOVxiYikSMz5msgZJeUnNWl8zmoNAKDV9AqTr50R99iQJK1+Z7XYEYiIyAqcr4nIXlhsiIiIiIhI8lhsiIiIiIhI8lhsSJLmr5gvdgQiIrIC52sishcWG5KkqM5RYkcgIiIrcL4mInthsSFJmjFihtgRiIjICpyvicheWGyIiIiIiEjyeB0bckjXIq6ZvX3k/JEWxxARkW1ZMw9zviYie+EeG5Kk+AXxYkcgIiIrcL4mInthsSEiIiIiIsljsSEiIiIiIsljsSEiIiIiIsljsSEiIiIiIsljsSEiIiIiIsljsSEiIiIiIsljsSEiIiIiIsnjBTpdyMdjP0bpzVIIgoCWbVti0spJcNe6ix2LiB7ApYOXkPx6MnTVOrR7qB0mLJ8AucKxP7NKfiMZZ746g5IbJViWt0zsOFYpyC7AplmbUJRTBLlCjuhR0RjztzFixyIiors49l8/alYvrHsB83+YjzcOvgHfMF/s+3if2JGI6AEYDAZsmb0Fz699HgtPLkRlSSVObD0hdiyLeoztgXn75okdo0nkSjnGLBqD/zn6P5i3fx6uHLuCs7vPih2LiIjuwmLjQjRaDQDjm6Hq8mrIZDKRExHRg8g6lQVtsBbBnYIBAHHPxSFtZ5rIqSyL6hcF75beYsdoEp9gH0T0iAAAKN2UCIkOQUF2gcipiIjobjwUzcV8Nvkz/HbiNwR1DMJTf39K7DhELklXKIO+rP4HC1W/yxv82i3YAJmi/v0UXSuCX6hf3fd+YX4o/L2wecPeJuiA6tz6n4U1llnhJUDpI9gkS1PU5MtgqGjCax1igKXPfMryy3B211nM3D6z2XISEdGDY7FxMS9tegkGgwG73tmFQ/8+hEdnPSp2JCKXY6gC8nep622/e1vt126heviPrm7wfgRBAO5+E27LHqEASk4qUXPdtGE1lBkQEDi2yoZhrKcvlqEgxbrXWtNOB3Wowez96ap0WPv8WgyeMRhBHYKaNywRET0QHormguRyOfpO6otjm4+JHYXIJbkFCXBvp7M8UCZA26+m0T0IvqG+JodDFfxeAN8Q32ZKeU8UGeDTvwbWtCdNBz1ULcTfWwMA6tYGuIXoLQ9UCPDuW2N2iEFvwIbpGxAaG8oPhYiIHBD32NyWdSoLXy/5GpnHMmHQGdCqcys88vIj6DGpiv8VAAAQ50lEQVS2h9jRmkVlcSWqyqvgE+wDADiz80zdcflEZH/avjpUZioAfePHPXl00kMV0HhBiOgRgaKcIlw/fx3BnYJxdONRdH28qy3iAgBULQRoOuhRcbHxPx0yleWCYE8yGaDtX4Ob2+WA0Phr7dVdB4WX+fvakrgFai81nnqHh/ESETkiFhsAl364hE/HfwqlWome43pC7aVG2s40rJu2DoW/FzrFJ3MVxRX4fOrn0FXqABkQ1D4IT7//tNixiFyWwkuAV3cdSk+qGrxdphLg1dt8QZAr5JiYNBFrn18LXbUObQe0Re+JvW0Rt4533xpUZigg6BouCV7ddVB4mL+PLXO24JeUX2DQG7AoehFiR8di/NLxNkhrpAoQ4NFRj/LzDf/Jk3sa4NXN/B60jCMZOPrFUbTq3ApLBy8FAMQ9G4fBCYObPS8REd0fly82ep0eWxK3QCaX4ZVdryAsNgwAMHL+SCwbtgxfvfMVuj3ZDf7h/iInfTB+YX6Yu2dug7dV35BBqRUg5yVtiOzKq5sO5ecVMJTVPyrYq5cOCo3l++gwqAP+cuQvNkjXMIUH4NVDh5Lj9QuZwssAz1jLh9hNXD7RFtHM8upTg4p0BYSa+oVMG6eDzMJfw6h+UUjKT7JROiIiag4uUWzO7j6Lw+sPI+tUFiqKK6BtqUVkXCSGzRmG4uvFuJl5E30n960rNYBxaeThc4Zj05834djmYxg1f5SIz8B2BD1Q8J0blL4CAh5r+ARlIrINmdJ4SFrhPjeT7QqtAZ7RVpyDIxLPWB3Kf1VAX2payLz71VgsCGJRaACvnjqUHDUtZKqWBri3teIcHCIicngO+ieoeeh1emxM2IjTO07DN8QXXR/vCndvd9xIv4G0nWnoM7EP0g+nAwA6Pdqp3s93GmLcln4o3a657an8gvHTYq/BjrGCEZGrcW+nh+qcATU37pQEbb+aBpd3dhQypbHEFKbeWVnMLVgP90jzK4qJzTPmdiErvuu1HlBtcXlnIiKSBqcuNsnzk3F6x2n0n9IfT737FNSed/4IF2QXQOOjwZGNRwAALdq2qPfz2iAt1F5q5KXn2S2zPQl6oPS0EqogPdwsLHFKRLZhPLm9Grf+azwW1C1ED3Vrx//v0T3SAFWw/vbyzwK0/Rtfvc1RyBTG0li7/LOmnQ5uLR1j9TYiInpwsqT8JKec1dMPp2PlYyvRaWgnJGxNgKyRv7ifjPsEF/ZfwJsn3kSLqPrlZlH0IlSVVmHJb0tsljVntRUH0hMRERERuaBW0yusGue017E58MkBAMCYRWMaLTVEREREROQcnPZQtAv7L8A/wh+hMaFmx7lrjYd/VBZXNnh7ZUklND623aNibQttTmW/KFB80A3+o6ugDnP8w16IXIEgwOEP57qXFDMD0s1NtlV7BEWr6RUmXzsyKWYGpJlbipkB6ea+H05ZbMqLylFVWoXw7uEWx9aeW5OXnldvfHFuMapKqxDRM8ImOWuJeSha/m615UFEREQu5O6/y1I5XFyKmQFp5pZiZkC6uQFXPxTt9llDpXmlFoe2HdAWAHB+3/l6t53fe95kDBEREREROSan3GPj4euBwMhA5F7MxYX9F9DxkY4mt+deykVQ+yAAQIfBHRDQJgCnkk9hUMKgumvZVBRX4Lvl30HhpkCfP/SxaV577g4U9MCN/6ih8BIQ8ASXOSUiIqolxUN2pJgZkGZuKWYGpJv7fjhlsQGAxxY+hnXT1mHVM6sQEx+DwKhAlOaVIvN4JoI7BmPahmkAAIVSgT+s+AM+Hf8pVj62Ej3H9YTaS420nWkouFqAJxc/iYCIAJGfTfOpvW6N7+AqlhoiIiIichpOW2x6jO0Bd6079n20DxcPXMS5lHPwDvRGRM8IDJ452GRs+4fb49Xdr+LrJV/j9I7T0Ov0aNW5FcYsGoOe43qK9AxsQxOlB4RqXreGiIiIiJyK0xYbAOg8tDM6D+1s1djWvVpjxpczbJxIfHJ3wDNaL3YMIiIiIqJm5ZyLBxARERERkUthsSEiIiIiIsljsSEiIiIiIsljsSEiIiIiIsljsSEiIiIiIsljsSEiIiIiIsljsSEiIiIiIsljsSEiIiIiIsljsSEiIiIiIsljsSEiIiIiIsljsSEiIiIiIsljsSEiIiIiIsljsSEiIiIiIsljsSEiIiIiIsljsSEiIiIiIsljsSEiIiIiIsljsSEiIiIiIsljsSEiIiIiIsljsSEiIiIiIsljsSEiIiIiIsljsSEiIiIiIsljsSEiIiIiIsljsSEiIiIiIsljsSEiIiIiIslTih2A7Oftbm9D7aGGXGXss899+hxCuoSInIqIiMg5XDp4CcmvJ0NXrUO7h9phwvIJkCsc+zPk5DeScearMyi5UYJlecvEjmOVguwCbJq1CUU5RZAr5IgeFY0xfxsjdiyLPh77MUpvlkIQBLRs2xKTVk6Cu9Zd7FhW+XLelzi87rDD/46w2LiYGdtmwDfUV+wYRERETsVgMGDL7C148YsXEdwpGP9+4d84sfUE+k7qK3Y0s3qM7YERc0dgUfQisaNYTa6UY8yiMYjoEQFdtQ6fjPsEZ3efRezoWLGjmfXCuheg0WoAADve3IF9H+9D/IJ4kVNZln44HdXl1WLHsIpjf4xAREREJAFZp7KgDdYiuFMwACDuuTik7UwTOZVlUf2i4N3SW+wYTeIT7IOIHhEAAKWbEiHRISjILhA5lWW1pcZgMKC6vBoymUzkRJbpqnT46u2v8OTiJ8WOYhXusXExn03+DIIgIHpkNEbNHwWFSiF2JCIiIskrulYEv1C/uu/9wvxQ+HuhiIlcQ1l+Gc7uOouZ22eKHcUqn03+DL+d+A1BHYPw1N+fEjuORd8u/RZxz8XBK9BL7ChWYbFxIa/uehV+YX6oKqvCppc3Ye9HezF8znCxYxEREYlCVyxDwXdu9bbnJasb/Np3SDVUfkKD9yUIAnD3B/AND2sWRQdVqM41PeimsczqcD20fXW2C2Ol6hsyFP1g3WstkwF+o6qg8DB/n7oqHdY+vxaDZwxGUIegZs0LAIIAFO5VQVdo3Wutaa+HV1fzr/VLm16CwWDArnd24dC/D+HRWY82b2gAlVlylBxX1dve4GutFOA/uhry+sNx7dw1/HbyN4x+c3SzZ7QVHormQvzCjJ8kqT3V6PfHfrhy7Iq4gYiIiESk1ApQ+hmguyWH7tadt0T3fq27JYfSW2i01ACAb6ivyeFQBb8XwDfENue0enTUQXdLZjGzLl8Gjw56m2RoKlULAXK1YNVrrWppsFhqDHoDNkzfgNDYUJuUA8BYsDTt9VZl1hfLoGlnXYGUy+XoO6kvjm0+1uyZAUAdZgAMsCq3OtzQYKkBgIyjGbh+4ToWd1+Mt7u9DYPegLe7vY3K4kqb5G4O3GMD4MTWE0g/nI7stGxc++Ua9NV6TPpoEuImx4kdrdlUlVVB0Atw17rDoDcgbWcaQqK5IhoREbk2bV8dKjMVgN7M+Q5yAd79aszeT0SPCBTlFOH6+esI7hSMoxuPouvjXZs5rZGqhQBNBz0qLpp/G+cZo4fS14a7jppAJgO0/Wtwc7scEBp/rWVuArx7m3+tAWBL4haovdR46h3bHs6lDjdAHaZHVbb5Q/e9eurMlrHK4kpUlVfBJ9gHAHBm55m687Gam0xufK3zd6vNjlN4GczuYRr4p4EY+KeBdd+/1uI1LEpz7EUmWGwA7Hp3FwquFsAzwBPaIC0Krjr+CWhNVZJXgs+nfA7BIEDQC2jTpw2Gv8bD0IiIyLUpvAR4ddOh9FQjH1sD8IzVQak1XxDkCjkmJk3E2ufXQletQ9sBbdF7Yu/mjlvHu28NKjMUEHQNlwSZWoBXTysKwpwt+CXlFxj0BiyKXoTY0bEYv3R8c8cFAKgCBHh01KP8fONvP7171UBuYQXkjCMZOPrFUbTq3ApLBy8FAMQ9G4fBCYObMy4AYyHz7l+Dqm2NFzKFtwGeMeb31lQUV+DzqZ9DV6kDZEBQ+yA8/f7TzZ63ljrMAHWEHlVZjRcy7zgdZE7WBGRJ+UmOUeVFdGH/BbRo2wL+4f5ITUrFV4u/cro9NuYIgvE/XCIiIldkqAHytrrDUFb/j6FcI6DFxErI658eIrrS08oGz6UAAO1D1fCMdozD0O6mrwDy/uMOoab+a63wMaDFM1WQOeCJEkU/qlB+ruEW4De8Cu6RBjsnskxXKEPel+oGC5kqSI+AJ6qd7v2fk/W0hp3dfRaH1x9G1qksVBRXQNtSi8i4SAybMwwhXULQ8ZGOYkcUVeFeFZRaAd59xD+5kIiIyN7kKuMekKJ99duLd58ahyw1gHFPUvmvCuhLTZuA0s8Aj86OV2oAQKExHrZVcrR+IdP2r3HIUgMY9yRVXFJAqDZtAm6t9FC3cbxSAwBKXwGeMXqUna3/dl87oMbpSg3g5IsH6HV6rJu2DmueW4NrP19D18e7YnDCYIR2DUXazjQUXSsSO6Loam7KUJmudPLfBCIiIvM07fRQtTR9g6oMMEDjICffN0SmNB5OdC9HLggA4Bmjg0Jr+lq7hemhDnfMggAAcndjuTElOHxB8OpZA5na9OAsTQcd3Fo45wFbTr3HJnl+Mk7vOI3+U/rjqXefgtrzzklUBdkF0PhoREznGEpOqSBzEyweG0pEROTMjCe3V+PWf++c4OHoBQEA3KP0UP2sR02u8VwKdYTeuCqWA5MpAG2/GhSk3H5fJhOg7efYBQEAPKL1KPvFAH2R8ZdC00kPVYBjFwS52rjXsfigcbejTCnAu4/lc6+kymmLTfrhdBz69yF0GtoJE5ZPqHd119qljx1BzmrxC1buOvEzEBEROZL8r8yvKuWIqrIUDvG+okkEGW5us7BigAOqOK9EhZmFEByRoJPhxhcS+/0A0Gp6hVXjHPxziPt34JMDAIAxi8bUKzVERERERORcpFUzm+DC/gvwj/BHaEyo2FEssraFNqeamzLc3O4Or1418O7Fw9CIiIhq1RTIzF6M0xHpy42HeMkltpNJiq+1rlgGhacAmflL2zgcKb7WTeWUxaa8qBxVpVUI7x4udhSriLnLuPSkCqUnG1+7n4iIiIhITK59KNrtMlqaVypuDiIiIiIisgun3GPj4euBwMhA5F7MxYX9F+pdpyb3Ui6C2geJlK4+ex+Klp/ihuprcrScVCm5XdZERERERA2RJeUnOeXBdqd3nMa6aesgV8gREx+DwKhAlOaVIvN4JoI7BmPahml1Yw+vP4yMoxkAgJxfcpCdlo3IuEgERgUCAKLiotB/Sn9Rnkdz47k1REREROSMnHKPDQD0GNsD7lp37PtoHy4euIhzKefgHeiNiJ4RGDxzsMnYjKMZOL75uMm2zKOZyDyaWfe9sxQbXYkMCm8Dr1tDRERERE7FaffYUOMEAxz+gmNERERERE3Bt7cuiKWGiIiIiJwN3+ISEREREZHksdgQEREREZHksdgQEREREZHksdgQEREREZHksdgQEREREZHksdgQEREREZHksdgQEREREZHksdgQEREREZHksdgQEREREZHksdgQEREREZHksdgQEREREZHksdgQEREREZHksdgQEREREZHksdgQEREREZHksdgQEREREZHksdgQEREREZHksdgQEREREZHksdgQEREREZHksdgQEREREZHksdgQEREREZHksdgQEREREZHksdgQEREREZHksdgQEREREZHksdgQEREREZHksdgQEREREZHksdgQEREREZHksdgQEREREZHk/X8KSsMsnlZQNAAAAABJRU5ErkJggg==\n",
+ "text/plain": [
+ "
░ ┌───┐ ░ ┌─┐ \n", + "qa_0: |0>──────░─┤ H ├─░────┤M├───────────────────────────\n", + " ┌───┐ ░ ├───┤ ░ └╥┘┌─┐ \n", + "qa_1: |0>┤ X ├─░─┤ H ├─░─────╫─┤M├────────────────────────\n", + " └───┘ ░ ├───┤ ░ ║ └╥┘┌─┐ \n", + "qa_2: |0>──────░─┤ H ├─░─────╫──╫─┤M├─────────────────────\n", + " ░ ├───┤ ░ ║ ║ └╥┘ ░ ┌─┐ \n", + "qb_0: |0>──────░─┤ H ├─■─────╫──╫──╫──X──░─┤M├────────────\n", + " ┌───┐ ░ ├───┤ │ ║ ║ ║ │ ░ └╥┘┌─┐ \n", + "qb_1: |0>┤ X ├─░─┤ H ├─X─────╫──╫──╫──┼──░──╫─┤M├─────────\n", + " ├───┤ ░ ├───┤ │ ║ ║ ║ │ ░ ║ └╥┘┌─┐ \n", + "qb_2: |0>┤ X ├─░─┤ H ├─X──■──╫──╫──╫──┼──░──╫──╫─┤M├──────\n", + " └───┘ ░ ├───┤ │ ║ ║ ║ │ ░ ║ ║ └╥┘┌─┐ \n", + "qb_3: |0>──────░─┤ H ├────X──╫──╫──╫──■──░──╫──╫──╫─┤M├───\n", + " ┌───┐ ░ ├───┤ │ ║ ║ ║ │ ░ ║ ║ ║ └╥┘┌─┐\n", + "qb_4: |0>┤ X ├─░─┤ H ├────X──╫──╫──╫──X──░──╫──╫──╫──╫─┤M├\n", + " └───┘ ░ └───┘ ║ ║ ║ ░ ║ ║ ║ ║ └╥┘\n", + " c0_0: 0 ════════════════════╩══╬══╬════════╬══╬══╬══╬══╬═\n", + " ║ ║ ║ ║ ║ ║ ║ \n", + " c0_1: 0 ═══════════════════════╩══╬════════╬══╬══╬══╬══╬═\n", + " ║ ║ ║ ║ ║ ║ \n", + " c0_2: 0 ══════════════════════════╩════════╬══╬══╬══╬══╬═\n", + " ║ ║ ║ ║ ║ \n", + " c1_0: 0 ═══════════════════════════════════╩══╬══╬══╬══╬═\n", + " ║ ║ ║ ║ \n", + " c1_1: 0 ══════════════════════════════════════╩══╬══╬══╬═\n", + " ║ ║ ║ \n", + " c1_2: 0 ═════════════════════════════════════════╩══╬══╬═\n", + " ║ ║ \n", + " c1_3: 0 ════════════════════════════════════════════╩══╬═\n", + " ║ \n", + " c1_4: 0 ═══════════════════════════════════════════════╩═\n", + "" + ], + "text/plain": [ + "
"
+ ]
+ },
+ "execution_count": 20,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "# Change the background color in mpl\n",
+ "\n",
+ "style = {'backgroundcolor': 'lightgreen'}\n",
+ "\n",
+ "circuit.draw(output='mpl', style=style)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 21,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:07:34.991487Z",
+ "start_time": "2019-08-21T09:07:34.585528Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "
"
+ ]
+ },
+ "execution_count": 21,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "# Scale the mpl output to 1/2 the normal size\n",
+ "circuit.draw(output='mpl', scale=0.5)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 25,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:07:57.081606Z",
+ "start_time": "2019-08-21T09:07:54.652530Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 25,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "# Scale the latex output to 1/2 the normal size\n",
+ "circuit.draw(output='latex', scale=0.5)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "\n",
+ "## LaTeX Source\n",
+ "\n",
+ "One additional option available with the `latex` output type is to return the raw LaTeX source code instead of rendering an image for it. This enables easy integration with a separate LaTeX document. To use this, set the `output` kwarg to `'latex_source'`. You can also use the `filename` kwarg to write this output directly to a file (and still return the string) instead of returning just a string."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 26,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:07:57.129785Z",
+ "start_time": "2019-08-21T09:07:57.118732Z"
+ }
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "% \\documentclass[preview]{standalone}\n",
+ "% If the image is too large to fit on this documentclass use\n",
+ "\\documentclass[draft]{beamer}\n",
+ "% img_width = 16, img_depth = 28\n",
+ "\\usepackage[size=custom,height=24,width=31,scale=0.7]{beamerposter}\n",
+ "% instead and customize the height and width (in cm) to fit.\n",
+ "% Large images may run out of memory quickly.\n",
+ "% To fix this use the LuaLaTeX compiler, which dynamically\n",
+ "% allocates memory.\n",
+ "\\usepackage[braket, qm]{qcircuit}\n",
+ "\\usepackage{amsmath}\n",
+ "\\pdfmapfile{+sansmathaccent.map}\n",
+ "% \\usepackage[landscape]{geometry}\n",
+ "% Comment out the above line if using the beamer documentclass.\n",
+ "\\begin{document}\n",
+ "\\begin{equation*}\n",
+ " \\Qcircuit @C=1.0em @R=0.0em @!R {\n",
+ "\t \t\\lstick{ qa_0 : \\ket{0} } & \\qw & \\qw \\barrier{7} & \\gate{H} & \\qw \\barrier{2} & \\qw & \\meter & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw\\\\\n",
+ "\t \t\\lstick{ qa_1 : \\ket{0} } & \\gate{X} & \\qw & \\gate{H} & \\qw & \\qw & \\qw & \\meter & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw\\\\\n",
+ "\t \t\\lstick{ qa_2 : \\ket{0} } & \\qw & \\qw & \\gate{H} & \\qw & \\qw & \\qw & \\qw & \\meter & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw\\\\\n",
+ "\t \t\\lstick{ qb_0 : \\ket{0} } & \\qw & \\qw & \\gate{H} & \\ctrl{1} & \\qw & \\qw & \\qw & \\qw & \\qswap \\qwx[4] & \\qw \\barrier[-1.15em]{4} & \\meter & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw\\\\\n",
+ "\t \t\\lstick{ qb_1 : \\ket{0} } & \\gate{X} & \\qw & \\gate{H} & \\qswap & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\meter & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw\\\\\n",
+ "\t \t\\lstick{ qb_2 : \\ket{0} } & \\gate{X} & \\qw & \\gate{H} & \\qswap \\qwx[-1] & \\ctrl{1} & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\meter & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw\\\\\n",
+ "\t \t\\lstick{ qb_3 : \\ket{0} } & \\qw & \\qw & \\gate{H} & \\qw & \\qswap & \\qw & \\qw & \\qw & \\ctrl{1} & \\qw & \\qw & \\qw & \\qw & \\meter & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw\\\\\n",
+ "\t \t\\lstick{ qb_4 : \\ket{0} } & \\gate{X} & \\qw & \\gate{H} & \\qw & \\qswap \\qwx[-1] & \\qw & \\qw & \\qw & \\qswap & \\qw & \\qw & \\qw & \\qw & \\qw & \\meter & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw\\\\\n",
+ "\t \t\\lstick{c0_{0}: 0} & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw \\cwx[-8] & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw\\\\\n",
+ "\t \t\\lstick{c0_{1}: 0} & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw \\cwx[-8] & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw\\\\\n",
+ "\t \t\\lstick{c0_{2}: 0} & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw \\cwx[-8] & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw\\\\\n",
+ "\t \t\\lstick{c1_{0}: 0} & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw \\cwx[-8] & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw\\\\\n",
+ "\t \t\\lstick{c1_{1}: 0} & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw \\cwx[-8] & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw\\\\\n",
+ "\t \t\\lstick{c1_{2}: 0} & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw \\cwx[-8] & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw\\\\\n",
+ "\t \t\\lstick{c1_{3}: 0} & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw \\cwx[-8] & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw\\\\\n",
+ "\t \t\\lstick{c1_{4}: 0} & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw \\cwx[-8] & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw\\\\\n",
+ "\t }\n",
+ "\\end{equation*}\n",
+ "\n",
+ "\\end{document}\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Print the latex source for the visualization\n",
+ "print(circuit.draw(output='latex_source'))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 27,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:07:57.278611Z",
+ "start_time": "2019-08-21T09:07:57.263080Z"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "# Save the latex source to a file\n",
+ "circuit.draw(output='latex_source', filename='/tmp/circuit.tex');"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## circuit_drawer() as function\n",
+ "\n",
+ "If you have an application where you prefer to draw a circuit with a self-contained function instead of as a method of a circuit object, you can directly use the `circuit_drawer()` function, which is part of the public stable interface from `qiskit.tools.visualization`. The function behaves identically to the `circuit.draw()` method, except that it takes in a circuit object as required argument.\n",
+ "\n",
+ "
\n",
+ "Note: In Qiskit Terra <= 0.7, the default behavior for the circuit_drawer() function is to use the latex output backend, and in 0.6.x that includes a fallback to mpl if latex fails for any reason. Starting with release > 0.7, the default changes to the text output.\n",
+ "
"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 28,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:07:57.321520Z",
+ "start_time": "2019-08-21T09:07:57.318296Z"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from qiskit.tools.visualization import circuit_drawer"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 29,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:07:57.752965Z",
+ "start_time": "2019-08-21T09:07:57.353458Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 29,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "circuit_drawer(circuit, output='mpl', plot_barriers=False)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 31,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:08:30.149127Z",
+ "start_time": "2019-08-21T09:08:30.140718Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "
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+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/html": [
+ ""
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "import qiskit.tools.jupyter\n",
+ "%qiskit_version_table\n",
+ "%qiskit_copyright"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "anaconda-cloud": {},
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
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+ "codemirror_mode": {
+ "name": "ipython",
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+ "mimetype": "text/x-python",
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+ "delete_cmd_postfix": "",
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+ "varRefreshCmd": "print(var_dic_list())"
+ },
+ "r": {
+ "delete_cmd_postfix": ") ",
+ "delete_cmd_prefix": "rm(",
+ "library": "var_list.r",
+ "varRefreshCmd": "cat(var_dic_list()) "
+ }
+ },
+ "types_to_exclude": [
+ "module",
+ "function",
+ "builtin_function_or_method",
+ "instance",
+ "_Feature"
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+ "window_display": false
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 1
+}
diff --git a/qiskit/advanced/terra/4_transpiler_passes_and_passmanager.ipynb b/qiskit/advanced/terra/4_transpiler_passes_and_passmanager.ipynb
new file mode 100644
index 000000000..884a2ee2e
--- /dev/null
+++ b/qiskit/advanced/terra/4_transpiler_passes_and_passmanager.ipynb
@@ -0,0 +1,1244 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ " Trusted Notebook\" align=\"middle\">"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Transpiler Passes and Pass Manager"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Introduction"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "A central component of Qiskit Terra is the transpiler, which is designed for modularity and extensibility. The goal is to be able to easily write new circuit transformations (known as transpiler **passes**), and combine them with other existing passes. Which passes are chained together and in which order has a major effect on the final outcome. This pipeline is determined by a **pass manager**, which schedules the passes and also allows passes to communicate with each other by providing a shared space. In this way, the transpiler opens up the door for research into aggressive optimization of quantum circuits.\n",
+ "\n",
+ "In this notebook, we look at the built-in passes, howto use the pass manager, and develop a simple custom transpiler pass. In order to do the latter, we first need to introduce the internal representation of quantum circuits in Qiskit, in the form of a Directed Acyclic Graph, or **DAG**. Then, we illustrate a simple swap mapper pass, which transforms an input circuit to be compatible with a limited-connectivity quantum device."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 73,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:31:52.001010Z",
+ "start_time": "2019-08-21T09:31:51.998537Z"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from qiskit import QuantumCircuit\n",
+ "from qiskit.compiler import transpile\n",
+ "from qiskit.transpiler import PassManager"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:12:12.822442Z",
+ "start_time": "2019-08-21T09:12:12.819902Z"
+ }
+ },
+ "source": [
+ "## PassManager object\n",
+ "\n",
+ "Lets you specify the set of passes you want."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 74,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:31:52.890042Z",
+ "start_time": "2019-08-21T09:31:52.883874Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ ""
+ ]
+ },
+ "execution_count": 74,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "circ = QuantumCircuit(3)\n",
+ "circ.ccx(0, 1, 2)\n",
+ "circ.draw()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:17:14.553611Z",
+ "start_time": "2019-08-21T09:17:14.293017Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "
Version Information
| Qiskit Software | Version |
|---|---|
| Qiskit | None |
| Terra | 0.9.0 |
| Aer | 0.3.0 |
| Ignis | 0.2.0 |
| Aqua | 0.5.6 |
| IBM Q Provider | 0.3.2rc1 |
| System information | |
| Python | 3.7.4 (default, Aug 13 2019, 15:17:50) \n", + "[Clang 4.0.1 (tags/RELEASE_401/final)] |
| OS | Darwin |
| CPUs | 4 |
| Memory (Gb) | 16.0 |
| Wed Aug 21 05:08:30 2019 EDT | |
This code is a part of Qiskit
© Copyright IBM 2017, 2019.
This code is licensed under the Apache License, Version 2.0. You may
obtain a copy of this license in the LICENSE.txt file in the root directory
of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
Any modifications or derivative works of this code must retain this
copyright notice, and modified files need to carry a notice indicating
that they have been altered from the originals.
Trusted Notebook\" align=\"middle\">"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Transpiler Passes and Pass Manager"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Introduction"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "A central component of Qiskit Terra is the transpiler, which is designed for modularity and extensibility. The goal is to be able to easily write new circuit transformations (known as transpiler **passes**), and combine them with other existing passes. Which passes are chained together and in which order has a major effect on the final outcome. This pipeline is determined by a **pass manager**, which schedules the passes and also allows passes to communicate with each other by providing a shared space. In this way, the transpiler opens up the door for research into aggressive optimization of quantum circuits.\n",
+ "\n",
+ "In this notebook, we look at the built-in passes, howto use the pass manager, and develop a simple custom transpiler pass. In order to do the latter, we first need to introduce the internal representation of quantum circuits in Qiskit, in the form of a Directed Acyclic Graph, or **DAG**. Then, we illustrate a simple swap mapper pass, which transforms an input circuit to be compatible with a limited-connectivity quantum device."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 73,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:31:52.001010Z",
+ "start_time": "2019-08-21T09:31:51.998537Z"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from qiskit import QuantumCircuit\n",
+ "from qiskit.compiler import transpile\n",
+ "from qiskit.transpiler import PassManager"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:12:12.822442Z",
+ "start_time": "2019-08-21T09:12:12.819902Z"
+ }
+ },
+ "source": [
+ "## PassManager object\n",
+ "\n",
+ "Lets you specify the set of passes you want."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 74,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:31:52.890042Z",
+ "start_time": "2019-08-21T09:31:52.883874Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n", + "q_0: |0>──■──\n", + " │ \n", + "q_1: |0>──■──\n", + " ┌─┴─┐\n", + "q_2: |0>┤ X ├\n", + " └───┘" + ], + "text/plain": [ + "
"
+ ]
+ },
+ "execution_count": 13,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "from qiskit.transpiler.passes import Unroller\n",
+ "pass_ = Unroller(['u1', 'u2', 'u3', 'cx'])\n",
+ "pm = PassManager(pass_)\n",
+ "new_circ = pm.run(circ)\n",
+ "new_circ.draw(output='mpl')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "All of Qiskit's transpiler passes are accessible from ``qiskit.transpiler.passes``."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:17:14.625245Z",
+ "start_time": "2019-08-21T09:17:14.620368Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "['ApplyLayout',\n",
+ " 'BarrierBeforeFinalMeasurements',\n",
+ " 'BasicSwap',\n",
+ " 'CXCancellation',\n",
+ " 'CXDirection',\n",
+ " 'CheckCXDirection',\n",
+ " 'CheckMap',\n",
+ " 'Collect2qBlocks',\n",
+ " 'CommutationAnalysis',\n",
+ " 'CommutativeCancellation',\n",
+ " 'ConsolidateBlocks',\n",
+ " 'CountOps',\n",
+ " 'CountOpsLongestPath',\n",
+ " 'DAGFixedPoint',\n",
+ " 'DAGLongestPath',\n",
+ " 'Decompose',\n",
+ " 'DenseLayout',\n",
+ " 'Depth',\n",
+ " 'EnlargeWithAncilla',\n",
+ " 'FixedPoint',\n",
+ " 'FullAncillaAllocation',\n",
+ " 'LookaheadSwap',\n",
+ " 'MergeAdjacentBarriers',\n",
+ " 'NoiseAdaptiveLayout',\n",
+ " 'NumTensorFactors',\n",
+ " 'Optimize1qGates',\n",
+ " 'OptimizeSwapBeforeMeasure',\n",
+ " 'RemoveDiagonalGatesBeforeMeasure',\n",
+ " 'RemoveResetInZeroState',\n",
+ " 'ResourceEstimation',\n",
+ " 'SetLayout',\n",
+ " 'Size',\n",
+ " 'StochasticSwap',\n",
+ " 'TrivialLayout',\n",
+ " 'Unroll3qOrMore',\n",
+ " 'Unroller',\n",
+ " 'Width']"
+ ]
+ },
+ "execution_count": 14,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "from qiskit.transpiler import passes\n",
+ "[pass_ for pass_ in dir(passes) if pass_[0].isupper()]"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Different Variants of the Same Pass\n",
+ "\n",
+ "There can be passes that do the same job, but in different ways. For example, the ``TrivialLayout``, ``DenseLayout`` and ``NoiseAdaptiveLayout`` all choose a layout (binding of virtual qubits to physical qubits), but use different algorithms and objectives. Similarly, the ``BasicSwap``, ``LookaheadSwap`` and ``StochasticSwap`` all insert swaps to make the circuit compatible with the coupling map. The modularity of the transpiler allows plug-and-play replacements for each pass.\n",
+ "\n",
+ "Below, we show the swapper passes all applied to the same circuit, to transform it to match a linear chain topology. You can see differences in performance, where the StochasticSwap is clearly the best. However, this can vary depending on the input circuit."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 38,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:21:03.276681Z",
+ "start_time": "2019-08-21T09:21:03.148709Z"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from qiskit.transpiler import CouplingMap, Layout\n",
+ "from qiskit.transpiler.passes import BasicSwap, LookaheadSwap, StochasticSwap\n",
+ "\n",
+ "coupling = [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6]]\n",
+ "\n",
+ "circuit = QuantumCircuit(7)\n",
+ "circuit.h(3)\n",
+ "circuit.cx(0, 6)\n",
+ "circuit.cx(6, 0)\n",
+ "circuit.cx(0, 1)\n",
+ "circuit.cx(3, 1)\n",
+ "circuit.cx(3, 0)\n",
+ "\n",
+ "coupling_map = CouplingMap(couplinglist=coupling)\n",
+ "\n",
+ "bs = BasicSwap(coupling_map=coupling_map)\n",
+ "pass_manager = PassManager(bs)\n",
+ "basic_circ = pass_manager.run(circuit)\n",
+ "\n",
+ "ls = LookaheadSwap(coupling_map=coupling_map)\n",
+ "pass_manager = PassManager(ls)\n",
+ "lookahead_circ = pass_manager.run(circuit)\n",
+ "\n",
+ "ss = StochasticSwap(coupling_map=coupling_map)\n",
+ "pass_manager = PassManager(ss)\n",
+ "stochastic_circ = pass_manager.run(circuit)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 39,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:21:03.596264Z",
+ "start_time": "2019-08-21T09:21:03.359412Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "
"
+ ]
+ },
+ "execution_count": 39,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "circuit.draw(output='mpl')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 40,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:21:03.998074Z",
+ "start_time": "2019-08-21T09:21:03.668091Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "
"
+ ]
+ },
+ "execution_count": 40,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "basic_circ.draw(output='mpl')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 41,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:21:04.351088Z",
+ "start_time": "2019-08-21T09:21:04.066824Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "
"
+ ]
+ },
+ "execution_count": 41,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "lookahead_circ.draw(output='mpl')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 42,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:21:06.302796Z",
+ "start_time": "2019-08-21T09:21:06.028573Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "
"
+ ]
+ },
+ "execution_count": 42,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "stochastic_circ.draw(output='mpl')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Preset Pass Managers\n",
+ "\n",
+ "Qiskit comes with several pre-defined pass managers, corresponding to various levels of optimization achieved through different pipelines of passes. Currently ``optimization_level`` 0 through 3 are supported; the higher the number, the more optimized it is, at the expense of more time. Choosing a good pass manager may take trial and error, as it depends heavily on the circuit being transpiled and the backend being targeted.\n",
+ "\n",
+ "Here we illustrate the different levels by looking at a state synthesis circuit. We initialize four qubits to an arbitrary state, and then try to optimize the circuit that achieves this.\n",
+ "\n",
+ "- ``optimization_level=0``: just maps the circuit to the backend, with no explicit optimization (except whatever optimizations the mapper does).\n",
+ "\n",
+ "- ``optimization_level=1``: maps the circuit, but also does light-weight optimizations by collapsing adjacent gates.\n",
+ "\n",
+ "- ``optimization_level=2``: medium-weight optimization, including a noise-adaptive layout and a gate-cancellation procedure based on gate commutation relationships.\n",
+ "\n",
+ "- ``optimization_level=3``: heavy-weight optimization, which in addition to previous steps, does resynthesis of two-qubit blocks of gates in the circuit."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 53,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:23:59.618721Z",
+ "start_time": "2019-08-21T09:23:59.614152Z"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "import math\n",
+ "from qiskit.test.mock import FakeTokyo\n",
+ "\n",
+ "backend = FakeTokyo() # mimics the tokyo device in terms of coupling map and basis gates\n",
+ "backend.properties = {} # remove fake properties"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 63,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:27:59.652947Z",
+ "start_time": "2019-08-21T09:27:59.379986Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "
"
+ ]
+ },
+ "execution_count": 63,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "qc = QuantumCircuit(10)\n",
+ "\n",
+ "random_state = [\n",
+ " 1 / math.sqrt(4) * complex(0, 1),\n",
+ " 1 / math.sqrt(8) * complex(1, 0),\n",
+ " 0,\n",
+ " 0,\n",
+ " 0,\n",
+ " 0,\n",
+ " 0,\n",
+ " 0,\n",
+ " 1 / math.sqrt(8) * complex(1, 0),\n",
+ " 1 / math.sqrt(8) * complex(0, 1),\n",
+ " 0,\n",
+ " 0,\n",
+ " 0,\n",
+ " 0,\n",
+ " 1 / math.sqrt(4) * complex(1, 0),\n",
+ " 1 / math.sqrt(8) * complex(1, 0)]\n",
+ "\n",
+ "qc.initialize(random_state, range(4))\n",
+ "qc.draw(output='mpl')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now map this to the 20-qubit Tokyo device, with different optimization levels:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 64,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:28:36.204697Z",
+ "start_time": "2019-08-21T09:28:35.799712Z"
+ }
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "gates = OrderedDict([('cx', 86), ('u3', 15), ('u1', 15)])\n",
+ "depth = 102\n"
+ ]
+ }
+ ],
+ "source": [
+ "optimized_0 = transpile(qc, backend=backend, seed_transpiler=11, optimization_level=0)\n",
+ "print('gates = ', optimized_0.count_ops())\n",
+ "print('depth = ', optimized_0.depth())"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 65,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:28:45.778414Z",
+ "start_time": "2019-08-21T09:28:45.133152Z"
+ }
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "gates = OrderedDict([('cx', 80), ('u3', 15), ('u1', 10)])\n",
+ "depth = 91\n"
+ ]
+ }
+ ],
+ "source": [
+ "optimized_1 = transpile(qc, backend=backend, seed_transpiler=11, optimization_level=1)\n",
+ "print('gates = ', optimized_1.count_ops())\n",
+ "print('depth = ', optimized_1.depth())"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 68,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:29:49.201450Z",
+ "start_time": "2019-08-21T09:29:47.926117Z"
+ }
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "gates = OrderedDict([('cx', 74), ('u3', 15), ('u1', 6), ('u2', 4)])\n",
+ "depth = 81\n"
+ ]
+ }
+ ],
+ "source": [
+ "optimized_2 = transpile(qc, backend=backend, seed_transpiler=11, optimization_level=2)\n",
+ "print('gates = ', optimized_2.count_ops())\n",
+ "print('depth = ', optimized_2.depth())"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 72,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:30:16.806739Z",
+ "start_time": "2019-08-21T09:30:14.481010Z"
+ }
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "gates = OrderedDict([('cx', 70), ('u3', 25), ('u2', 18), ('u1', 4)])\n",
+ "depth = 84\n"
+ ]
+ }
+ ],
+ "source": [
+ "optimized_3 = transpile(qc, backend=backend, seed_transpiler=11, optimization_level=3)\n",
+ "print('gates = ', optimized_3.count_ops())\n",
+ "print('depth = ', optimized_3.depth())"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Introducing the DAG"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "In Qiskit, we represent circuits internally using a Directed Acyclic Graph (DAG). The advantage of this representation over a pure list of gates (i.e., *netlist*) is that the flow of information between operations are explicit, making it easier for passes to make transformation decisions without changing the semantics of the circuit.\n",
+ "\n",
+ "Let's start by building a simple circuit, and examining its DAG."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 76,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:32:51.586864Z",
+ "start_time": "2019-08-21T09:32:51.574956Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ ""
+ ]
+ },
+ "execution_count": 76,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit\n",
+ "from qiskit.dagcircuit import DAGCircuit\n",
+ "q = QuantumRegister(3, 'q')\n",
+ "c = ClassicalRegister(3, 'c')\n",
+ "circ = QuantumCircuit(q, c)\n",
+ "circ.h(q[0])\n",
+ "circ.cx(q[0], q[1])\n",
+ "circ.measure(q[0], c[0])\n",
+ "circ.rz(0.5, q[1]).c_if(c, 2)\n",
+ "circ.draw()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "In the DAG, there are three kinds of graph nodes: qubit/clbit input nodes (green), operation nodes (blue), and output nodes (red). Each edge indicates data flow (or dependency) between two nodes. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 77,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:32:53.068504Z",
+ "start_time": "2019-08-21T09:32:52.513464Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 77,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "from qiskit.converters import circuit_to_dag\n",
+ "from qiskit.tools.visualization import dag_drawer\n",
+ "dag = circuit_to_dag(circ)\n",
+ "dag_drawer(dag)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Therefore, writing a transpiler pass means using Qiskit's DAGCircuit API to analyze or transform the circuit. Let's see some examples of this."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**a. Get all op nodes in the DAG:**"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 78,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:32:53.836613Z",
+ "start_time": "2019-08-21T09:32:53.832940Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "[,\n",
+ " ,\n",
+ " ,\n",
+ " ]"
+ ]
+ },
+ "execution_count": 78,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "dag.op_nodes()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Each node is an instance of the ``DAGNode`` class. Let's examine the information stored in the second op node."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 79,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:32:54.600301Z",
+ "start_time": "2019-08-21T09:32:54.594170Z"
+ }
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "node name: rz\n",
+ "node op: \n",
+ "node qargs: [Qubit(QuantumRegister(3, 'q'), 1)]\n",
+ "node cargs: []\n",
+ "node condition: (ClassicalRegister(3, 'c'), 2)\n"
+ ]
+ }
+ ],
+ "source": [
+ "node = dag.op_nodes()[3]\n",
+ "print(\"node name: \", node.name)\n",
+ "print(\"node op: \", node.op)\n",
+ "print(\"node qargs: \", node.qargs)\n",
+ "print(\"node cargs: \", node.cargs)\n",
+ "print(\"node condition: \", node.condition)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**b. Add an operation to the back:**"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 80,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:32:56.030671Z",
+ "start_time": "2019-08-21T09:32:55.489839Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 80,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "from qiskit.extensions.standard import HGate\n",
+ "dag.apply_operation_back(HGate(), qargs=[q[0]])\n",
+ "dag_drawer(dag)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**c. Add an operation to the front:**"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 81,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:32:57.355728Z",
+ "start_time": "2019-08-21T09:32:56.802542Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 81,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "from qiskit.extensions.standard import ToffoliGate\n",
+ "dag.apply_operation_front(ToffoliGate(), qargs=[q[0], q[1], q[2]], cargs=[])\n",
+ "dag_drawer(dag)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**d. Substitute a node with a subcircuit:**"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 82,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:32:58.822354Z",
+ "start_time": "2019-08-21T09:32:58.290414Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 82,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "from qiskit.extensions.standard import CHGate, U2Gate, CnotGate\n",
+ "mini_dag = DAGCircuit()\n",
+ "p = QuantumRegister(2, \"p\")\n",
+ "mini_dag.add_qreg(p)\n",
+ "mini_dag.apply_operation_back(CHGate(), qargs=[p[1], p[0]])\n",
+ "mini_dag.apply_operation_back(U2Gate(0.1, 0.2), qargs=[p[1]])\n",
+ "\n",
+ "# substitute the cx node with the above mini-dag\n",
+ "cx_node = dag.op_nodes(op=CnotGate).pop()\n",
+ "dag.substitute_node_with_dag(node=cx_node, input_dag=mini_dag, wires=[p[0], p[1]])\n",
+ "dag_drawer(dag)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Finally, after all transformations are complete, we can convert back to a regular QuantumCircuit object.\n",
+ "This is what the transpiler does! It takes a circuit, operates on it in DAG form, and outputs a transformed circuit."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 83,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:32:59.570155Z",
+ "start_time": "2019-08-21T09:32:59.560578Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ ""
+ ]
+ },
+ "execution_count": 83,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "from qiskit.converters import dag_to_circuit\n",
+ "circuit = dag_to_circuit(dag)\n",
+ "circuit.draw()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Implementing a BasicMapper Pass"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now that we are familiar with the DAG, let's use it to write a transpiler pass. Here we will implement a basic pass for mapping an arbitrary circuit to a device with limited qubit connectivity. We call this the BasicMapper. This pass is included in Qiskit Terra as well.\n",
+ "\n",
+ "The first thing to do when writing a transpiler pass is to decide whether the pass class derives from a ``TransformationPass`` or ``AnalysisPass``. Transformation passes modify the circuit, while analysis passes only collect information about a circuit (to be used by other passes). Then, the ``run(dag)`` method is implemented, which does the main task. Finally, the pass is registered inside the ``qiskit.transpiler.passes`` module.\n",
+ "\n",
+ "This pass functions as follows: it traverses the DAG layer-by-layer (each layer is a group of operations that does not act on independent qubits, so in theory all operations in a layer can be done independently). For each operation, if it does not already meet the coupling map constraints, the pass identifies a swap path and inserts swaps to bring the two qubits close to each other.\n",
+ "\n",
+ "Follow the comments in the code for more details."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 84,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:33:00.337651Z",
+ "start_time": "2019-08-21T09:33:00.324975Z"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from copy import copy\n",
+ "\n",
+ "from qiskit.transpiler.basepasses import TransformationPass\n",
+ "from qiskit.transpiler import Layout\n",
+ "from qiskit.extensions.standard import SwapGate\n",
+ "\n",
+ "\n",
+ "class BasicSwap(TransformationPass):\n",
+ " \"\"\"\n",
+ " Maps (with minimum effort) a DAGCircuit onto a `coupling_map` adding swap gates.\n",
+ " \"\"\"\n",
+ "\n",
+ " def __init__(self,\n",
+ " coupling_map,\n",
+ " initial_layout=None):\n",
+ " \"\"\"\n",
+ " Maps a DAGCircuit onto a `coupling_map` using swap gates.\n",
+ " Args:\n",
+ " coupling_map (CouplingMap): Directed graph represented a coupling map.\n",
+ " initial_layout (Layout): initial layout of qubits in mapping\n",
+ " \"\"\"\n",
+ " super().__init__()\n",
+ " self.coupling_map = coupling_map\n",
+ " self.initial_layout = initial_layout\n",
+ "\n",
+ " def run(self, dag):\n",
+ " \"\"\"\n",
+ " Runs the BasicSwap pass on `dag`.\n",
+ " Args:\n",
+ " dag (DAGCircuit): DAG to map.\n",
+ "\n",
+ " Returns:\n",
+ " DAGCircuit: A mapped DAG.\n",
+ "\n",
+ " Raises:\n",
+ " TranspilerError: if the coupling map or the layout are not\n",
+ " compatible with the DAG\n",
+ " \"\"\"\n",
+ " new_dag = DAGCircuit()\n",
+ "\n",
+ " if self.initial_layout is None:\n",
+ " if self.property_set[\"layout\"]:\n",
+ " self.initial_layout = self.property_set[\"layout\"]\n",
+ " else:\n",
+ " self.initial_layout = Layout.generate_trivial_layout(*dag.qregs.values())\n",
+ "\n",
+ " if len(dag.qubits()) != len(self.initial_layout):\n",
+ " raise TranspilerError('The layout does not match the amount of qubits in the DAG')\n",
+ "\n",
+ " if len(self.coupling_map.physical_qubits) != len(self.initial_layout):\n",
+ " raise TranspilerError(\n",
+ " \"Mappers require to have the layout to be the same size as the coupling map\")\n",
+ "\n",
+ " current_layout = self.initial_layout.copy()\n",
+ "\n",
+ " for layer in dag.serial_layers():\n",
+ " subdag = layer['graph']\n",
+ "\n",
+ " for gate in subdag.twoQ_gates():\n",
+ " physical_q0 = current_layout[gate.qargs[0]]\n",
+ " physical_q1 = current_layout[gate.qargs[1]]\n",
+ " if self.coupling_map.distance(physical_q0, physical_q1) != 1:\n",
+ " # Insert a new layer with the SWAP(s).\n",
+ " swap_layer = DAGCircuit()\n",
+ "\n",
+ " path = self.coupling_map.shortest_undirected_path(physical_q0, physical_q1)\n",
+ " for swap in range(len(path) - 2):\n",
+ " connected_wire_1 = path[swap]\n",
+ " connected_wire_2 = path[swap + 1]\n",
+ "\n",
+ " qubit_1 = current_layout[connected_wire_1]\n",
+ " qubit_2 = current_layout[connected_wire_2]\n",
+ "\n",
+ " # create qregs\n",
+ " for qreg in current_layout.get_registers():\n",
+ " if qreg not in swap_layer.qregs.values():\n",
+ " swap_layer.add_qreg(qreg)\n",
+ "\n",
+ " # create the swap operation\n",
+ " swap_layer.apply_operation_back(SwapGate(),\n",
+ " qargs=[qubit_1, qubit_2],\n",
+ " cargs=[])\n",
+ "\n",
+ " # layer insertion\n",
+ " edge_map = current_layout.combine_into_edge_map(self.initial_layout)\n",
+ " new_dag.compose_back(swap_layer, edge_map)\n",
+ "\n",
+ " # update current_layout\n",
+ " for swap in range(len(path) - 2):\n",
+ " current_layout.swap(path[swap], path[swap + 1])\n",
+ "\n",
+ " edge_map = current_layout.combine_into_edge_map(self.initial_layout)\n",
+ " new_dag.extend_back(subdag, edge_map)\n",
+ "\n",
+ " return new_dag"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Let's test this pass on a small example circuit."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 85,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:33:01.206220Z",
+ "start_time": "2019-08-21T09:33:01.199378Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 85,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "q = QuantumRegister(7, 'q')\n",
+ "in_circ = QuantumCircuit(q)\n",
+ "in_circ.h(q[0])\n",
+ "in_circ.cx(q[0], q[4])\n",
+ "in_circ.cx(q[2], q[3])\n",
+ "in_circ.cx(q[6], q[1])\n",
+ "in_circ.cx(q[5], q[0])\n",
+ "in_circ.rz(0.1, q[2])\n",
+ "in_circ.cx(q[5], q[0])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now we construct a pass manager that contains our new pass. We pass the example circuit above to this pass manager, and obtain a new, transformed circuit."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 86,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:33:01.972754Z",
+ "start_time": "2019-08-21T09:33:01.958393Z"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from qiskit.transpiler import PassManager\n",
+ "from qiskit.transpiler import CouplingMap\n",
+ "from qiskit import BasicAer\n",
+ "pm = PassManager()\n",
+ "coupling = [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6]]\n",
+ "coupling_map = CouplingMap(couplinglist=coupling)\n",
+ "\n",
+ "pm.append([BasicSwap(coupling_map)])\n",
+ "\n",
+ "out_circ = pm.run(in_circ)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 87,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:33:03.071554Z",
+ "start_time": "2019-08-21T09:33:02.707293Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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GUxCKiIjRFIQiImI0BaGIiBhNQSgiIkZTEIqIiNEUhCIiYjQFoYiIGE1BKCIiRlMQioiI0RSEIiJiNAWhiIgYTUEoIiJGC7e6ABEx1+tlgf+a0xYH/mtKcNOIUEREjKYgFBERoykIRUTEaApCERExmhbLiEjQe2DZtbScPordHobdHsaEMbksnPk81wy7zurSpB/QiFBEgtrh4/s4cqKJn33nT/z3ky388vHdHDv1Z35R9bjVpUk/oSAUkaD26d7NDIwawphrxgMwZNAIkhKyOXryoMWVSX+hIBSRoPbp3s2kjr4Fm82G09nG5k9+R/XWl7nzpoesLk36CeOC0OVyUVZWRnJyMlFRUWRlZVFdXU1qairz5s2zujyfcbnh0yZ46xN4tw4On7S6IpEr8+nezdTWv8tXlg5j+j9E8f9enMV3Z/6C/ImFVpcm/YRxi2UKCwtZu3YtS5cuJScnhw0bNjB79mwOHTrEokWLrC7PJ+oOwMt/hOYW7/YJ18JDuRATZU1dIldiZ2MN//DQr7g946s0n2ji/zx3Fw1//sTqsqQfMWpEuHr1asrLy6msrGTx4sVMnTqVJUuWkJubS1tbGzk5OZw9e5a5c+eSkJDAsGHDuPPOO9mxY4fVpffaroPw7JtwpKXzvh374ZnX4cz5wNclciX2Hd7FydajJI/OBmDEkFHcn/dd/mfjs7hcLgCczjb+7rm7+O6KO5j/4ywWPJ1jZckSgowKwtLSUvLz88nLy/NqT0pKIiIigoyMDNra2khKSmLTpk00Nzczbdo0HnjgAYsq7hu3G35T4/m3u6v9wMHjsGFnoCsTuTKf7t3M4IGxxA0f29F2a/q9HDt5kNr6dwEICwvnR/Pf4HsPrWZUbCL/9I21VpUrIcqYIGxsbKS2tpaZM2d22tfQ0EB6ejqRkZEMGjSI73//+yQkJBAWFsZjjz3GRx99xJkzZyyoum8aj8L+Y12H4MXeUxBKiKjbu5mka2/yahs6yMGEcbfyzraKjramI5/zr7/9W759/3NcM3xMoMuUEGfMNcLGxkYA4uPjvdpbW1uprq5m+vTpXb5uw4YNjBs3jqgo/11Ys9lsPuknedIspj/2co/HHT7pwmYL88nX9Idvv+iJcl+dF+me1ef6tR9d/s+2b834cZftTy14p+PjPQc/pvz3/8jiWS8QEz2sx69p1fdq9bm+UqFaN4Db3dOwwMOYEaHD4QCgrq7Oq3358uU0NTWRnZ3d6TVHjx6luLiYJ598MiA1Xq22s6d6d9y54B/divTW489/kYNH9/DEyq/w3RV3cKr1uNUlSYgxZkSYmJhIZmYmJSUlxMbGkpCQQEVFBVVVVQDk5HhfYG9tbWXGjBk88MADPPSQf+9X6u1fLT05ex6W/gbOtXV/jA3ITR3Iv/noa/rDd1Z5/u2r8yLds/pc++L9CH/1/cY+HW/V92r1ub5SoVp3XxgzIrTb7axZs4b09HSKioooKCjA4XBQXFxMeHg4mZmZHce2tbUxa9YskpOTQ2Y0CBAZAbcn93CQDaaMD0g5IiIhwZgRIUBKSgrr16/3apszZw5paWlER0d3tD366KO4XC5+/vOfB7rEq3bPjXCoBT7a6xn9tf8NZ/vLP2ZPhjEjrKtPRCTYGBWEXampqWHy5Mkdn+/Zs4fy8nKioqIYNuzChfePP/6YMWOCfzVamB0Kboft+zxPlPn0gKf9thS4PQXih1pbn4hIsDFmarQrLS0t1NXVeS2UGTt2LG63m9bWVlpaWjq2UAjBdnY7ZFwHRXddaLv/FoWghJY1b5Wxa98WVlQuZOHP/op/+69vdzpm1RtP8sCya/mP332/o+2pinm0nuvdwjERMDwIY2JicDqdPPbYY1aXIiIXcblcbK9/D7fbzZlzp3hqwTu0tZ3j072bvY6bPvFRvjd7lVdb7oQZrN/yq0CWKyHO6CAUkeC0u2krjmGj+XjP+2QnTwMgO3kaO/Zs9Dpu+OC4Tve3Zd1wB5t2vBqwWiX0KQhFJOjsO7yTuOHjaDlzjIGRQwAYFDWUk61He3xtdGQMJ043+7tE6UcUhCISdNrvWYuJGsbpsycAOHX2RK+eHCPSVwpCEQk6o0emcPBoPRPG5rJl5xsAbNn5OmljJvfwSmg928LggbH+LlH6EQWhiASdxFFZHDq2l+TR2URERLHwZ3+FzWZn/JiJHDlxgFVveB50sW7TL3juv7/Lm39axU9/UwzAh5+tZ+L4rp8dLNIV4+8jFJHgY7fb+cK429m1bwvF9/7Ea1/skHgevmsJAF+e+AhfnviI1/6NH/8335rxVMBqldCnIBSRoDTzjsVX9LqF94feE6HEWgpCEbHMtCvLOhGf0jVCERExmoJQRESMpiAUERGjKQhFRMRoCkIRETGaglBERIymIBQREaMpCEVExGgKQhERMZqCUEREjKYgFBERoykIRUTEaApCERExmoJQRESMpiAUERGjKQhFRMRoCkIRETGaglBERIymIOzHWs5c+Phcm3V1iIgEs3CrCxDfcbmh7gBs3AWfH4LjrRf2Pf4KxA2B8dfCbcngGGxdnSIiwURB2E/sOQwvbYSm413vd7k9+5qOw/odcMv18NUcGBgZ2DpFRIKNgjDEud3w+nao2gruPrxu8+fw6QEonALjHH4rT0Qk6OkaYYhbtw1e7WMItjvRCj97A+oP+7wsEZGQoSAMYdv2wh9qL3/M0w97tu6ca4MX3obTZ31bm4hIqFAQhqhTZ2HNJt/0daIV1n7gm75EREKNcUHocrkoKysjOTmZqKgosrKyqK6uJjU1lXnz5lldXq9t2Aknz/R8XG9t/hwOn/RdfyIiocK4ICwsLGTZsmXMnz+fdevWMWvWLGbPns3u3bvJycmxurxecbk8Qehr7/mhTxGRYGdUEK5evZry8nIqKytZvHgxU6dOZcmSJeTm5tLW1tYRhA8//DBxcXEMHTqUiRMn8v7771tcubeDJ+Doad/3+8l+3/cpIhLsjArC0tJS8vPzycvL82pPSkoiIiKCjIwMAJYsWcLevXs5fvw4TzzxBF/72tesKLdbe4/4p98DJ/QEGhExjzH3ETY2NlJbW8vChQs77WtoaCA9PZ3ISM/d5RMmTADA7XYTERHBgQMHOHPmDFFRUX6pzWaz9en4iV9ZSu79P/Bqu9zK0Mvt/86qCx+73RA3OpljB3f1qR5f+/aLnptB+npepO90rgMnVM91qNYNnt/hvWHMiLCxsRGA+Ph4r/bW1laqq6s7XR98+OGHiY6O5ktf+hILFizwWwheCbs9zG992/zYt4hIMDJmROhweB6fUldXx/Tp0zvaly9fTlNTE9nZ2V7Hr1q1ipUrV1JVVcXJk/5dTtnbv1raVX/S+XaHi0d2F2sfCXa3/1J7dn/CYIszv73Wvp4X6Tud68AJ1XMdqnX3hTFBmJiYSGZmJiUlJcTGxpKQkEBFRQVVVVUAXa4YjYiI4N577yUrK4uJEyeSkpIS6LK7NHq4f/odGo3lISgiEmjGTI3a7XbWrFlDeno6RUVFFBQU4HA4KC4uJjw8nMzMzG5fe+7cOerr6wNXbA9Gx0K4H2Ywx430fZ8iIsHOmBEhQEpKCuvXr/dqmzNnDmlpaURHRwPQ3NzMm2++yT333EN4eDjPP/88+/fv7zR1aqXICMgeC5t2+7bf3CTf9iciEgqMGRF2p6amptO06DPPPMOoUaOIi4vjpZde4tVXX+24xhgspqSCL9dwxQ+FlPiejxMR6W+MGhFeqqWlhbq6OhYsWNDRNmLECN5++20Lq+qd0bGQNx7e+uTq+7IBD04Ge+itjhYRuWpGB2FMTAxOp9PqMq7Y9Cz47M+Xv8G+N6tFv5yl9yQUEXMZPzUaygaEw7fuhOtir7yPu9M9m4iIqRSEIW5QJDx2N9wxvm/XDGOiPO9Of8+NEIIPjBAR8Rmjp0b7iwHh8JUcuPl6ePtT+NMeaOtmxnfYQLgtGW5N9oSoiIjpFIT9yOhYeCgX7rsZ9h2BxqNw+pxnpDh8EIwZAXFDwK55ABGRDgrCfigqAm6I82wiInJ5GhuIiIjRFIQiImI0BaGIiBhNQSgiIkZTEIqIiNEUhCIiYjQFoYiIGE1BKCIiRlMQioiI0RSEIiJiNAWhiIgYTUEoIiJGUxCKiIjRFIQiImI0BaGIiBhNQSgiIkZTEIqIiNEUhCIiYjQFoYiIGE1BKCIiRlMQioiI0cKtLkBEAuvYaag7AHuPXGh7cQOMHg7jRsLYEWCzWVefSKApCEUM0XgE/lALtY3gcnvvq/ncswGMGgp5aTAxEewKRDGAglCkn3O64PcfwevbOwdgV5qOw0sbPcE4ezKMiPF/jSJW0jVCkX6szQn/8Y5nJNibELzYroPw9O+h6Zh/ahMJFgpCkX7spT96pkKv1Mkz8LM34ESr72oSCTYKQpF+6sOGC9f9uvP0w57tck6egVc2gbuPI0qRUGFcELpcLsrKykhOTiYqKoqsrCyqq6tJTU1l3rx5Vpcn4hNtTvj1Zt/1V9sIO/b7rj+RYGJcEBYWFrJs2TLmz5/PunXrmDVrFrNnz2b37t3k5ORYXZ6IT2xt8IzkfOndOt/2JxIsjArC1atXU15eTmVlJYsXL2bq1KksWbKE3Nxc2traOgXhyy+/jM1mo6KiwqKKRa7M5h6mRK/Ejv2+D1eRYGBUEJaWlpKfn09eXp5Xe1JSEhEREWRkZHS0nT59mieffJL09PRAlylyVdxuaGj2Q7/AXj/0K2I1Y4KwsbGR2tpaZs6c2WlfQ0MD6enpREZGdrSVlpYyd+5cHA5HIMsUuWrHW+H0Of/0vV+3Ukg/ZMwN9Y2NnjXk8fHxXu2tra1UV1czffr0jrb6+noqKyupqamhsrLS77XZ9DwrL99+0bM8UeflygwblcI3fvSpV1tPK0O72/+dVd6fL/2nZdxd8Y9XUZ25QvXnOlTrBnD3cqmzMSPC9pFdXZ33Ff/ly5fT1NREdnZ2R9uiRYtYtmwZERERAa1RxBdcbX4aDvq5bxGrGDMiTExMJDMzk5KSEmJjY0lISKCiooKqqiqAjoUyb775JidOnGDGjBkBq623f7WYon0UovNyZZwu+PtXPLdQtLt0ZNeufSTY3f5LPfv0Mm5au+zqCjRUqP5ch2rdfWHMiNBut7NmzRrS09MpKiqioKAAh8NBcXEx4eHhZGZmAvD222+zceNGHA4HDoeD9957j8LCQkpLSy3+DkR6J8wOCcP80/d1sf7pV8RKxowIAVJSUli/fr1X25w5c0hLSyM6OhrwTIs++uijHftnzpxJQUEBDz74YEBrFbkaWWNgj49XeF47XA/glv7JqCDsSk1NDZMnT+74fMiQIQwZMqTj88jISGJjY73aRILdxESo2gptLt/1eVuy3qdQ+idjpka70tLSQl1dnddCmUu99dZb3H///QGsSuTqxUTBNB/eAhs/FCYl+q4/kWBi9IgwJiYGp9PZ84EiIejuL3ieEdp49Or6sdvgoVwID/NNXSLBxuggFOnPwuzw6B3wzGvQ3NL1MT2tFrUBX78VxozwdXUiwcPoqVGR/m7YQPjfd0PiyL6/dlAkPJIH2eN8XpZIUNGIUKSfGzoQ/vZuz7tHvFbb84Oz7TbIHgv35sDgqMDUKGIlBaGIAew2mJIKtybBtr3wSRPsPQJHWjwP6R4YCaNjYZwDbkmEodFWVywSOApCEYOEh3mmOjXdKXKBrhGKiIjRFIQiImI0BaGIiBhNQSgiIkZTEIqIiNEUhCIiYjQFoYiIGE1BKCIiRlMQioiI0RSEIiJiNAWhiIgYTUEoIiJGUxCKiIjRFIQiImI0BaGIiBhNQSgiIkZTEIqIiNEUhCIiYjQFoYiIGE1BKCIiRlMQioiI0RSEIiJiNAWhiIgYTUEoIiJGUxCKiIjRFIQiImI0BaGIiBhNQSgi4mdu94WPXe7ujws2551WVxAYxgWhy+WirKyM5ORkoqKiyMrKorq6mtTUVObNm2d1eSLSj7jc8P4u+OdXL7T94Lfw+nY412ZdXT05cBxWbYDHX7nQVv4u7D1iXU3+FG51AYFWWFjI2rVrWbp0KTk5OWzYsIHZs2dz6NAhFi1aZHV5ItJPuNywegPU1IPtovZjp+7moy4AAAfCSURBVOF/PoTtjfCtuyAyyH4Lf/ZnePZNaHPCxYPXD/fAtr3wyBSYkGBZeX5h1Ihw9erVlJeXU1lZyeLFi5k6dSpLliwhNzeXtrY2cnJyALjjjjuIjo4mJiaGmJgY5s6da23hIhJy/viZJwTBO1DafX4YqrYGsqKenXfCC293DkHwfO5ywcp3ofWcFdX5j1FBWFpaSn5+Pnl5eV7tSUlJREREkJGR0dH2y1/+kpaWFlpaWli5cmWAKxWRUOZ2Q/Un3iPBrmzcBWeDaIr0wz1w6mzXwQ2e9nNtsPnzQFblf8YEYWNjI7W1tcycObPTvoaGBtLT04mMjLSgMrDZbNou2nRetIX6Fh0znAPHuw+Udmfb4PoJt1peb/v2D6W/wOW8fDK7nG0sX/Eby2vtzdZbRgUhQHx8vFd7a2sr1dXVHdOi7YqKirjmmmu455572LlzZ8DqFJHQZ7OH+eVYf+tVLTZbUNXsC8YEocPhAKCurs6rffny5TQ1NZGdne3VVl9fT319PdnZ2cyYMYO2Nv/NX7jdbm0XbTov2kJ9O3XiMMMG9vz/fpgd6ra+Y3m97dvSRXOxh11+9Y7dHkZxwb2W19qbrbeMCcLExEQyMzMpKSnhP//zP3njjTcoKirihRdeAPAaEU6cOJFBgwYxcOBAfvCDH9Dc3NwpQEVEumO3we0plz/GBmSPhUHWXJHp0s3XQ0QPgz27DXJvCEw9gWJMENrtdtasWUN6ejpFRUUUFBTgcDgoLi4mPDyczMzMLl/X17lmERGAvPFw/ciu99mAYYPgb24KaEk9ih4AD07yfHzpb732z792MwztxWg3lATZHSz+lZKSwvr1673a5syZQ1paGtHR0QAcO3aMzZs3M2XKFNxuNyUlJQwbNoyUlB7+vBMRuUhEGBTdCeu2wYZdcPa8pz3MDtnjYMaNMDja0hK7lHM9DIyEdVuh4aIb6OOHQX4GZI2xrjZ/MSoIu1JTU8PkyZM7Pj9//jyPP/44dXV1DBgwgEmTJlFZWUl4uPGnSkT6aEA43JsNX86EfUc9t1XEDQ2u6dCupF3r2Q6egJOtnnrjh0J/nRwz+rd7S0sLdXV1LFiwoKNt5MiRfPDBBxZWJSL9zYDw7qdJg1ncEM/W3xkdhDExMTidhjxVVkREumTMYhkREZGuKAhFRMRoCkIRETGaglBERIymIBQREaMpCEVExGgKQhERMZqCUEREjKYgFBERoykIRUTEaApCERExmoJQRESMpiAUERGjKQhFRMRoCkIRETGaglBERIymIBQREaMpCEVExGgKQhERMZqCUEREjKYgFBERoykIRUTEaApCERExmoJQRESMpiAUERGjKQhFRMRoCkIRETGaglBERIymIBQREaMpCEVExGgKQhERMZqCUEREjGZcELpcLsrKykhOTiYqKoqsrCyqq6tJTU1l3rx5VpdnNJcbPt534fPfbYOjp6yrR0TMEG51AYFWWFjI2rVrWbp0KTk5OWzYsIHZs2dz6NAhFi1aZHV5xmpugefWw59PXGj73Ufw+49gWjpMzwKbzbr6RKT/MmpEuHr1asrLy6msrGTx4sVMnTqVJUuWkJubS1tbGzk5OQC43W6eeOIJRo0axZAhQ5g2bZrFlfdvrefgX1+HQyc673MDr22H17cHvCwRMYRRI8LS0lLy8/PJy8vzak9KSiIiIoKMjAwA/uVf/oUtW7bw4Ycf4nA42Lp1qxXlGmPT7p6nQF/bDlNSITIiMDWJiDmMGRE2NjZSW1vLzJkzO+1raGggPT2dyMhInE4nTz31FD//+c+Ji4sjLCyM7OxsCyo2x6bd0NOs57k2qG0MSDkiYhijghAgPj7eq721tZXq6uqOadGGhgZsNhvPPPMMI0eO5Atf+AK//e1v/VqbzWYzeqv7vAl3L87TN4sXWV6rNm3aQmfrLWOC0OFwAFBXV+fVvnz5cpqamjpGffv372ffvn20trbS2NjIihUr+MY3vkF9fX2gSzZG64lDuF2uno87eTgA1YiIaWxut7s3f4yHPJfLxU033URTUxNlZWUkJCRQUVFBVVUVDQ0NbNy4kUmTJrFlyxays7Npbm4mNjYWgBkzZnDfffcxd+5ca7+JfurNj6Fyy+WPiQiDH9wH0QMCU5OImMOYEaHdbmfNmjWkp6dTVFREQUEBDoeD4uJiwsPDyczMBCA5OZmICK3ICKRJN8DgqMvfHnHHeIWgiPiHMSPC7syZM4etW7eybdu2jraZM2cybtw4SkpK+OCDD8jPz+fDDz9k3Lhx1hXazx04Ds++CcdO/yUQ3XRcN7w9Be67Gey6j1BE/MCo2ye6UlNTw+TJk73aVqxYwdy5cxk+fDgJCQmsXLlSIehn8UPh+zNg2174qBHOO2FEDOQmefaJiPiL0SPClpYWhg4dytNPP81jjz1mdTkiImIBo4NQRETEmMUyIiIiXVEQioiI0RSEIiJiNAWhiIgYTUEoIiJGUxCKiIjRFIQiImI0BaGIiBhNQSgiIkZTEIqIiNEUhCIiYjQFoYiIGE1BKCIiRlMQioiI0RSEIiJiNAWhiIgYTUEoIiJGUxCKiIjRFIQiImI0BaGIiBhNQSgiIkZTEIqIiNEUhCIiYjQFoYiIGE1BKCIiRlMQioiI0RSEIiJitP8PWhBSXXpBhBoAAAAASUVORK5CYII=\n",
+ "text/plain": [
+ "
┌───┐ ┌─┐ \n", + "q_0: |0>┤ H ├──■──┤M├───────────\n", + " └───┘┌─┴─┐└╥┘┌─────────┐\n", + "q_1: |0>─────┤ X ├─╫─┤ Rz(0.5) ├\n", + " └───┘ ║ └────┬────┘\n", + "q_2: |0>───────────╫──────┼─────\n", + " ║ ┌──┴──┐ \n", + " c_0: 0 ═══════════╩═══╡ ╞══\n", + " │ │ \n", + " c_1: 0 ═══════════════╡ = 2 ╞══\n", + " │ │ \n", + " c_2: 0 ═══════════════╡ ╞══\n", + " └─────┘" + ], + "text/plain": [ + "
┌───┐┌───┐┌─┐ ┌───┐ \n", + "q_0: |0>──■──┤ H ├┤ H ├┤M├──────────────────┤ H ├───\n", + " │ └───┘└─┬─┘└╥┘┌─────────────┐┌──┴───┴──┐\n", + "q_1: |0>──■─────────■───╫─┤ U2(0.1,0.2) ├┤ Rz(0.5) ├\n", + " ┌─┴─┐ ║ └─────────────┘└────┬────┘\n", + "q_2: |0>┤ X ├───────────╫─────────────────────┼─────\n", + " └───┘ ║ ┌──┴──┐ \n", + " c_0: 0 ════════════════╩══════════════════╡ ╞══\n", + " │ │ \n", + " c_1: 0 ═══════════════════════════════════╡ = 2 ╞══\n", + " │ │ \n", + " c_2: 0 ═══════════════════════════════════╡ ╞══\n", + " └─────┘" + ], + "text/plain": [ + "
"
+ ]
+ },
+ "execution_count": 87,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "in_circ.draw(output='mpl')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 88,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:33:04.118829Z",
+ "start_time": "2019-08-21T09:33:03.837654Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "
"
+ ]
+ },
+ "execution_count": 88,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "out_circ.draw(output='mpl')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Note that this pass only inserts the swaps necessary to make every two-qubit interaction conform to the device coupling map. It does not, for example, care about the direction of interactions, or the native gate set supported by the device. This is a design philosophy of Qiskit's transpiler: every pass performs a small, well-defined action, and the aggressive circuit optimization is achieved by the pass manager through combining multiple passes."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 90,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:33:51.937152Z",
+ "start_time": "2019-08-21T09:33:51.928935Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "
"
+ ],
+ "text/plain": [
+ ""
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+ "metadata": {},
+ "output_type": "display_data"
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+ {
+ "data": {
+ "text/html": [
+ ""
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "import qiskit.tools.jupyter\n",
+ "%qiskit_version_table\n",
+ "%qiskit_copyright"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.7.4"
+ },
+ "varInspector": {
+ "cols": {
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+ "lenType": 16,
+ "lenVar": 40
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+ "kernels_config": {
+ "python": {
+ "delete_cmd_postfix": "",
+ "delete_cmd_prefix": "del ",
+ "library": "var_list.py",
+ "varRefreshCmd": "print(var_dic_list())"
+ },
+ "r": {
+ "delete_cmd_postfix": ") ",
+ "delete_cmd_prefix": "rm(",
+ "library": "var_list.r",
+ "varRefreshCmd": "cat(var_dic_list()) "
+ }
+ },
+ "types_to_exclude": [
+ "module",
+ "function",
+ "builtin_function_or_method",
+ "instance",
+ "_Feature"
+ ],
+ "window_display": false
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/qiskit/advanced/terra/pulse_schedules.ipynb b/qiskit/advanced/terra/5_pulse_schedules.ipynb
similarity index 95%
rename from qiskit/advanced/terra/pulse_schedules.ipynb
rename to qiskit/advanced/terra/5_pulse_schedules.ipynb
index 2eb04d57e..23e422e26 100644
--- a/qiskit/advanced/terra/pulse_schedules.ipynb
+++ b/qiskit/advanced/terra/5_pulse_schedules.ipynb
@@ -27,7 +27,12 @@
{
"cell_type": "code",
"execution_count": 1,
- "metadata": {},
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:37:07.612595Z",
+ "start_time": "2019-08-21T09:37:07.282572Z"
+ }
+ },
"outputs": [],
"source": [
"%matplotlib inline"
@@ -35,8 +40,13 @@
},
{
"cell_type": "code",
- "execution_count": 63,
- "metadata": {},
+ "execution_count": 2,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:37:09.536033Z",
+ "start_time": "2019-08-21T09:37:07.614539Z"
+ }
+ },
"outputs": [],
"source": [
"import numpy as np\n",
@@ -72,7 +82,12 @@
{
"cell_type": "code",
"execution_count": 3,
- "metadata": {},
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:37:09.542493Z",
+ "start_time": "2019-08-21T09:37:09.538117Z"
+ }
+ },
"outputs": [],
"source": [
"drive_ch0 = DriveChannel(0, buffer=2)\n",
@@ -98,7 +113,12 @@
{
"cell_type": "code",
"execution_count": 4,
- "metadata": {},
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:37:09.547658Z",
+ "start_time": "2019-08-21T09:37:09.544266Z"
+ }
+ },
"outputs": [
{
"name": "stdout",
@@ -124,7 +144,12 @@
{
"cell_type": "code",
"execution_count": 5,
- "metadata": {},
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:37:09.554299Z",
+ "start_time": "2019-08-21T09:37:09.549286Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -144,7 +169,12 @@
{
"cell_type": "code",
"execution_count": 6,
- "metadata": {},
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:37:09.560099Z",
+ "start_time": "2019-08-21T09:37:09.555772Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -164,7 +194,12 @@
{
"cell_type": "code",
"execution_count": 7,
- "metadata": {},
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:37:09.573283Z",
+ "start_time": "2019-08-21T09:37:09.564364Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -201,8 +236,13 @@
},
{
"cell_type": "code",
- "execution_count": 31,
- "metadata": {},
+ "execution_count": 8,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:37:09.581021Z",
+ "start_time": "2019-08-21T09:37:09.576398Z"
+ }
+ },
"outputs": [],
"source": [
"sine_pulse = SamplePulse(np.sin(np.linspace(0,4*np.pi, 20)), name='random_pulse')\n",
@@ -226,8 +266,13 @@
},
{
"cell_type": "code",
- "execution_count": 32,
- "metadata": {},
+ "execution_count": 9,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:37:09.745120Z",
+ "start_time": "2019-08-21T09:37:09.583265Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -236,7 +281,7 @@
"
Version Information
| Qiskit Software | Version |
|---|---|
| Qiskit | None |
| Terra | 0.9.0 |
| Aer | 0.3.0 |
| Ignis | 0.2.0 |
| Aqua | 0.5.6 |
| IBM Q Provider | 0.3.2rc1 |
| System information | |
| Python | 3.7.4 (default, Aug 13 2019, 15:17:50) \n", + "[Clang 4.0.1 (tags/RELEASE_401/final)] |
| OS | Darwin |
| CPUs | 4 |
| Memory (Gb) | 16.0 |
| Wed Aug 21 05:33:51 2019 EDT | |
This code is a part of Qiskit
© Copyright IBM 2017, 2019.
This code is licensed under the Apache License, Version 2.0. You may
obtain a copy of this license in the LICENSE.txt file in the root directory
of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
Any modifications or derivative works of this code must retain this
copyright notice, and modified files need to carry a notice indicating
that they have been altered from the originals.
"
]
},
- "execution_count": 32,
+ "execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
@@ -255,8 +300,13 @@
},
{
"cell_type": "code",
- "execution_count": 33,
- "metadata": {},
+ "execution_count": 10,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:37:09.749162Z",
+ "start_time": "2019-08-21T09:37:09.746579Z"
+ }
+ },
"outputs": [],
"source": [
"acquire = Acquire(100)"
@@ -273,7 +323,12 @@
{
"cell_type": "code",
"execution_count": 11,
- "metadata": {},
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:37:09.753095Z",
+ "start_time": "2019-08-21T09:37:09.750667Z"
+ }
+ },
"outputs": [],
"source": [
"snapshot = Snapshot('test_snapshot', 'state')"
@@ -289,7 +344,12 @@
{
"cell_type": "code",
"execution_count": 12,
- "metadata": {},
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:37:09.763294Z",
+ "start_time": "2019-08-21T09:37:09.754606Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -309,7 +369,12 @@
{
"cell_type": "code",
"execution_count": 13,
- "metadata": {},
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:37:09.772942Z",
+ "start_time": "2019-08-21T09:37:09.767606Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -337,8 +402,13 @@
},
{
"cell_type": "code",
- "execution_count": 48,
- "metadata": {},
+ "execution_count": 14,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:37:09.777333Z",
+ "start_time": "2019-08-21T09:37:09.774445Z"
+ }
+ },
"outputs": [],
"source": [
"sine_instr = sine_pulse.to_instruction(drive_ch0)\n",
@@ -354,8 +424,13 @@
},
{
"cell_type": "code",
- "execution_count": 34,
- "metadata": {},
+ "execution_count": 15,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:37:09.782185Z",
+ "start_time": "2019-08-21T09:37:09.779074Z"
+ }
+ },
"outputs": [],
"source": [
"acquire_instr = acquire([acquire_ch0, acquire_ch1], [memory_slot0, memory_slot1])"
@@ -370,8 +445,13 @@
},
{
"cell_type": "code",
- "execution_count": 38,
- "metadata": {},
+ "execution_count": 16,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:37:09.961068Z",
+ "start_time": "2019-08-21T09:37:09.784515Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -380,7 +460,7 @@
"
"
]
},
- "execution_count": 38,
+ "execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
@@ -391,8 +471,13 @@
},
{
"cell_type": "code",
- "execution_count": 39,
- "metadata": {},
+ "execution_count": 17,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:37:10.200475Z",
+ "start_time": "2019-08-21T09:37:09.962415Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -401,7 +486,7 @@
"
"
]
},
- "execution_count": 39,
+ "execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
@@ -419,8 +504,13 @@
},
{
"cell_type": "code",
- "execution_count": 40,
- "metadata": {},
+ "execution_count": 18,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:37:10.205764Z",
+ "start_time": "2019-08-21T09:37:10.201949Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -428,7 +518,7 @@
"0"
]
},
- "execution_count": 40,
+ "execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
@@ -439,8 +529,13 @@
},
{
"cell_type": "code",
- "execution_count": 41,
- "metadata": {},
+ "execution_count": 19,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:37:10.211036Z",
+ "start_time": "2019-08-21T09:37:10.207283Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -448,7 +543,7 @@
"20"
]
},
- "execution_count": 41,
+ "execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
@@ -466,8 +561,13 @@
},
{
"cell_type": "code",
- "execution_count": 42,
- "metadata": {},
+ "execution_count": 20,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:37:10.216789Z",
+ "start_time": "2019-08-21T09:37:10.212652Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -475,7 +575,7 @@
"False"
]
},
- "execution_count": 42,
+ "execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
@@ -486,8 +586,13 @@
},
{
"cell_type": "code",
- "execution_count": 43,
- "metadata": {},
+ "execution_count": 21,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:37:10.221917Z",
+ "start_time": "2019-08-21T09:37:10.218087Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -495,7 +600,7 @@
"True"
]
},
- "execution_count": 43,
+ "execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
@@ -514,8 +619,13 @@
},
{
"cell_type": "code",
- "execution_count": 44,
- "metadata": {},
+ "execution_count": 22,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:37:10.226387Z",
+ "start_time": "2019-08-21T09:37:10.223619Z"
+ }
+ },
"outputs": [],
"source": [
"sched = Schedule(name='test_schedule')"
@@ -523,8 +633,13 @@
},
{
"cell_type": "code",
- "execution_count": 52,
- "metadata": {},
+ "execution_count": 23,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:37:10.241491Z",
+ "start_time": "2019-08-21T09:37:10.235778Z"
+ }
+ },
"outputs": [],
"source": [
"pulse_sched = Schedule(sine_instr, name='sine_schedule')\n",
@@ -546,8 +661,13 @@
},
{
"cell_type": "code",
- "execution_count": 53,
- "metadata": {},
+ "execution_count": 24,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:37:10.247069Z",
+ "start_time": "2019-08-21T09:37:10.244426Z"
+ }
+ },
"outputs": [],
"source": [
"union_sched = pulse_sched.union(acquire_sched)"
@@ -555,8 +675,13 @@
},
{
"cell_type": "code",
- "execution_count": 54,
- "metadata": {},
+ "execution_count": 25,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:37:10.446395Z",
+ "start_time": "2019-08-21T09:37:10.251460Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -565,7 +690,7 @@
"
"
]
},
- "execution_count": 54,
+ "execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
@@ -576,8 +701,13 @@
},
{
"cell_type": "code",
- "execution_count": 55,
- "metadata": {},
+ "execution_count": 26,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:37:10.605486Z",
+ "start_time": "2019-08-21T09:37:10.447772Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -586,7 +716,7 @@
"
"
]
},
- "execution_count": 55,
+ "execution_count": 26,
"metadata": {},
"output_type": "execute_result"
}
@@ -598,8 +728,13 @@
},
{
"cell_type": "code",
- "execution_count": 56,
- "metadata": {},
+ "execution_count": 27,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:37:10.788721Z",
+ "start_time": "2019-08-21T09:37:10.607328Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -608,7 +743,7 @@
"
"
]
},
- "execution_count": 56,
+ "execution_count": 27,
"metadata": {},
"output_type": "execute_result"
}
@@ -626,8 +761,13 @@
},
{
"cell_type": "code",
- "execution_count": 57,
- "metadata": {},
+ "execution_count": 28,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:37:10.963001Z",
+ "start_time": "2019-08-21T09:37:10.790141Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -636,7 +776,7 @@
"
"
]
},
- "execution_count": 57,
+ "execution_count": 28,
"metadata": {},
"output_type": "execute_result"
}
@@ -665,8 +805,13 @@
},
{
"cell_type": "code",
- "execution_count": 58,
- "metadata": {},
+ "execution_count": 29,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:37:11.135023Z",
+ "start_time": "2019-08-21T09:37:10.964433Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -675,7 +820,7 @@
"
"
]
},
- "execution_count": 58,
+ "execution_count": 29,
"metadata": {},
"output_type": "execute_result"
}
@@ -689,8 +834,13 @@
},
{
"cell_type": "code",
- "execution_count": 59,
- "metadata": {},
+ "execution_count": 30,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:37:11.310890Z",
+ "start_time": "2019-08-21T09:37:11.137068Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -699,7 +849,7 @@
"
"
]
},
- "execution_count": 59,
+ "execution_count": 30,
"metadata": {},
"output_type": "execute_result"
}
@@ -811,6 +961,55 @@
"result.get_counts(schedule)\n",
"```"
]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 32,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:37:30.807701Z",
+ "start_time": "2019-08-21T09:37:30.798864Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "
"
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/html": [
+ ""
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "import qiskit.tools.jupyter\n",
+ "%qiskit_version_table\n",
+ "%qiskit_copyright"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
}
],
"metadata": {
@@ -829,7 +1028,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
- "version": "3.7.3"
+ "version": "3.7.4"
},
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diff --git a/qiskit/advanced/terra/creating_a_provider.ipynb b/qiskit/advanced/terra/6_creating_a_provider.ipynb
similarity index 81%
rename from qiskit/advanced/terra/creating_a_provider.ipynb
rename to qiskit/advanced/terra/6_creating_a_provider.ipynb
index f821f4668..7bae75532 100644
--- a/qiskit/advanced/terra/creating_a_provider.ipynb
+++ b/qiskit/advanced/terra/6_creating_a_provider.ipynb
@@ -11,13 +11,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "# _*Creating a new provider*_ \n",
- "\n",
- "The latest version of this notebook is available on https://github.com/qiskit/qiskit-tutorial.\n",
- "\n",
- "***\n",
- "### Contributors\n",
- "Yael Ben-Haim"
+ "# Creating a new provider\n"
]
},
{
@@ -37,7 +31,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "# An external simulator for this tutorial\n",
+ "## An external simulator for this tutorial\n",
"\n",
"We shall construct a very simple simulator. The simulator accepts only a single quantum circuit, where all the gates are Hadamard gates, and all qubits are measured at the end. The input format is a list of qubits on which Hadamard gates are applied. The simulator returns the counts of each basis state, in the form of a list, where the basis states are assumed to be ordered lexicographically."
]
@@ -45,7 +39,12 @@
{
"cell_type": "code",
"execution_count": 1,
- "metadata": {},
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:35:01.054811Z",
+ "start_time": "2019-08-21T09:35:01.041684Z"
+ }
+ },
"outputs": [
{
"data": {
@@ -117,7 +116,12 @@
{
"cell_type": "code",
"execution_count": 2,
- "metadata": {},
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:35:03.510628Z",
+ "start_time": "2019-08-21T09:35:01.072835Z"
+ }
+ },
"outputs": [],
"source": [
"from qiskit.providers import BaseJob\n",
@@ -149,7 +153,12 @@
{
"cell_type": "code",
"execution_count": 3,
- "metadata": {},
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:35:03.547831Z",
+ "start_time": "2019-08-21T09:35:03.534819Z"
+ }
+ },
"outputs": [],
"source": [
"from qiskit.providers import BaseBackend\n",
@@ -264,6 +273,10 @@
"cell_type": "code",
"execution_count": 4,
"metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:35:03.573285Z",
+ "start_time": "2019-08-21T09:35:03.559936Z"
+ },
"scrolled": true
},
"outputs": [
@@ -271,7 +284,7 @@
"name": "stdout",
"output_type": "stream",
"text": [
- "{'0110': 256, '0000': 256, '0010': 256, '0100': 256}\n"
+ "{'0010': 256, '0110': 256, '0000': 256, '0100': 256}\n"
]
}
],
@@ -311,7 +324,12 @@
{
"cell_type": "code",
"execution_count": 5,
- "metadata": {},
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:35:03.601247Z",
+ "start_time": "2019-08-21T09:35:03.591084Z"
+ }
+ },
"outputs": [],
"source": [
"from qiskit.providers import BaseProvider\n",
@@ -345,16 +363,21 @@
{
"cell_type": "code",
"execution_count": 6,
- "metadata": {},
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:35:04.061510Z",
+ "start_time": "2019-08-21T09:35:04.030137Z"
+ }
+ },
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Hadamard simulator:\n",
- "{'0110': 256, '0000': 256, '0010': 256, '0100': 256}\n",
+ "{'0010': 256, '0110': 256, '0000': 256, '0100': 256}\n",
"Aer simulator:\n",
- "{'0110': 263, '0000': 247, '0010': 270, '0100': 244}\n"
+ "{'0010': 274, '0110': 262, '0000': 261, '0100': 227}\n"
]
}
],
@@ -378,6 +401,48 @@
"print(aer_result.get_counts(qc))"
]
},
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T09:35:24.611599Z",
+ "start_time": "2019-08-21T09:35:24.600854Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "
"
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/html": [
+ ""
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "import qiskit.tools.jupyter\n",
+ "%qiskit_version_table\n",
+ "%qiskit_copyright"
+ ]
+ },
{
"cell_type": "code",
"execution_count": null,
diff --git a/qiskit/advanced/terra/advanced_circuits.ipynb b/qiskit/advanced/terra/advanced_circuits.ipynb
deleted file mode 100644
index 3e57247ec..000000000
--- a/qiskit/advanced/terra/advanced_circuits.ipynb
+++ /dev/null
@@ -1,1046 +0,0 @@
-{
- "cells": [
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- " Trusted Notebook\" align=\"middle\">"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "# Terra 0.8 - Circuit API Updates"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "In this tutorial, we'll introduce three new components of the Terra circuit-building API added in the Terra 0.8 release. Their purpose is to facilitate circuit construction, reduce boilerplate, and aid reuse through composition and parameterization. These three new components are:\n",
- "\n",
- " 1. [Optional register declarations](#1.-Optional-register-declarations)\n",
- " 2. [Portable `Instruction`s and `CompositeGate` replacement](#2.-Portable-Instructions-and-CompositeGate-replacement)\n",
- " 3. [Parameterized Circuit](#3.-Parameterized-circuits)\n"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 1,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2019-05-08T15:55:44.572329Z",
- "start_time": "2019-05-08T15:55:41.364548Z"
- }
- },
- "outputs": [],
- "source": [
- "from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## 1. Optional registers\n",
- "\n",
- "For circuits that require only a single register, register declarations can amount to unneeded overhead.\n",
- "Terra 0.8 adds more concise syntax to create and build circuits without explicit register declaration."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### Registerless `QuantumCircuit` declaration"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "An alternate constructor has been added to `QuantumCircuit` that accepts one or two integers: the number of qubits (required), and the number of classical bits (optional)."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 2,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2019-05-08T15:55:44.578631Z",
- "start_time": "2019-05-08T15:55:44.574825Z"
- }
- },
- "outputs": [],
- "source": [
- "qc = QuantumCircuit(3, 2)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "This will create a quantum circuit equivalent to the following (still valid) circuit declaration:"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 3,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2019-05-08T15:55:44.585018Z",
- "start_time": "2019-05-08T15:55:44.581251Z"
- }
- },
- "outputs": [],
- "source": [
- "qr = QuantumRegister(3, name='q')\n",
- "cr = ClassicalRegister(2, name='c')\n",
- "qc = QuantumCircuit(qr, cr)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Registers are created automatically and can be accessed through the circuit as needed."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 4,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2019-05-08T15:55:44.592407Z",
- "start_time": "2019-05-08T15:55:44.587535Z"
- }
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "[QuantumRegister(3, 'q')]\n",
- "[ClassicalRegister(2, 'c')]\n"
- ]
- }
- ],
- "source": [
- "print(qc.qregs)\n",
- "print(qc.cregs)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### Quantum/classical bit index-based addressing"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "In the spirit of register-less circuits, qubits and classical bits (clbits) can now be addressed directly by index, without a need for referencing a register.\n",
- "In the following example, `bell.h(0)` attaches a Hadamard gate to the first quantum bit."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 5,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2019-05-08T15:55:45.283289Z",
- "start_time": "2019-05-08T15:55:44.595092Z"
- },
- "scrolled": true
- },
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 5,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "bell = QuantumCircuit(2,2)\n",
- "bell.h(0)\n",
- "bell.cx(0, 1)\n",
- "bell.measure([0,1], [0,1])\n",
- "\n",
- "bell.draw()"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "The gate's argument types will determine if an index references a qubit or a clbit (e.g. `cx` expects `(qubit, qubit)`; `measure` expects `(qubit, clbit)`).\n",
- "This syntax works with both forms of `QuantumCircuit` construction, and users can switch between register-based and index-based commands as convenient."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "In circuits with multiple registers, index ordering will be set by the order in which registers were added to the circuit, and can be verified by inspecting the circuit's `qubits` and `clbits` properties."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 6,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2019-05-08T15:55:45.303630Z",
- "start_time": "2019-05-08T15:55:45.286775Z"
- }
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Qubit ordering: [(QuantumRegister(1, 'q2'), 0), (QuantumRegister(1, 'q1'), 0)]\n",
- "Classical bit ordering: [(ClassicalRegister(2, 'c'), 0), (ClassicalRegister(2, 'c'), 1)]\n"
- ]
- },
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 6,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "qr1 = QuantumRegister(1, 'q1')\n",
- "qr2 = QuantumRegister(1, 'q2')\n",
- "cr = ClassicalRegister(2, 'c')\n",
- "circuit = QuantumCircuit(qr2, qr1, cr)\n",
- "\n",
- "print('Qubit ordering:', circuit.qubits)\n",
- "print('Classical bit ordering:', circuit.clbits)\n",
- "\n",
- "circuit.h([1,0])\n",
- "circuit.measure(1,[0,1])\n",
- "circuit.draw()"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## 2. Portable `Instruction`s and `CompositeGate` replacement"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "slideshow": {
- "slide_type": "slide"
- }
- },
- "source": [
- "Starting with Terra 0.8, `Instruction` instances have become more portable and serve as the basis for composing re-usable circuit components through the new `append` method on `QuantumCircuit`s."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "ExecuteTime": {
- "end_time": "2019-04-24T04:16:16.208643Z",
- "start_time": "2019-04-24T04:16:16.205855Z"
- }
- },
- "source": [
- "### Opaque gates"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "The `Gate` and `Instruction` constructors have been updated to accept an integer number of qubits (`num_qubits`) and an integer number of classical bits (`num_cbits`), which define the gate's quantum and classical width."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 7,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2019-05-08T15:55:45.314382Z",
- "start_time": "2019-05-08T15:55:45.306533Z"
- }
- },
- "outputs": [],
- "source": [
- "from qiskit.circuit import Gate\n",
- "\n",
- "my_gate = Gate(name='my_gate', num_qubits=2, params=[])"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "ExecuteTime": {
- "end_time": "2019-04-24T14:15:12.883919Z",
- "start_time": "2019-04-24T14:15:12.878579Z"
- }
- },
- "source": [
- "An `append(instruction, qargs, cargs)` method has been added to the `QuantumCircuit` class, which takes an anonymous `Instruction` instance and attaches it to the circuit at the specified `qargs` and `cargs`."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 8,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2019-05-08T15:55:45.348586Z",
- "start_time": "2019-05-08T15:55:45.322645Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 8,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "qr = QuantumRegister(3, 'q')\n",
- "circ = QuantumCircuit(qr)\n",
- "circ.append(my_gate, [qr[0], qr[1]])\n",
- "circ.append(my_gate, [qr[1], qr[2]])\n",
- "\n",
- "circ.draw()"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### Composite Gates"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Composite gates and complex circuit components can now be constructed and managed as independent `QuantumCircuit`s and, through the `to_instruction` method, converted to `Instruction`s to be appended to a target circuit at a given location."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 9,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2019-05-08T15:55:45.380805Z",
- "start_time": "2019-05-08T15:55:45.352726Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 9,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "# Build a sub-circuit\n",
- "sub_q = QuantumRegister(2)\n",
- "sub_circ = QuantumCircuit(sub_q, name='sub_circ')\n",
- "sub_circ.h(sub_q[0])\n",
- "sub_circ.crz(1, sub_q[0], sub_q[1])\n",
- "sub_circ.barrier()\n",
- "sub_circ.iden(sub_q[1])\n",
- "sub_circ.u3(1, 2, -2, sub_q[0])\n",
- "\n",
- "# Convert to a gate and stick it into an arbitrary place in the bigger circuit\n",
- "sub_inst = sub_circ.to_instruction()\n",
- "\n",
- "q = QuantumRegister(3, 'q')\n",
- "circ = QuantumCircuit(q)\n",
- "circ.h(qr[0])\n",
- "circ.cx(qr[0], qr[1])\n",
- "circ.cx(qr[1], qr[2])\n",
- "circ.append(sub_inst, [q[1], q[2]])\n",
- "\n",
- "circ.draw()\n"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Circuits are not immediately decomposed upon conversion `to_instruction` to allow circuit design at higher levels of abstraction.\n",
- "When desired, or before compilation, sub-circuits will be decomposed via the `decompose` method."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 10,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2019-05-08T15:55:45.422613Z",
- "start_time": "2019-05-08T15:55:45.397190Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 10,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "decomposed_circ = circ.decompose() # Does not modify original circuit\n",
- "decomposed_circ.draw()"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## 3. Parameterized circuits"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Parameterization is a common feature of many quantum algorithms, as well as a standard building block for constructing libraries of standard gates and subcircuits.\n",
- "\n",
- "Terra 0.8 introduces a `Parameter` class that can be used to specify a placeholder wherever a numeric parameter can be used."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "In the following example, we want to quickly construct a series of experiments that vary the angle of a global $R_z$ rotation over a set of entangled qubits."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 11,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2019-05-08T15:55:45.463002Z",
- "start_time": "2019-05-08T15:55:45.427353Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 11,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "from qiskit.circuit import Parameter\n",
- "\n",
- "theta = Parameter('θ')\n",
- "\n",
- "n = 5\n",
- "\n",
- "qc = QuantumCircuit(5, 1)\n",
- "\n",
- "qc.h(0)\n",
- "for i in range(n-1):\n",
- " qc.cx(i, i+1)\n",
- "\n",
- "qc.barrier()\n",
- "qc.rz(theta, range(5))\n",
- "qc.barrier()\n",
- "\n",
- "for i in reversed(range(n-1)):\n",
- " qc.cx(i, i+1)\n",
- "qc.h(0)\n",
- "qc.measure(0, 0)\n",
- "\n",
- "qc.draw()"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "ExecuteTime": {
- "end_time": "2019-05-07T13:51:25.524355Z",
- "start_time": "2019-05-07T13:51:25.518233Z"
- }
- },
- "source": [
- "We can inspect the circuit's parameters"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 12,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2019-05-08T15:55:45.512819Z",
- "start_time": "2019-05-08T15:55:45.506563Z"
- }
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "{Parameter(θ)}\n"
- ]
- }
- ],
- "source": [
- "print(qc.parameters)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### Binding parameters to values"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "All circuit parameters must be bound before sending the circuit to a backend. This can be done in one of two ways:\n",
- "- The `bind_parameters` method accepts a dictionary mapping `Parameter`s to values, and returns a new circuit with each parameter replaced by its corresponding value. Partial binding is supported, in which case the returned circuit will be parameterized by any `Parameter`s that were not mapped to a value."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 13,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2019-05-08T15:55:45.854582Z",
- "start_time": "2019-05-08T15:55:45.516344Z"
- }
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- " ┌───┐ ░ ┌────────────┐ ░ ┌───┐┌─┐\n",
- "q_0: |0>┤ H ├──■──────────────────░─┤ Rz(6.2832) ├─░──────────────────■──┤ H ├┤M├\n",
- " └───┘┌─┴─┐ ░ ├────────────┤ ░ ┌─┴─┐└───┘└╥┘\n",
- "q_1: |0>─────┤ X ├──■─────────────░─┤ Rz(6.2832) ├─░─────────────■──┤ X ├──────╫─\n",
- " └───┘┌─┴─┐ ░ ├────────────┤ ░ ┌─┴─┐└───┘ ║ \n",
- "q_2: |0>──────────┤ X ├──■────────░─┤ Rz(6.2832) ├─░────────■──┤ X ├───────────╫─\n",
- " └───┘┌─┴─┐ ░ ├────────────┤ ░ ┌─┴─┐└───┘ ║ \n",
- "q_3: |0>───────────────┤ X ├──■───░─┤ Rz(6.2832) ├─░───■──┤ X ├────────────────╫─\n",
- " └───┘┌─┴─┐ ░ ├────────────┤ ░ ┌─┴─┐└───┘ ║ \n",
- "q_4: |0>────────────────────┤ X ├─░─┤ Rz(6.2832) ├─░─┤ X ├─────────────────────╫─\n",
- " └───┘ ░ └────────────┘ ░ └───┘ ║ \n",
- " c_0: 0 ═══════════════════════════════════════════════════════════════════════╩═\n",
- " \n",
- "set()\n"
- ]
- }
- ],
- "source": [
- "import numpy as np\n",
- "\n",
- "theta_range = np.linspace(0, 2 * np.pi, 128)\n",
- "\n",
- "circuits = [qc.bind_parameters({theta: theta_val})\n",
- " for theta_val in theta_range]\n",
- "\n",
- "print(circuits[-1].draw(line_length=120))\n",
- "print(circuits[-1].parameters)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "- `qiskit.execute` now accepts a `parameter_binds` keyword argument which, when specified as a list of dictionaries mapping `Parameter`s to values, will bind and execute a circuit on the backend for every mapping dictionary in the list."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 14,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2019-05-08T15:55:47.921854Z",
- "start_time": "2019-05-08T15:55:45.857178Z"
- }
- },
- "outputs": [],
- "source": [
- "from qiskit import BasicAer, execute\n",
- "\n",
- "job = execute(qc,\n",
- " backend=BasicAer.get_backend('qasm_simulator'),\n",
- " parameter_binds=[{theta: theta_val} for theta_val in theta_range])\n",
- "\n",
- "# Note: Bind labels are not presrved in executed experiments.\n",
- "counts = [job.result().get_counts(i) for i in range(len(job.result().results))]\n"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "In the example circuit, we apply a global $R_z(\\theta)$ rotation on a five-qubit entangled state, and so expect to see oscillation in qubit-0 at $5\\theta$."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 15,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2019-05-08T15:55:48.432562Z",
- "start_time": "2019-05-08T15:55:47.923519Z"
- }
- },
- "outputs": [
- {
- "data": {
- "image/png": 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\n",
- "text/plain": [
- "
Version Information
| Qiskit Software | Version |
|---|---|
| Qiskit | None |
| Terra | 0.9.0 |
| Aer | 0.3.0 |
| Ignis | 0.2.0 |
| Aqua | 0.5.6 |
| IBM Q Provider | 0.3.2rc1 |
| System information | |
| Python | 3.7.4 (default, Aug 13 2019, 15:17:50) \n", + "[Clang 4.0.1 (tags/RELEASE_401/final)] |
| OS | Darwin |
| CPUs | 4 |
| Memory (Gb) | 16.0 |
| Wed Aug 21 05:37:30 2019 EDT | |
This code is a part of Qiskit
© Copyright IBM 2017, 2019.
This code is licensed under the Apache License, Version 2.0. You may
obtain a copy of this license in the LICENSE.txt file in the root directory
of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
Any modifications or derivative works of this code must retain this
copyright notice, and modified files need to carry a notice indicating
that they have been altered from the originals.
Version Information
| Qiskit Software | Version |
|---|---|
| Qiskit | None |
| Terra | 0.9.0 |
| Aer | 0.3.0 |
| Ignis | 0.2.0 |
| Aqua | 0.5.6 |
| IBM Q Provider | 0.3.2rc1 |
| System information | |
| Python | 3.7.4 (default, Aug 13 2019, 15:17:50) \n", + "[Clang 4.0.1 (tags/RELEASE_401/final)] |
| OS | Darwin |
| CPUs | 4 |
| Memory (Gb) | 16.0 |
| Wed Aug 21 05:35:24 2019 EDT | |
This code is a part of Qiskit
© Copyright IBM 2017, 2019.
This code is licensed under the Apache License, Version 2.0. You may
obtain a copy of this license in the LICENSE.txt file in the root directory
of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
Any modifications or derivative works of this code must retain this
copyright notice, and modified files need to carry a notice indicating
that they have been altered from the originals.
Trusted Notebook\" align=\"middle\">"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "# Terra 0.8 - Circuit API Updates"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "In this tutorial, we'll introduce three new components of the Terra circuit-building API added in the Terra 0.8 release. Their purpose is to facilitate circuit construction, reduce boilerplate, and aid reuse through composition and parameterization. These three new components are:\n",
- "\n",
- " 1. [Optional register declarations](#1.-Optional-register-declarations)\n",
- " 2. [Portable `Instruction`s and `CompositeGate` replacement](#2.-Portable-Instructions-and-CompositeGate-replacement)\n",
- " 3. [Parameterized Circuit](#3.-Parameterized-circuits)\n"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 1,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2019-05-08T15:55:44.572329Z",
- "start_time": "2019-05-08T15:55:41.364548Z"
- }
- },
- "outputs": [],
- "source": [
- "from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## 1. Optional registers\n",
- "\n",
- "For circuits that require only a single register, register declarations can amount to unneeded overhead.\n",
- "Terra 0.8 adds more concise syntax to create and build circuits without explicit register declaration."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### Registerless `QuantumCircuit` declaration"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "An alternate constructor has been added to `QuantumCircuit` that accepts one or two integers: the number of qubits (required), and the number of classical bits (optional)."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 2,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2019-05-08T15:55:44.578631Z",
- "start_time": "2019-05-08T15:55:44.574825Z"
- }
- },
- "outputs": [],
- "source": [
- "qc = QuantumCircuit(3, 2)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "This will create a quantum circuit equivalent to the following (still valid) circuit declaration:"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 3,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2019-05-08T15:55:44.585018Z",
- "start_time": "2019-05-08T15:55:44.581251Z"
- }
- },
- "outputs": [],
- "source": [
- "qr = QuantumRegister(3, name='q')\n",
- "cr = ClassicalRegister(2, name='c')\n",
- "qc = QuantumCircuit(qr, cr)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Registers are created automatically and can be accessed through the circuit as needed."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 4,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2019-05-08T15:55:44.592407Z",
- "start_time": "2019-05-08T15:55:44.587535Z"
- }
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "[QuantumRegister(3, 'q')]\n",
- "[ClassicalRegister(2, 'c')]\n"
- ]
- }
- ],
- "source": [
- "print(qc.qregs)\n",
- "print(qc.cregs)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### Quantum/classical bit index-based addressing"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "In the spirit of register-less circuits, qubits and classical bits (clbits) can now be addressed directly by index, without a need for referencing a register.\n",
- "In the following example, `bell.h(0)` attaches a Hadamard gate to the first quantum bit."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 5,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2019-05-08T15:55:45.283289Z",
- "start_time": "2019-05-08T15:55:44.595092Z"
- },
- "scrolled": true
- },
- "outputs": [
- {
- "data": {
- "text/html": [
- "┌───┐ ┌─┐ \n", - "q_0: |0>┤ H ├──■──┤M├───\n", - " └───┘┌─┴─┐└╥┘┌─┐\n", - "q_1: |0>─────┤ X ├─╫─┤M├\n", - " └───┘ ║ └╥┘\n", - " c_0: 0 ═══════════╩══╬═\n", - " ║ \n", - " c_1: 0 ══════════════╩═\n", - "" - ], - "text/plain": [ - "
┌───┐ \n", - "q2_0: |0>┤ H ├──────\n", - " ├───┤┌─┐┌─┐\n", - "q1_0: |0>┤ H ├┤M├┤M├\n", - " └───┘└╥┘└╥┘\n", - " c_0: 0 ══════╩══╬═\n", - " ║ \n", - " c_1: 0 ═════════╩═\n", - "" - ], - "text/plain": [ - "
┌──────────┐ \n", - "q_0: |0>┤0 ├────────────\n", - " │ my_gate │┌──────────┐\n", - "q_1: |0>┤1 ├┤0 ├\n", - " └──────────┘│ my_gate │\n", - "q_2: |0>────────────┤1 ├\n", - " └──────────┘" - ], - "text/plain": [ - "
┌───┐ \n", - "q_0: |0>┤ H ├──■────────────────────\n", - " └───┘┌─┴─┐ ┌───────────┐\n", - "q_1: |0>─────┤ X ├──■──┤0 ├\n", - " └───┘┌─┴─┐│ sub_circ │\n", - "q_2: |0>──────────┤ X ├┤1 ├\n", - " └───┘└───────────┘" - ], - "text/plain": [ - "
┌──────────┐ \n", - "q_0: |0>┤ U2(0,pi) ├──■──────────────────────────────────────\n", - " └──────────┘┌─┴─┐ ┌───┐ ░ ┌────────────┐\n", - "q_1: |0>────────────┤ X ├──■──┤ H ├────■─────░─┤ U3(1,2,-2) ├\n", - " └───┘┌─┴─┐└───┘┌───┴───┐ ░ └───┬────┬───┘\n", - "q_2: |0>─────────────────┤ X ├─────┤ Rz(1) ├─░─────┤ Id ├────\n", - " └───┘ └───────┘ ░ └────┘" - ], - "text/plain": [ - "
┌───┐ ░ ┌───────┐ ░ ┌───┐┌─┐\n", - "q_0: |0>┤ H ├──■──────────────────░─┤ Rz(θ) ├─░──────────────────■──┤ H ├┤M├\n", - " └───┘┌─┴─┐ ░ ├───────┤ ░ ┌─┴─┐└───┘└╥┘\n", - "q_1: |0>─────┤ X ├──■─────────────░─┤ Rz(θ) ├─░─────────────■──┤ X ├──────╫─\n", - " └───┘┌─┴─┐ ░ ├───────┤ ░ ┌─┴─┐└───┘ ║ \n", - "q_2: |0>──────────┤ X ├──■────────░─┤ Rz(θ) ├─░────────■──┤ X ├───────────╫─\n", - " └───┘┌─┴─┐ ░ ├───────┤ ░ ┌─┴─┐└───┘ ║ \n", - "q_3: |0>───────────────┤ X ├──■───░─┤ Rz(θ) ├─░───■──┤ X ├────────────────╫─\n", - " └───┘┌─┴─┐ ░ ├───────┤ ░ ┌─┴─┐└───┘ ║ \n", - "q_4: |0>────────────────────┤ X ├─░─┤ Rz(θ) ├─░─┤ X ├─────────────────────╫─\n", - " └───┘ ░ └───────┘ ░ └───┘ ║ \n", - " c_0: 0 ══════════════════════════════════════════════════════════════════╩═\n", - "" - ], - "text/plain": [ - "
"
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "%matplotlib inline\n",
- "import matplotlib.pyplot as plt\n",
- "plt.style.use('ggplot')\n",
- "\n",
- "fig = plt.figure()\n",
- "ax = fig.add_subplot(111)\n",
- "\n",
- "ax.plot(theta_range, list(map(lambda c: c.get('0', 0), counts)), '.-', label='0')\n",
- "ax.plot(theta_range, list(map(lambda c: c.get('1', 0), counts)), '.-', label='1') \n",
- "\n",
- "ax.set_xticks([i * np.pi / 2 for i in range(5)])\n",
- "ax.set_xticklabels(['0', r'$\\frac{\\pi}{2}$', r'$\\pi$', r'$\\frac{3\\pi}{2}$', r'$2\\pi$'], fontsize=14)\n",
- "ax.set_xlabel('θ')\n",
- "ax.legend()\n",
- "plt.show()"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "ExecuteTime": {
- "end_time": "2019-04-24T14:50:01.020312Z",
- "start_time": "2019-04-24T14:49:58.618Z"
- }
- },
- "source": [
- "### Reducing compilation cost"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Compiling over a parameterized circuit prior to binding can, in some cases, significantly reduce compilation time as compared to compiling over a set of bound circuits."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 16,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2019-05-08T15:58:25.106263Z",
- "start_time": "2019-05-08T15:55:48.434839Z"
- }
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Time compiling over set of bound circuits: 156.54600715637207\n"
- ]
- }
- ],
- "source": [
- "import time\n",
- "from itertools import combinations\n",
- "from qiskit.compiler import transpile, assemble\n",
- "from qiskit.test.mock import FakeTokyo\n",
- "\n",
- "start = time.time()\n",
- "qcs = []\n",
- "\n",
- "theta_range = np.linspace(0, 2*np.pi, 32)\n",
- "\n",
- "for n in theta_range:\n",
- " qc = QuantumCircuit(5)\n",
- "\n",
- " for k in range(8):\n",
- " for i,j in combinations(range(5), 2):\n",
- " qc.cx(i,j)\n",
- " qc.rz(n, range(5))\n",
- " for i,j in combinations(range(5), 2):\n",
- " qc.cx(i,j)\n",
- "\n",
- " qcs.append(qc)\n",
- " \n",
- "compiled_circuits = transpile(qcs, backend=FakeTokyo())\n",
- "qobj = assemble(compiled_circuits, backend=FakeTokyo())\n",
- "\n",
- "end = time.time()\n",
- "print('Time compiling over set of bound circuits: ', end-start)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 17,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2019-05-08T15:58:45.191802Z",
- "start_time": "2019-05-08T15:58:25.108688Z"
- }
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Time compiling over parameterized circuit, then binding: 20.07519006729126\n"
- ]
- }
- ],
- "source": [
- "start = time.time()\n",
- "qc = QuantumCircuit(5)\n",
- "theta = Parameter('theta')\n",
- "\n",
- "for k in range(8):\n",
- " for i,j in combinations(range(5), 2):\n",
- " qc.cx(i,j)\n",
- " qc.rz(theta, range(5))\n",
- " for i,j in combinations(range(5), 2):\n",
- " qc.cx(i,j)\n",
- "\n",
- "transpiled_qc = transpile(qc, backend=FakeTokyo())\n",
- "qobj = assemble([transpiled_qc.bind_parameters({theta: n})\n",
- " for n in theta_range], backend=FakeTokyo())\n",
- "end = time.time()\n",
- "print('Time compiling over parameterized circuit, then binding: ', end-start)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### Composition"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Parameterized circuits can be composed like standard `QuantumCircuit`s.\n",
- "Generally, when composing two parameterized circuits, the resulting circuit will be parameterized by the union of the parameters of the input circuits."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "ExecuteTime": {
- "end_time": "2019-05-08T15:07:47.268889Z",
- "start_time": "2019-05-08T15:07:47.262971Z"
- }
- },
- "source": [
- "However, parameter names must be unique within a given circuit.\n",
- "When attempting to add a parameter whose name is already present in the target circuit:\n",
- " - if the source and target share the same `Parameter` instance, the parameters will be assumed to be the same and combined\n",
- " - if the source and target have different `Parameter` instances, an error will be raised\n"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 18,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2019-05-08T15:58:45.206012Z",
- "start_time": "2019-05-08T15:58:45.193855Z"
- }
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- " ┌────────────┐┌────────────┐\n",
- "q_0: |0>┤0 ├┤0 ├\n",
- " │ sc_1(phi) ││ sc_2(phi) │\n",
- "q_1: |0>┤1 ├┤1 ├\n",
- " ├────────────┤└────────────┘\n",
- "q_2: |0>┤0 ├──────────────\n",
- " │ sc_2(phi) │ \n",
- "q_3: |0>┤1 ├──────────────\n",
- " └────────────┘ \n"
- ]
- }
- ],
- "source": [
- "phi = Parameter('phi')\n",
- "\n",
- "sub_circ1 = QuantumCircuit(2, name='sc_1')\n",
- "sub_circ1.rz(phi, 0)\n",
- "sub_circ1.rx(phi, 1)\n",
- "\n",
- "sub_circ2 = QuantumCircuit(2, name='sc_2')\n",
- "sub_circ2.rx(phi, 0)\n",
- "sub_circ2.rz(phi, 1)\n",
- "\n",
- "qc = QuantumCircuit(4)\n",
- "qr = qc.qregs[0]\n",
- "\n",
- "qc.append(sub_circ1.to_instruction(), [qr[0], qr[1]])\n",
- "qc.append(sub_circ2.to_instruction(), [qr[0], qr[1]])\n",
- "\n",
- "qc.append(sub_circ2.to_instruction(), [qr[2], qr[3]])\n",
- "\n",
- "print(qc.draw())\n",
- "\n",
- "# The following raises an error: \"QiskitError: 'Name conflict on adding parameter: phi'\"\n",
- "# phi2 = Parameter('phi')\n",
- "# qc.u3(0.1, phi2, 0.3, 0)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "To insert a subcircuit under a different parameterization, the `to_instruction` method accepts an optional argument (`parameter_map`) which, when present, will generate instructions with the source parameter replaced by a new parameter."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 19,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2019-05-08T15:58:45.235919Z",
- "start_time": "2019-05-08T15:58:45.208290Z"
- }
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- " ┌────────────────┐\n",
- "q1_0: |0>┤0 ├\n",
- " │ │\n",
- "q1_1: |0>┤1 oracle(theta) ├\n",
- " │ │\n",
- "q1_2: |0>┤2 ├\n",
- " └┬──────────────┬┘\n",
- "q1_3: |0>─┤0 ├─\n",
- " │ │ \n",
- "q1_4: |0>─┤1 oracle(phi) ├─\n",
- " │ │ \n",
- "q1_5: |0>─┤2 ├─\n",
- " ┌┴──────────────┴┐\n",
- "q1_6: |0>┤0 ├\n",
- " │ │\n",
- "q1_7: |0>┤1 oracle(gamma) ├\n",
- " │ │\n",
- "q1_8: |0>┤2 ├\n",
- " └────────────────┘\n",
- " ┌───────────┐ \n",
- "q1_0: |0>┤ Rz(theta) ├──■─────────────────────────────────\n",
- " └───────────┘┌─┴─┐┌───────────┐ \n",
- "q1_1: |0>─────────────┤ X ├┤ Rz(theta) ├──■───────────────\n",
- " └───┘└───────────┘┌─┴─┐┌───────────┐\n",
- "q1_2: |0>───────────────────────────────┤ X ├┤ Rz(theta) ├\n",
- " ┌─────────┐ └───┘└───────────┘\n",
- "q1_3: |0>─┤ Rz(phi) ├───■─────────────────────────────────\n",
- " └─────────┘ ┌─┴─┐ ┌─────────┐ \n",
- "q1_4: |0>─────────────┤ X ├─┤ Rz(phi) ├───■───────────────\n",
- " └───┘ └─────────┘ ┌─┴─┐ ┌─────────┐ \n",
- "q1_5: |0>───────────────────────────────┤ X ├─┤ Rz(phi) ├─\n",
- " ┌───────────┐ └───┘ └─────────┘ \n",
- "q1_6: |0>┤ Rz(gamma) ├──■─────────────────────────────────\n",
- " └───────────┘┌─┴─┐┌───────────┐ \n",
- "q1_7: |0>─────────────┤ X ├┤ Rz(gamma) ├──■───────────────\n",
- " └───┘└───────────┘┌─┴─┐┌───────────┐\n",
- "q1_8: |0>───────────────────────────────┤ X ├┤ Rz(gamma) ├\n",
- " └───┘└───────────┘\n"
- ]
- }
- ],
- "source": [
- "p = Parameter('p')\n",
- "qc = QuantumCircuit(3, name='oracle')\n",
- "qc.rz(p, 0)\n",
- "qc.cx(0, 1)\n",
- "qc.rz(p, 1)\n",
- "qc.cx(1, 2)\n",
- "qc.rz(p, 2)\n",
- "\n",
- "theta = Parameter('theta')\n",
- "phi = Parameter('phi')\n",
- "gamma = Parameter('gamma')\n",
- "\n",
- "qr = QuantumRegister(9)\n",
- "larger_qc = QuantumCircuit(qr)\n",
- "larger_qc.append(qc.to_instruction({p: theta}), qr[0:3])\n",
- "larger_qc.append(qc.to_instruction({p: phi}), qr[3:6])\n",
- "larger_qc.append(qc.to_instruction({p: gamma}), qr[6:9])\n",
- "print(larger_qc.draw())\n",
- "\n",
- "print(larger_qc.decompose().draw())"
- ]
- }
- ],
- "metadata": {
- "kernelspec": {
- "display_name": "Python 3",
- "language": "python",
- "name": "python3"
- },
- "language_info": {
- "codemirror_mode": {
- "name": "ipython",
- "version": 3
- },
- "file_extension": ".py",
- "mimetype": "text/x-python",
- "name": "python",
- "nbconvert_exporter": "python",
- "pygments_lexer": "ipython3",
- "version": "3.7.3"
- },
- "varInspector": {
- "cols": {
- "lenName": 16,
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- "lenVar": 40
- },
- "kernels_config": {
- "python": {
- "delete_cmd_postfix": "",
- "delete_cmd_prefix": "del ",
- "library": "var_list.py",
- "varRefreshCmd": "print(var_dic_list())"
- },
- "r": {
- "delete_cmd_postfix": ") ",
- "delete_cmd_prefix": "rm(",
- "library": "var_list.r",
- "varRefreshCmd": "cat(var_dic_list()) "
- }
- },
- "types_to_exclude": [
- "module",
- "function",
- "builtin_function_or_method",
- "instance",
- "_Feature"
- ],
- "window_display": false
- }
- },
- "nbformat": 4,
- "nbformat_minor": 2
-}
diff --git a/qiskit/advanced/terra/quantum_circuits.ipynb b/qiskit/advanced/terra/quantum_circuits.ipynb
deleted file mode 100644
index 8df6f8605..000000000
--- a/qiskit/advanced/terra/quantum_circuits.ipynb
+++ /dev/null
@@ -1,1009 +0,0 @@
-{
- "cells": [
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "![\"Note:](\"../../images/qiskit-heading.gif\")
Trusted Notebook\" width=\"500 px\" align=\"left\">"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "# Quantum Circuits\n",
- "\n",
- "The `QuantumCircuit`, `QuantumRegister`, and `ClassicalRegister` are the main objects for Qiskit Terra. Most users will be able to do all they want with these objects. "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 1,
- "metadata": {},
- "outputs": [],
- "source": [
- "import numpy as np\n",
- "from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister\n",
- "from qiskit import BasicAer, execute\n",
- "from qiskit.quantum_info import Pauli, state_fidelity, basis_state, process_fidelity "
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Quantum and Classical Registers\n",
- "\n",
- "Quantum and Classical Registers are declared using the following:"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 2,
- "metadata": {},
- "outputs": [],
- "source": [
- "q0 = QuantumRegister(2, 'q0')\n",
- "c0 = ClassicalRegister(2, 'c0')\n",
- "q1 = QuantumRegister(2, 'q1')\n",
- "c1 = ClassicalRegister(2, 'c1')\n",
- "q_test = QuantumRegister(2, 'q0')"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "The name is optional. If not given, Qiskit will name it $qi$, where $i$ is an interger which will count from 0. The name and size can be returned using the following:"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 3,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "q0\n",
- "2\n"
- ]
- }
- ],
- "source": [
- "print(q0.name)\n",
- "print(q0.size)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "You can test if the registers are the same or different. "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 4,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "True"
- ]
- },
- "execution_count": 4,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "q0==q0"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 5,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "True"
- ]
- },
- "execution_count": 5,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "q0==q_test"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 6,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "False"
- ]
- },
- "execution_count": 6,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "q0==q1"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Quantum Circuits\n",
- "\n",
- "Quantum Circuits are made using registers, which are created either when initiated or by using the `add_register` command. "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 7,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 7,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "circ = QuantumCircuit(q0, q1)\n",
- "circ.x(q0[1])\n",
- "circ.x(q1[0])\n",
- "circ.draw()"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "is the same as "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 8,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 8,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "circ2 = QuantumCircuit()\n",
- "circ2.add_register(q0)\n",
- "circ2.add_register(q1)\n",
- "circ2.x(q0[1])\n",
- "circ2.x(q1[0])\n",
- "circ2.draw()"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- ""
- ]
- },
- "execution_count": 9,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "from copy import deepcopy\n",
- "\n",
- "q3 = QuantumRegister(2, 'q3')\n",
- "circ3 = deepcopy(circ)\n",
- "circ3.add_register(q3)\n",
- "circ3.draw()"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- ""
- ]
- },
- "execution_count": 10,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "meas = QuantumCircuit(q0, q1, c0, c1)\n",
- "meas.measure(q0, c0)\n",
- "meas.measure(q1, c1)\n",
- "\n",
- "qc = circ + meas\n",
- "\n",
- "qc.draw()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 11,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 11,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "meas2 = QuantumCircuit()\n",
- "meas2.add_register(q0)\n",
- "meas2.add_register(q1)\n",
- "meas2.add_register(c0)\n",
- "meas2.add_register(c1)\n",
- "meas2.measure(q0, c0)\n",
- "meas2.measure(q1, c1)\n",
- "\n",
- "qc2 = circ2 + meas2\n",
- "\n",
- "qc2.draw()"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "It even works when the circuits have different registers. Let's start by making two new circuits:"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 12,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 12,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "circ4 = QuantumCircuit(q1)\n",
- "circ4.x(q1)\n",
- "circ4.draw()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 13,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 13,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "circ5 = QuantumCircuit(q3)\n",
- "circ5.h(q3)\n",
- "circ5.draw()"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "The new register is added to the circuit:"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 14,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 14,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "(circ4+circ5).draw()"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "We have also overloaded `+=` to the `QuantumCircuit` object:"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 15,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 15,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "circ4 += circ5\n",
- "circ4.draw()"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Outcomes of Quantum Circuits\n",
- "\n",
- "In the circuit output, the most significant bit (MSB) is to the left, and the least significant bit (LSB) is to the right (i.e., we follow little-endian ordering from computer science). In this example:"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 16,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 16,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "circ.draw()"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "qubit register $Q_0$ is prepared in the state $|10\\rangle$ and $Q_1$ is in the state $|01\\rangle$, giving a total state $|0110\\rangle$ ($Q1\\otimes Q0$). \n",
- "\n",
- ""
- ]
- },
- "execution_count": 20,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "qc.draw()"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "This will map the quantum state to the classical world. Since the state has no superpositions, it will be deterministic and equal to `'01 10'`. Here a space is used to separate the registers."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 21,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "{'01 10': 1024}\n"
- ]
- }
- ],
- "source": [
- "backend_sim = BasicAer.get_backend('qasm_simulator')\n",
- "result = execute(qc, backend_sim).result()\n",
- "counts = result.get_counts(qc)\n",
- "print(counts)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "To show that it does not matter how you add the registers, we run the same as above on the second example circuit:"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 22,
- "metadata": {},
- "outputs": [],
- "source": [
- "backend_sim = BasicAer.get_backend('statevector_simulator')\n",
- "result = execute(circ2, backend_sim).result()\n",
- "states = result.get_statevector(circ2)\n",
- "\n",
- "backend_sim = BasicAer.get_backend('qasm_simulator')\n",
- "result = execute(qc2, backend_sim).result()\n",
- "counts = result.get_counts(qc2)\n",
- "\n",
- "backend_sim = BasicAer.get_backend('unitary_simulator')\n",
- "result = execute(circ2, backend_sim).result()\n",
- "unitary = result.get_unitary(circ2)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 23,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "{'01 10': 1024}\n"
- ]
- }
- ],
- "source": [
- "print(counts)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 24,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "1.0"
- ]
- },
- "execution_count": 24,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "state_fidelity(basis_state('0110', 4), state)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 25,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "1.0"
- ]
- },
- "execution_count": 25,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "process_fidelity(Pauli(label='IXXI').to_matrix(), unitary)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Counting circuit resources\n",
- "\n",
- "A `QuantumCircuit` object provides methods for inquiring its resource use. This includes the number of qubits, operations, and a few other things."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 26,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 26,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "q = QuantumRegister(6)\n",
- "circuit = QuantumCircuit(q)\n",
- "circuit.h(q[0])\n",
- "circuit.ccx(q[0], q[1], q[2])\n",
- "circuit.cx(q[1], q[3])\n",
- "circuit.x(q)\n",
- "circuit.h(q[2])\n",
- "circuit.h(q[3])\n",
- "circuit.draw()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 27,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "11"
- ]
- },
- "execution_count": 27,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "# total number of operations in the circuit. no unrolling is done.\n",
- "circuit.size()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 28,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "5"
- ]
- },
- "execution_count": 28,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "# depth of circuit (number of ops on the critical path)\n",
- "circuit.depth()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 29,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "6"
- ]
- },
- "execution_count": 29,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "# number of qubits in the circuit\n",
- "circuit.width()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 30,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "{'x': 6, 'h': 3, 'ccx': 1, 'cx': 1}"
- ]
- },
- "execution_count": 30,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "# a breakdown of operations by type\n",
- "circuit.count_ops()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 31,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "3"
- ]
- },
- "execution_count": 31,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "# number of unentangled subcircuits in this circuit.\n",
- "# each subcircuit can in principle be executed on a different quantum processor!\n",
- "circuit.num_tensor_factors()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": []
- }
- ],
- "metadata": {
- "kernelspec": {
- "display_name": "Python [default]",
- "language": "python",
- "name": "python3"
- },
- "language_info": {
- "codemirror_mode": {
- "name": "ipython",
- "version": 3
- },
- "file_extension": ".py",
- "mimetype": "text/x-python",
- "name": "python",
- "nbconvert_exporter": "python",
- "pygments_lexer": "ipython3",
- "version": "3.6.4"
- }
- },
- "nbformat": 4,
- "nbformat_minor": 2
-}
diff --git a/qiskit/advanced/terra/summary_of_quantum_operations.ipynb b/qiskit/advanced/terra/summary_of_quantum_operations.ipynb
deleted file mode 100644
index 2706bad98..000000000
--- a/qiskit/advanced/terra/summary_of_quantum_operations.ipynb
+++ /dev/null
@@ -1,3114 +0,0 @@
-{
- "cells": [
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- " Trusted Notebook\" align=\"middle\">"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "# Summary of Quantum Operations "
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- " In this section we will go into the different operations that are available in Qiskit Terra. These are:\n",
- "- Single-qubit quantum gates\n",
- "- Multi-qubit quantum gates\n",
- "- Measurements\n",
- "- Reset\n",
- "- Conditionals\n",
- "- State initialization\n",
- "\n",
- "We will also show you how to use the three different simulators:\n",
- "- unitary_simulator\n",
- "- qasm_simulator\n",
- "- statevector_simulator"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 1,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:22.356783Z",
- "start_time": "2018-09-29T00:15:22.017905Z"
- }
- },
- "outputs": [],
- "source": [
- "# Useful additional packages \n",
- "import matplotlib.pyplot as plt\n",
- "%matplotlib inline\n",
- "import numpy as np\n",
- "from math import pi"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 2,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:24.371649Z",
- "start_time": "2018-09-29T00:15:22.358409Z"
- }
- },
- "outputs": [],
- "source": [
- "from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister, execute\n",
- "from qiskit.tools.visualization import circuit_drawer\n",
- "from qiskit.quantum_info import state_fidelity\n",
- "from qiskit import BasicAer\n",
- "\n",
- "backend = BasicAer.get_backend('unitary_simulator')"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Single Qubit Quantum states\n",
- "\n",
- "A single qubit quantum state can be written as\n",
- "\n",
- "$$\\left|\\psi\\right\\rangle = \\alpha\\left|0\\right\\rangle + \\beta \\left|1\\right\\rangle$$\n",
- "\n",
- "\n",
- "where $\\alpha$ and $\\beta$ are complex numbers. In a measurement the probability of the bit being in $\\left|0\\right\\rangle$ is $|\\alpha|^2$ and $\\left|1\\right\\rangle$ is $|\\beta|^2$. As a vector this is\n",
- "\n",
- "$$\n",
- "\\left|\\psi\\right\\rangle = \n",
- "\\begin{pmatrix}\n",
- "\\alpha \\\\\n",
- "\\beta\n",
- "\\end{pmatrix}.\n",
- "$$\n",
- "\n",
- "Note due to conservation probability $|\\alpha|^2+ |\\beta|^2 = 1$ and since global phase is undetectable $\\left|\\psi\\right\\rangle := e^{i\\delta} \\left|\\psi\\right\\rangle$ we only requires two real numbers to describe a single qubit quantum state.\n",
- "\n",
- "A convenient representation is\n",
- "\n",
- "$$\\left|\\psi\\right\\rangle = \\cos(\\theta/2)\\left|0\\right\\rangle + \\sin(\\theta/2)e^{i\\phi}\\left|1\\right\\rangle$$\n",
- "\n",
- "where $0\\leq \\phi < 2\\pi$, and $0\\leq \\theta \\leq \\pi$. From this it is clear that there is a one-to-one correspondence between qubit states ($\\mathbb{C}^2$) and the points on the surface of a unit sphere ($\\mathbb{R}^3$). This is called the Bloch sphere representation of a qubit state.\n",
- "\n",
- "Quantum gates/operations are usually represented as matrices. A gate which acts on a qubit is represented by a $2\\times 2$ unitary matrix $U$. The action of the quantum gate is found by multiplying the matrix representing the gate with the vector which represents the quantum state.\n",
- "\n",
- "$$\\left|\\psi'\\right\\rangle = U\\left|\\psi\\right\\rangle$$\n",
- "\n",
- "A general unitary must be able to take the $\\left|0\\right\\rangle$ to the above state. That is \n",
- "\n",
- "$$\n",
- "U = \\begin{pmatrix}\n",
- "\\cos(\\theta/2) & a \\\\\n",
- "e^{i\\phi}\\sin(\\theta/2) & b \n",
- "\\end{pmatrix}\n",
- "$$ \n",
- "\n",
- "where $a$ and $b$ are complex numbers constrained such that $U^\\dagger U = I$ for all $0\\leq\\theta\\leq\\pi$ and $0\\leq \\phi<2\\pi$. This gives 3 constraints and as such $a\\rightarrow -e^{i\\lambda}\\sin(\\theta/2)$ and $b\\rightarrow e^{i\\lambda+i\\phi}\\cos(\\theta/2)$ where $0\\leq \\lambda<2\\pi$ giving \n",
- "\n",
- "$$\n",
- "U = \\begin{pmatrix}\n",
- "\\cos(\\theta/2) & -e^{i\\lambda}\\sin(\\theta/2) \\\\\n",
- "e^{i\\phi}\\sin(\\theta/2) & e^{i\\lambda+i\\phi}\\cos(\\theta/2) \n",
- "\\end{pmatrix}.\n",
- "$$\n",
- "\n",
- "This is the most general form of a single qubit unitary."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Single-Qubit Gates\n",
- "\n",
- "The single-qubit gates available are:\n",
- "- u gates\n",
- "- Identity gate\n",
- "- Pauli gates\n",
- "- Clifford gates\n",
- "- $C3$ gates\n",
- "- Standard rotation gates \n",
- "\n",
- "We have provided a backend: `unitary_simulator` to allow you to calculate the unitary matrices. "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 3,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:24.381507Z",
- "start_time": "2018-09-29T00:15:24.373378Z"
- }
- },
- "outputs": [],
- "source": [
- "q = QuantumRegister(1)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### u gates\n",
- "\n",
- "In Qiskit we give you access to the general unitary using the $u3$ gate\n",
- "\n",
- "$$\n",
- "u3(\\theta, \\phi, \\lambda) = U(\\theta, \\phi, \\lambda) \n",
- "$$\n"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 4,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:25.666961Z",
- "start_time": "2018-09-29T00:15:24.386736Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 4,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "qc = QuantumCircuit(q)\n",
- "qc.u3(pi/2,pi/2,pi/2,q)\n",
- "qc.draw()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 5,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:25.686483Z",
- "start_time": "2018-09-29T00:15:25.669083Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- "array([[ 0.707+0.j , 0. -0.707j],\n",
- " [ 0. +0.707j, -0.707+0.j ]])"
- ]
- },
- "execution_count": 5,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "job = execute(qc, backend)\n",
- "job.result().get_unitary(qc, decimals=3)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "The $u2(\\phi, \\lambda) =u3(\\pi/2, \\phi, \\lambda)$ has the matrix form\n",
- "\n",
- "$$\n",
- "u2(\\phi, \\lambda) = \n",
- "\\frac{1}{\\sqrt{2}} \\begin{pmatrix}\n",
- "1 & -e^{i\\lambda} \\\\\n",
- "e^{i\\phi} & e^{i(\\phi + \\lambda)}\n",
- "\\end{pmatrix}.\n",
- "$$\n",
- "\n",
- "This is a useful gate as it allows us to create superpositions"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 6,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:26.803656Z",
- "start_time": "2018-09-29T00:15:25.688915Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 6,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "qc = QuantumCircuit(q)\n",
- "qc.u2(pi/2,pi/2,q)\n",
- "qc.draw()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 7,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:26.820459Z",
- "start_time": "2018-09-29T00:15:26.805575Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- "array([[ 0.707+0.j , 0. -0.707j],\n",
- " [ 0. +0.707j, -0.707+0.j ]])"
- ]
- },
- "execution_count": 7,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "job = execute(qc, backend)\n",
- "job.result().get_unitary(qc, decimals=3)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "The $u1(\\lambda)= u3(0, 0, \\lambda)$ gate has the matrix form\n",
- "\n",
- "$$\n",
- "u1(\\lambda) = \n",
- "\\begin{pmatrix}\n",
- "1 & 0 \\\\\n",
- "0 & e^{i \\lambda}\n",
- "\\end{pmatrix},\n",
- "$$\n",
- "\n",
- "which is a useful as it allows us to apply a quantum phase."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 8,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:27.935053Z",
- "start_time": "2018-09-29T00:15:26.822215Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 8,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "qc = QuantumCircuit(q)\n",
- "qc.u1(pi/2,q)\n",
- "qc.draw()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 9,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:27.964213Z",
- "start_time": "2018-09-29T00:15:27.940835Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- "array([[1.+0.j, 0.+0.j],\n",
- " [0.+0.j, 0.+1.j]])"
- ]
- },
- "execution_count": 9,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "job = execute(qc, backend)\n",
- "job.result().get_unitary(qc, decimals=3)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "The $u0(\\delta)= u3(0, 0, 0)$ gate is the identity matrix. It has the matrix form\n",
- "\n",
- "$$\n",
- "u0(\\delta) = \n",
- "\\begin{pmatrix}\n",
- "1 & 0 \\\\\n",
- "0 & 1\n",
- "\\end{pmatrix}.\n",
- "$$\n",
- "\n",
- "The identity gate does nothing (but can add noise in the real device for a period of time equal to fractions of the single qubit gate time)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 10,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:29.040953Z",
- "start_time": "2018-09-29T00:15:27.968687Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 10,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "qc = QuantumCircuit(q)\n",
- "qc.u0(pi/2,q)\n",
- "qc.draw()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 11,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:29.059033Z",
- "start_time": "2018-09-29T00:15:29.043032Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- "array([[1.+0.j, 0.+0.j],\n",
- " [0.+0.j, 1.+0.j]])"
- ]
- },
- "execution_count": 11,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "job = execute(qc, backend)\n",
- "job.result().get_unitary(qc, decimals=3)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### Identity gate\n",
- "\n",
- "The identity gate is $Id = u0(1)$."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 12,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:30.125226Z",
- "start_time": "2018-09-29T00:15:29.062116Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 12,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "qc = QuantumCircuit(q)\n",
- "qc.iden(q)\n",
- "qc.draw()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 13,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:30.140784Z",
- "start_time": "2018-09-29T00:15:30.127428Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- "array([[1.+0.j, 0.+0.j],\n",
- " [0.+0.j, 1.+0.j]])"
- ]
- },
- "execution_count": 13,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "job = execute(qc, backend)\n",
- "job.result().get_unitary(qc, decimals=3)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### Pauli gates\n",
- "\n",
- "#### $X$: bit-flip gate\n",
- "\n",
- "The bit-flip gate $X$ is defined as:\n",
- "\n",
- "$$\n",
- "X = \n",
- "\\begin{pmatrix}\n",
- "0 & 1\\\\\n",
- "1 & 0\n",
- "\\end{pmatrix}= u3(\\pi,0,\\pi)\n",
- "$$"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 14,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:31.251259Z",
- "start_time": "2018-09-29T00:15:30.142518Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 14,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "qc = QuantumCircuit(q)\n",
- "qc.x(q)\n",
- "qc.draw()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 15,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:31.268863Z",
- "start_time": "2018-09-29T00:15:31.253685Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- "array([[0.+0.j, 1.+0.j],\n",
- " [1.+0.j, 0.+0.j]])"
- ]
- },
- "execution_count": 15,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "job = execute(qc, backend)\n",
- "job.result().get_unitary(qc, decimals=3)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "#### $Y$: bit- and phase-flip gate\n",
- "\n",
- "The $Y$ gate is defined as:\n",
- "\n",
- "$$\n",
- "Y = \n",
- "\\begin{pmatrix}\n",
- "0 & -i\\\\\n",
- "i & 0\n",
- "\\end{pmatrix}=u3(\\pi,\\pi/2,\\pi/2)\n",
- "$$"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 16,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:32.367457Z",
- "start_time": "2018-09-29T00:15:31.270412Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 16,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "qc = QuantumCircuit(q)\n",
- "qc.y(q)\n",
- "qc.draw()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 17,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:33.152683Z",
- "start_time": "2018-09-29T00:15:32.369796Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- "array([[0.+0.j, 0.-1.j],\n",
- " [0.+1.j, 0.+0.j]])"
- ]
- },
- "execution_count": 17,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "job = execute(qc, backend)\n",
- "job.result().get_unitary(qc, decimals=3)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "#### $Z$: phase-flip gate\n",
- "\n",
- "The phase flip gate $Z$ is defined as:\n",
- "\n",
- "$$\n",
- "Z = \n",
- "\\begin{pmatrix}\n",
- "1 & 0\\\\\n",
- "0 & -1\n",
- "\\end{pmatrix}=u1(\\pi)\n",
- "$$"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 18,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:34.348628Z",
- "start_time": "2018-09-29T00:15:33.158278Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 18,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "qc = QuantumCircuit(q)\n",
- "qc.z(q)\n",
- "qc.draw()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 19,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:34.367128Z",
- "start_time": "2018-09-29T00:15:34.350725Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- "array([[ 1.+0.j, 0.+0.j],\n",
- " [ 0.+0.j, -1.+0.j]])"
- ]
- },
- "execution_count": 19,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "job = execute(qc, backend)\n",
- "job.result().get_unitary(qc, decimals=3)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### Clifford gates\n",
- "\n",
- "#### Hadamard gate\n",
- "\n",
- "$$\n",
- "H = \n",
- "\\frac{1}{\\sqrt{2}}\n",
- "\\begin{pmatrix}\n",
- "1 & 1\\\\\n",
- "1 & -1\n",
- "\\end{pmatrix}= u2(0,\\pi)\n",
- "$$"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 20,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:35.530446Z",
- "start_time": "2018-09-29T00:15:34.368793Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 20,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "qc = QuantumCircuit(q)\n",
- "qc.h(q)\n",
- "qc.draw()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 21,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:35.550723Z",
- "start_time": "2018-09-29T00:15:35.532971Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- "array([[ 0.707+0.j, 0.707+0.j],\n",
- " [ 0.707+0.j, -0.707+0.j]])"
- ]
- },
- "execution_count": 21,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "job = execute(qc, backend)\n",
- "job.result().get_unitary(qc, decimals=3)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "#### $S$ (or, $\\sqrt{Z}$ phase) gate\n",
- "\n",
- "$$\n",
- "S = \n",
- "\\begin{pmatrix}\n",
- "1 & 0\\\\\n",
- "0 & i\n",
- "\\end{pmatrix}= u1(\\pi/2)\n",
- "$$"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 22,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:36.627291Z",
- "start_time": "2018-09-29T00:15:35.552841Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 22,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "qc = QuantumCircuit(q)\n",
- "qc.s(q)\n",
- "qc.draw()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 23,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:36.661217Z",
- "start_time": "2018-09-29T00:15:36.631382Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- "array([[1.+0.j, 0.+0.j],\n",
- " [0.+0.j, 0.+1.j]])"
- ]
- },
- "execution_count": 23,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "job = execute(qc, backend)\n",
- "job.result().get_unitary(qc, decimals=3)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "#### $S^{\\dagger}$ (or, conjugate of $\\sqrt{Z}$ phase) gate\n",
- "\n",
- "$$\n",
- "S^{\\dagger} = \n",
- "\\begin{pmatrix}\n",
- "1 & 0\\\\\n",
- "0 & -i\n",
- "\\end{pmatrix}= u1(-\\pi/2)\n",
- "$$\n"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 24,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:37.965580Z",
- "start_time": "2018-09-29T00:15:36.668521Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 24,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "qc = QuantumCircuit(q)\n",
- "qc.sdg(q)\n",
- "qc.draw()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 25,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:37.995581Z",
- "start_time": "2018-09-29T00:15:37.968281Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- "array([[1.+0.j, 0.+0.j],\n",
- " [0.+0.j, 0.-1.j]])"
- ]
- },
- "execution_count": 25,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "job = execute(qc, backend)\n",
- "job.result().get_unitary(qc, decimals=3)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### $C3$ gates\n",
- "#### $T$ (or, $\\sqrt{S}$ phase) gate\n",
- "\n",
- "$$\n",
- "T = \n",
- "\\begin{pmatrix}\n",
- "1 & 0\\\\\n",
- "0 & e^{i \\pi/4}\n",
- "\\end{pmatrix}= u1(\\pi/4) \n",
- "$$"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 26,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:39.268078Z",
- "start_time": "2018-09-29T00:15:38.005726Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 26,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "qc = QuantumCircuit(q)\n",
- "qc.t(q)\n",
- "qc.draw()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 27,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:39.285757Z",
- "start_time": "2018-09-29T00:15:39.270165Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- "array([[1. +0.j , 0. +0.j ],\n",
- " [0. +0.j , 0.707+0.707j]])"
- ]
- },
- "execution_count": 27,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "job = execute(qc, backend)\n",
- "job.result().get_unitary(qc, decimals=3)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "#### $T^{\\dagger}$ (or, conjugate of $\\sqrt{S}$ phase) gate\n",
- "\n",
- "$$\n",
- "T^{\\dagger} = \n",
- "\\begin{pmatrix}\n",
- "1 & 0\\\\\n",
- "0 & e^{-i \\pi/4}\n",
- "\\end{pmatrix}= u1(-pi/4)\n",
- "$$\n",
- "\n",
- "They can be added as below."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 28,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:40.466163Z",
- "start_time": "2018-09-29T00:15:39.287535Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 28,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "qc = QuantumCircuit(q)\n",
- "qc.tdg(q)\n",
- "qc.draw()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 29,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:40.500673Z",
- "start_time": "2018-09-29T00:15:40.468194Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- "array([[1. +0.j , 0. +0.j ],\n",
- " [0. +0.j , 0.707-0.707j]])"
- ]
- },
- "execution_count": 29,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "job = execute(qc, backend)\n",
- "job.result().get_unitary(qc, decimals=3)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### Standard Rotations\n",
- "\n",
- "The standard rotation gates are those that define rotations around the Paulis $P=\\{X,Y,Z\\}$. They are defined as \n",
- "\n",
- "$$ R_P(\\theta) = \\exp(-i \\theta P/2) = \\cos(\\theta/2)I -i \\sin(\\theta/2)P$$\n",
- "\n",
- "#### Rotation around X-axis\n",
- "\n",
- "$$\n",
- "R_x(\\theta) = \n",
- "\\begin{pmatrix}\n",
- "\\cos(\\theta/2) & -i\\sin(\\theta/2)\\\\\n",
- "-i\\sin(\\theta/2) & \\cos(\\theta/2)\n",
- "\\end{pmatrix} = u3(\\theta, -\\pi/2,\\pi/2)\n",
- "$$"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 30,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:41.848889Z",
- "start_time": "2018-09-29T00:15:40.504414Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 30,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "qc = QuantumCircuit(q)\n",
- "qc.rx(pi/2,q)\n",
- "qc.draw()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 31,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:41.870040Z",
- "start_time": "2018-09-29T00:15:41.850897Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- "array([[0.707+0.j , 0. -0.707j],\n",
- " [0. -0.707j, 0.707+0.j ]])"
- ]
- },
- "execution_count": 31,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "job = execute(qc, backend)\n",
- "job.result().get_unitary(qc, decimals=3)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "#### Rotation around Y-axis\n",
- "\n",
- "$$\n",
- "R_y(\\theta) =\n",
- "\\begin{pmatrix}\n",
- "\\cos(\\theta/2) & - \\sin(\\theta/2)\\\\\n",
- "\\sin(\\theta/2) & \\cos(\\theta/2).\n",
- "\\end{pmatrix} =u3(\\theta,0,0)\n",
- "$$"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 32,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:42.977649Z",
- "start_time": "2018-09-29T00:15:41.873513Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 32,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "qc = QuantumCircuit(q)\n",
- "qc.ry(pi/2,q)\n",
- "qc.draw()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 33,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:42.996374Z",
- "start_time": "2018-09-29T00:15:42.980438Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- "array([[ 0.707+0.j, -0.707+0.j],\n",
- " [ 0.707+0.j, 0.707+0.j]])"
- ]
- },
- "execution_count": 33,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "job = execute(qc, backend)\n",
- "job.result().get_unitary(qc, decimals=3)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "#### Rotation around Z-axis\n",
- "\n",
- "$$\n",
- "R_z(\\phi) = \n",
- "\\begin{pmatrix}\n",
- "e^{-i \\phi/2} & 0 \\\\\n",
- "0 & e^{i \\phi/2}\n",
- "\\end{pmatrix}\\equiv u1(\\phi)\n",
- "$$\n",
- "\n",
- "Note here we have used an equivalent as is different to u1 by global phase $e^{-i \\phi/2}$."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 34,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:44.157100Z",
- "start_time": "2018-09-29T00:15:42.998031Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 34,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "qc = QuantumCircuit(q)\n",
- "qc.rz(pi/2,q)\n",
- "qc.draw()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 35,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:44.179782Z",
- "start_time": "2018-09-29T00:15:44.159445Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- "array([[1.+0.j, 0.+0.j],\n",
- " [0.+0.j, 0.+1.j]])"
- ]
- },
- "execution_count": 35,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "job = execute(qc, backend)\n",
- "job.result().get_unitary(qc, decimals=3)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Note this is different due only to a global phase"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Multi-Qubit Gates\n",
- "\n",
- "### Mathematical Preliminaries\n",
- "\n",
- "The space of quantum computer grows exponential with the number of qubits. For $n$ qubits the complex vector space has dimensions $d=2^n$. To describe states of a multi-qubit system, the tensor product is used to \"glue together\" operators and basis vectors.\n",
- "\n",
- "Let's start by considering a 2-qubit system. Given two operators $A$ and $B$ that each act on one qubit, the joint operator $A \\otimes B$ acting on two qubits is\n",
- "\n",
- "$$\\begin{equation}\n",
- "\tA\\otimes B = \n",
- "\t\\begin{pmatrix} \n",
- "\t\tA_{00} \\begin{pmatrix} \n",
- "\t\t\tB_{00} & B_{01} \\\\\n",
- "\t\t\tB_{10} & B_{11}\n",
- "\t\t\\end{pmatrix} & A_{01} \t\\begin{pmatrix} \n",
- "\t\t\t\tB_{00} & B_{01} \\\\\n",
- "\t\t\t\tB_{10} & B_{11}\n",
- "\t\t\t\\end{pmatrix} \\\\\n",
- "\t\tA_{10} \t\\begin{pmatrix} \n",
- "\t\t\t\t\tB_{00} & B_{01} \\\\\n",
- "\t\t\t\t\tB_{10} & B_{11}\n",
- "\t\t\t\t\\end{pmatrix} & A_{11} \t\\begin{pmatrix} \n",
- "\t\t\t\t\t\t\tB_{00} & B_{01} \\\\\n",
- "\t\t\t\t\t\t\tB_{10} & B_{11}\n",
- "\t\t\t\t\t\t\\end{pmatrix}\n",
- "\t\\end{pmatrix},\t\t\t\t\t\t\n",
- "\\end{equation}$$\n",
- "\n",
- "where $A_{jk}$ and $B_{lm}$ are the matrix elements of $A$ and $B$, respectively.\n",
- "\n",
- "Analogously, the basis vectors for the 2-qubit system are formed using the tensor product of basis vectors for a single qubit:\n",
- "$$\\begin{equation}\\begin{split}\n",
- "\t\\left|{00}\\right\\rangle &= \\begin{pmatrix} \n",
- "\t\t1 \\begin{pmatrix} \n",
- "\t\t\t1 \\\\\n",
- "\t\t\t0\n",
- "\t\t\\end{pmatrix} \\\\\n",
- "\t\t0 \\begin{pmatrix} \n",
- "\t\t\t1 \\\\\n",
- "\t\t\t0 \n",
- "\t\t\\end{pmatrix}\n",
- "\t\\end{pmatrix} = \\begin{pmatrix} 1 \\\\ 0 \\\\ 0 \\\\0 \\end{pmatrix}~~~\\left|{01}\\right\\rangle = \\begin{pmatrix} \n",
- "\t1 \\begin{pmatrix} \n",
- "\t0 \\\\\n",
- "\t1\n",
- "\t\\end{pmatrix} \\\\\n",
- "\t0 \\begin{pmatrix} \n",
- "\t0 \\\\\n",
- "\t1 \n",
- "\t\\end{pmatrix}\n",
- "\t\\end{pmatrix} = \\begin{pmatrix}0 \\\\ 1 \\\\ 0 \\\\ 0 \\end{pmatrix}\\end{split}\n",
- "\\end{equation}$$\n",
- " \n",
- "$$\\begin{equation}\\begin{split}\\left|{10}\\right\\rangle = \\begin{pmatrix} \n",
- "\t0\\begin{pmatrix} \n",
- "\t1 \\\\\n",
- "\t0\n",
- "\t\\end{pmatrix} \\\\\n",
- "\t1\\begin{pmatrix} \n",
- "\t1 \\\\\n",
- "\t0 \n",
- "\t\\end{pmatrix}\n",
- "\t\\end{pmatrix} = \\begin{pmatrix} 0 \\\\ 0 \\\\ 1 \\\\ 0 \\end{pmatrix}~~~ \t\\left|{11}\\right\\rangle = \\begin{pmatrix} \n",
- "\t0 \\begin{pmatrix} \n",
- "\t0 \\\\\n",
- "\t1\n",
- "\t\\end{pmatrix} \\\\\n",
- "\t1\\begin{pmatrix} \n",
- "\t0 \\\\\n",
- "\t1 \n",
- "\t\\end{pmatrix}\n",
- "\t\\end{pmatrix} = \\begin{pmatrix} 0 \\\\ 0 \\\\ 0 \\\\1 \\end{pmatrix}\\end{split}\n",
- "\\end{equation}.$$\n",
- "\n",
- "Note we've introduced a shorthand for the tensor product of basis vectors, wherein $\\left|0\\right\\rangle \\otimes \\left|0\\right\\rangle$ is written as $\\left|00\\right\\rangle$. The state of an $n$-qubit system can described using the $n$-fold tensor product of single-qubit basis vectors. Notice that the basis vectors for a 2-qubit system are 4-dimensional; in general, the basis vectors of an $n$-qubit sytsem are $2^{n}$-dimensional, as noted earlier.\n",
- "\n",
- "### Basis vector ordering in Qiskit\n",
- "\n",
- "Within the physics community, the qubits of a multi-qubit systems are typically ordered with the first qubit on the left-most side of the tensor product and the last qubit on the right-most side. For instance, if the first qubit is in state $\\left|0\\right\\rangle$ and second is in state $\\left|1\\right\\rangle$, their joint state would be $\\left|01\\right\\rangle$. Qiskit uses a slightly different ordering of the qubits, in which the qubits are represented from the most significant bit (MSB) on the left to the least significant bit (LSB) on the right (big-endian). This is similar to bitstring representation on classical computers, and enables easy conversion from bitstrings to integers after measurements are performed. For the example just given, the joint state would be represented as $\\left|10\\right\\rangle$. Importantly, _this change in the representation of multi-qubit states affects the way multi-qubit gates are represented in Qiskit_, as discussed below.\n",
- "\n",
- "The representation used in Qiskit enumerates the basis vectors in increasing order of the integers they represent. For instance, the basis vectors for a 2-qubit system would be ordered as $\\left|00\\right\\rangle$, $\\left|01\\right\\rangle$, $\\left|10\\right\\rangle$, and $\\left|11\\right\\rangle$. Thinking of the basis vectors as bit strings, they encode the integers 0,1,2 and 3, respectively.\n",
- "\n",
- "\n",
- "### Controlled operations on qubits\n",
- "\n",
- "A common multi-qubit gate involves the application of a gate to one qubit, conditioned on the state of another qubit. For instance, we might want to flip the state of the second qubit when the first qubit is in $\\left|0\\right\\rangle$. Such gates are known as _controlled gates_. The standard multi-qubit gates consist of two-qubit gates and three-qubit gates. The two-qubit gates are:\n",
- "- controlled Pauli gates\n",
- "- controlled Hadamard gate\n",
- "- controlled rotation gates\n",
- "- controlled phase gate\n",
- "- controlled u3 gate\n",
- "- swap gate\n",
- "\n",
- "The three-qubit gates are: \n",
- "- Toffoli gate \n",
- "- Fredkin gate"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Two-qubit gates\n",
- "\n",
- "Most of the two-gates are of the controlled type (the SWAP gate being the exception). In general, a controlled two-qubit gate $C_{U}$ acts to apply the single-qubit unitary $U$ to the second qubit when the state of the first qubit is in $\\left|1\\right\\rangle$. Suppose $U$ has a matrix representation\n",
- "\n",
- "$$U = \\begin{pmatrix} u_{00} & u_{01} \\\\ u_{10} & u_{11}\\end{pmatrix}.$$\n",
- "\n",
- "We can work out the action of $C_{U}$ as follows. Recall that the basis vectors for a two-qubit system are ordered as $\\left|00\\right\\rangle, \\left|01\\right\\rangle, \\left|10\\right\\rangle, \\left|11\\right\\rangle$. Suppose the **control qubit** is **qubit 0** (which, according to Qiskit's convention, is one the _right-hand_ side of the tensor product). If the control qubit is in $\\left|1\\right\\rangle$, $U$ should be applied to the **target** (qubit 1, on the _left-hand_ side of the tensor product). Therefore, under the action of $C_{U}$, the basis vectors are transformed according to\n",
- "\n",
- "$$\\begin{align*}\n",
- "C_{U}: \\underset{\\text{qubit}~1}{\\left|0\\right\\rangle}\\otimes \\underset{\\text{qubit}~0}{\\left|0\\right\\rangle} &\\rightarrow \\underset{\\text{qubit}~1}{\\left|0\\right\\rangle}\\otimes \\underset{\\text{qubit}~0}{\\left|0\\right\\rangle}\\\\\n",
- "C_{U}: \\underset{\\text{qubit}~1}{\\left|0\\right\\rangle}\\otimes \\underset{\\text{qubit}~0}{\\left|1\\right\\rangle} &\\rightarrow \\underset{\\text{qubit}~1}{U\\left|0\\right\\rangle}\\otimes \\underset{\\text{qubit}~0}{\\left|1\\right\\rangle}\\\\\n",
- "C_{U}: \\underset{\\text{qubit}~1}{\\left|1\\right\\rangle}\\otimes \\underset{\\text{qubit}~0}{\\left|0\\right\\rangle} &\\rightarrow \\underset{\\text{qubit}~1}{\\left|1\\right\\rangle}\\otimes \\underset{\\text{qubit}~0}{\\left|0\\right\\rangle}\\\\\n",
- "C_{U}: \\underset{\\text{qubit}~1}{\\left|1\\right\\rangle}\\otimes \\underset{\\text{qubit}~0}{\\left|1\\right\\rangle} &\\rightarrow \\underset{\\text{qubit}~1}{U\\left|1\\right\\rangle}\\otimes \\underset{\\text{qubit}~0}{\\left|1\\right\\rangle}\\\\\n",
- "\\end{align*}.$$\n",
- "\n",
- "In matrix form, the action of $C_{U}$ is\n",
- "\n",
- "$$\\begin{equation}\n",
- "\tC_U = \\begin{pmatrix}\n",
- "\t1 & 0 & 0 & 0 \\\\\n",
- "\t0 & u_{00} & 0 & u_{01} \\\\\n",
- "\t0 & 0 & 1 & 0 \\\\\n",
- "\t0 & u_{10} &0 & u_{11}\n",
- "\t\t\\end{pmatrix}.\n",
- "\\end{equation}$$\n",
- "\n",
- "To work out these matrix elements, let\n",
- "\n",
- "$$C_{(jk), (lm)} = \\left(\\underset{\\text{qubit}~1}{\\left\\langle j \\right|} \\otimes \\underset{\\text{qubit}~0}{\\left\\langle k \\right|}\\right) C_{U} \\left(\\underset{\\text{qubit}~1}{\\left| l \\right\\rangle} \\otimes \\underset{\\text{qubit}~0}{\\left| k \\right\\rangle}\\right),$$\n",
- "\n",
- "compute the action of $C_{U}$ (given above), and compute the inner products.\n",
- "\n",
- "As shown in the examples below, this operation is implemented in Qiskit as `cU(q[0],q[1])`.\n",
- "\n",
- "\n",
- "If **qubit 1 is the control and qubit 0 is the target**, then the basis vectors are transformed according to\n",
- "$$\\begin{align*}\n",
- "C_{U}: \\underset{\\text{qubit}~1}{\\left|0\\right\\rangle}\\otimes \\underset{\\text{qubit}~0}{\\left|0\\right\\rangle} &\\rightarrow \\underset{\\text{qubit}~1}{\\left|0\\right\\rangle}\\otimes \\underset{\\text{qubit}~0}{\\left|0\\right\\rangle}\\\\\n",
- "C_{U}: \\underset{\\text{qubit}~1}{\\left|0\\right\\rangle}\\otimes \\underset{\\text{qubit}~0}{\\left|1\\right\\rangle} &\\rightarrow \\underset{\\text{qubit}~1}{\\left|0\\right\\rangle}\\otimes \\underset{\\text{qubit}~0}{\\left|1\\right\\rangle}\\\\\n",
- "C_{U}: \\underset{\\text{qubit}~1}{\\left|1\\right\\rangle}\\otimes \\underset{\\text{qubit}~0}{\\left|0\\right\\rangle} &\\rightarrow \\underset{\\text{qubit}~1}{\\left|1\\right\\rangle}\\otimes \\underset{\\text{qubit}~0}{U\\left|0\\right\\rangle}\\\\\n",
- "C_{U}: \\underset{\\text{qubit}~1}{\\left|1\\right\\rangle}\\otimes \\underset{\\text{qubit}~0}{\\left|1\\right\\rangle} &\\rightarrow \\underset{\\text{qubit}~1}{\\left|1\\right\\rangle}\\otimes \\underset{\\text{qubit}~0}{U\\left|1\\right\\rangle}\\\\\n",
- "\\end{align*},$$\n",
- "\n",
- "\n",
- "which implies the matrix form of $C_{U}$ is\n",
- "$$\\begin{equation}\n",
- "\tC_U = \\begin{pmatrix}\n",
- "\t1 & 0 & 0 & 0 \\\\\n",
- "\t0 & 1 & 0 & 0 \\\\\n",
- "\t0 & 0 & u_{00} & u_{01} \\\\\n",
- "\t0 & 0 & u_{10} & u_{11}\n",
- "\t\t\\end{pmatrix}.\n",
- "\\end{equation}$$"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 36,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:44.186355Z",
- "start_time": "2018-09-29T00:15:44.182554Z"
- }
- },
- "outputs": [],
- "source": [
- "q = QuantumRegister(2)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### Controlled Pauli Gates\n",
- "\n",
- "#### Controlled-X (or, controlled-NOT) gate\n",
- "The controlled-not gate flips the `target` qubit when the control qubit is in the state $\\left|1\\right\\rangle$. If we take the MSB as the control qubit (e.g. `cx(q[1],q[0])`), then the matrix would look like\n",
- "\n",
- "$$\n",
- "C_X = \n",
- "\\begin{pmatrix}\n",
- "1 & 0 & 0 & 0\\\\\n",
- "0 & 1 & 0 & 0\\\\\n",
- "0 & 0 & 0 & 1\\\\\n",
- "0 & 0 & 1 & 0\n",
- "\\end{pmatrix}. \n",
- "$$\n",
- "\n",
- "However, when the LSB is the control qubit, (e.g. `cx(q[0],q[1])`), this gate is equivalent to the following matrix:\n",
- "\n",
- "$$\n",
- "C_X = \n",
- "\\begin{pmatrix}\n",
- "1 & 0 & 0 & 0\\\\\n",
- "0 & 0 & 0 & 1\\\\\n",
- "0 & 0 & 1 & 0\\\\\n",
- "0 & 1 & 0 & 0\n",
- "\\end{pmatrix}. \n",
- "$$\n",
- "\n"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 37,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:45.529617Z",
- "start_time": "2018-09-29T00:15:44.189643Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 37,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "qc = QuantumCircuit(q)\n",
- "qc.cx(q[0],q[1])\n",
- "qc.draw()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 38,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:45.546415Z",
- "start_time": "2018-09-29T00:15:45.531833Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- "array([[1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n",
- " [0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j],\n",
- " [0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],\n",
- " [0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j]])"
- ]
- },
- "execution_count": 38,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "job = execute(qc, backend)\n",
- "job.result().get_unitary(qc, decimals=3)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "#### Controlled $Y$ gate\n",
- "\n",
- "Apply the $Y$ gate to the target qubit if the control qubit is the MSB\n",
- "\n",
- "$$\n",
- "C_Y = \n",
- "\\begin{pmatrix}\n",
- "1 & 0 & 0 & 0\\\\\n",
- "0 & 1 & 0 & 0\\\\\n",
- "0 & 0 & 0 & -i\\\\\n",
- "0 & 0 & i & 0\n",
- "\\end{pmatrix},\n",
- "$$\n",
- "\n",
- "or when the LSB is the control\n",
- "\n",
- "$$\n",
- "C_Y = \n",
- "\\begin{pmatrix}\n",
- "1 & 0 & 0 & 0\\\\\n",
- "0 & 0 & 0 & -i\\\\\n",
- "0 & 0 & 1 & 0\\\\\n",
- "0 & i & 0 & 0\n",
- "\\end{pmatrix}.\n",
- "$$"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 39,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:46.767098Z",
- "start_time": "2018-09-29T00:15:45.549354Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 39,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "qc = QuantumCircuit(q)\n",
- "qc.cy(q[0],q[1])\n",
- "qc.draw()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 40,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:46.788301Z",
- "start_time": "2018-09-29T00:15:46.769145Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- "array([[1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n",
- " [0.+0.j, 0.+0.j, 0.+0.j, 0.-1.j],\n",
- " [0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],\n",
- " [0.+0.j, 0.+1.j, 0.+0.j, 0.+0.j]])"
- ]
- },
- "execution_count": 40,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "job = execute(qc, backend)\n",
- "job.result().get_unitary(qc, decimals=3)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "#### Controlled $Z$ (or, controlled Phase) gate\n",
- "\n",
- "Similarly, the controlled Z gate flips the phase of the target qubit if the control qubit is $\\left|1\\right\\rangle$. The matrix looks the same regardless of whether the MSB or LSB is the control qubit:\n",
- "\n",
- "$$\n",
- "C_Z = \n",
- "\\begin{pmatrix}\n",
- "1 & 0 & 0 & 0\\\\\n",
- "0 & 1 & 0 & 0\\\\\n",
- "0 & 0 & 1 & 0\\\\\n",
- "0 & 0 & 0 & -1\n",
- "\\end{pmatrix}\n",
- "$$\n"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 41,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:47.989274Z",
- "start_time": "2018-09-29T00:15:46.791557Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 41,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "qc = QuantumCircuit(q)\n",
- "qc.cz(q[0],q[1])\n",
- "qc.draw()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 42,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:48.017523Z",
- "start_time": "2018-09-29T00:15:47.991182Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- "array([[ 1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n",
- " [ 0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j],\n",
- " [ 0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],\n",
- " [ 0.+0.j, 0.+0.j, 0.+0.j, -1.+0.j]])"
- ]
- },
- "execution_count": 42,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "job = execute(qc, backend)\n",
- "job.result().get_unitary(qc, decimals=3)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### Controlled Hadamard gate\n",
- "\n",
- "Apply $H$ gate to the target qubit if the control qubit is $\\left|1\\right\\rangle$. Below is the case where the control is the LSB qubit.\n",
- "\n",
- "$$\n",
- "C_H = \n",
- "\\begin{pmatrix}\n",
- "1 & 0 & 0 & 0\\\\\n",
- "0 & \\frac{1}{\\sqrt{2}} & 0 & \\frac{1}{\\sqrt{2}}\\\\\n",
- "0 & 0 & 1 & 0\\\\\n",
- "0 & \\frac{1}{\\sqrt{2}} & 0& -\\frac{1}{\\sqrt{2}}\n",
- "\\end{pmatrix}\n",
- "$$"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 43,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:49.150237Z",
- "start_time": "2018-09-29T00:15:48.019326Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 43,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "qc = QuantumCircuit(q)\n",
- "qc.ch(q[0],q[1])\n",
- "qc.draw()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 44,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:49.184874Z",
- "start_time": "2018-09-29T00:15:49.152802Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- "array([[ 0.707+0.707j, 0. +0.j , 0. +0.j , 0. +0.j ],\n",
- " [ 0. +0.j , 0.5 +0.5j , 0. +0.j , 0.5 +0.5j ],\n",
- " [ 0. +0.j , 0. +0.j , 0.707+0.707j, 0. +0.j ],\n",
- " [ 0. +0.j , 0.5 +0.5j , 0. +0.j , -0.5 -0.5j ]])"
- ]
- },
- "execution_count": 44,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "job = execute(qc, backend)\n",
- "job.result().get_unitary(qc, decimals=3)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### Controlled rotation gates\n",
- "\n",
- "#### Controlled rotation around Z-axis\n",
- "\n",
- "Perform rotation around Z-axis on the target qubit if the control qubit (here LSB) is $\\left|1\\right\\rangle$.\n",
- "\n",
- "$$\n",
- "C_{Rz}(\\lambda) = \n",
- "\\begin{pmatrix}\n",
- "1 & 0 & 0 & 0\\\\\n",
- "0 & e^{-i\\lambda/2} & 0 & 0\\\\\n",
- "0 & 0 & 1 & 0\\\\\n",
- "0 & 0 & 0 & e^{i\\lambda/2}\n",
- "\\end{pmatrix}\n",
- "$$"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 45,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:50.307303Z",
- "start_time": "2018-09-29T00:15:49.188784Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 45,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "qc = QuantumCircuit(q)\n",
- "qc.crz(pi/2,q[0],q[1])\n",
- "qc.draw()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 46,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:50.327982Z",
- "start_time": "2018-09-29T00:15:50.310167Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- "array([[1. +0.j , 0. +0.j , 0. +0.j , 0. +0.j ],\n",
- " [0. +0.j , 0.707-0.707j, 0. +0.j , 0. +0.j ],\n",
- " [0. +0.j , 0. +0.j , 1. +0.j , 0. +0.j ],\n",
- " [0. +0.j , 0. +0.j , 0. +0.j , 0.707+0.707j]])"
- ]
- },
- "execution_count": 46,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "job = execute(qc, backend)\n",
- "job.result().get_unitary(qc, decimals=3)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### Controlled phase rotation\n",
- "\n",
- "Perform a phase rotation if both qubits are in the $\\left|11\\right\\rangle$ state. The matrix looks the same regardless of whether the MSB or LSB is the control qubit.\n",
- "\n",
- "$$\n",
- "C_{u1}(\\lambda) = \n",
- "\\begin{pmatrix}\n",
- "1 & 0 & 0 & 0\\\\\n",
- "0 & 1 & 0 & 0\\\\\n",
- "0 & 0 & 1 & 0\\\\\n",
- "0 & 0 & 0 & e^{i\\lambda}\n",
- "\\end{pmatrix}\n",
- "$$"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 47,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:51.580519Z",
- "start_time": "2018-09-29T00:15:50.329669Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 47,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "qc = QuantumCircuit(q)\n",
- "qc.cu1(pi/2,q[0], q[1])\n",
- "qc.draw()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 48,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:51.608625Z",
- "start_time": "2018-09-29T00:15:51.583186Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- "array([[1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n",
- " [0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j],\n",
- " [0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],\n",
- " [0.+0.j, 0.+0.j, 0.+0.j, 0.+1.j]])"
- ]
- },
- "execution_count": 48,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "job = execute(qc, backend)\n",
- "job.result().get_unitary(qc, decimals=3)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### Controlled $u3$ rotation\n",
- "\n",
- "Perform controlled-$u3$ rotation on the target qubit if the control qubit (here LSB) is $\\left|1\\right\\rangle$. \n",
- "\n",
- "$$\n",
- "C_{u3}(\\theta, \\phi, \\lambda) \\equiv \n",
- "\\begin{pmatrix}\n",
- "1 & 0 & 0 & 0\\\\\n",
- "0 & e^{-i(\\phi+\\lambda)/2}\\cos(\\theta/2) & 0 & -e^{-i(\\phi-\\lambda)/2}\\sin(\\theta/2)\\\\\n",
- "0 & 0 & 1 & 0\\\\\n",
- "0 & e^{i(\\phi-\\lambda)/2}\\sin(\\theta/2) & 0 & e^{i(\\phi+\\lambda)/2}\\cos(\\theta/2)\n",
- "\\end{pmatrix}.\n",
- "$$"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 49,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:52.853130Z",
- "start_time": "2018-09-29T00:15:51.610840Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 49,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "qc = QuantumCircuit(q)\n",
- "qc.cu3(pi/2, pi/2, pi/2, q[0], q[1])\n",
- "qc.draw()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 50,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:52.874428Z",
- "start_time": "2018-09-29T00:15:52.855187Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- "array([[ 1. +0.j , 0. +0.j , 0. +0.j , 0. +0.j ],\n",
- " [ 0. +0.j , 0. -0.707j, 0. +0.j , -0.707+0.j ],\n",
- " [ 0. +0.j , 0. +0.j , 1. +0.j , 0. +0.j ],\n",
- " [ 0. +0.j , 0.707+0.j , 0. +0.j , 0. +0.707j]])"
- ]
- },
- "execution_count": 50,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "job = execute(qc, backend)\n",
- "job.result().get_unitary(qc, decimals=3)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### SWAP gate\n",
- "\n",
- "The SWAP gate exchanges the two qubits. It transforms the basis vectors as\n",
- "\n",
- "$$\\left|00\\right\\rangle \\rightarrow \\left|00\\right\\rangle~,~\\left|01\\right\\rangle \\rightarrow \\left|10\\right\\rangle~,~\\left|10\\right\\rangle \\rightarrow \\left|01\\right\\rangle~,~\\left|11\\right\\rangle \\rightarrow \\left|11\\right\\rangle,$$\n",
- "\n",
- "which gives a matrix representation of the form\n",
- "\n",
- "$$\n",
- "\\mathrm{SWAP} = \n",
- "\\begin{pmatrix}\n",
- "1 & 0 & 0 & 0\\\\\n",
- "0 & 0 & 1 & 0\\\\\n",
- "0 & 1 & 0 & 0\\\\\n",
- "0 & 0 & 0 & 1\n",
- "\\end{pmatrix}.\n",
- "$$"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 51,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:54.104384Z",
- "start_time": "2018-09-29T00:15:52.877953Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 51,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "qc = QuantumCircuit(q)\n",
- "qc.swap(q[0], q[1])\n",
- "qc.draw()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 52,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:54.123272Z",
- "start_time": "2018-09-29T00:15:54.106315Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- "array([[1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n",
- " [0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],\n",
- " [0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j],\n",
- " [0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j]])"
- ]
- },
- "execution_count": 52,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "job = execute(qc, backend)\n",
- "job.result().get_unitary(qc, decimals=3)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Three-qubit gates\n",
- "\n",
- "\n",
- "There are two commonly-used three-qubit gates. For three qubits, the basis vectors are ordered as\n",
- "\n",
- "$$\\left|000\\right\\rangle, \\left|001\\right\\rangle, \\left|010\\right\\rangle, \\left|011\\right\\rangle, \\left|100\\right\\rangle, \\left|101\\right\\rangle, \\left|110\\right\\rangle, \\left|111\\right\\rangle,$$\n",
- "\n",
- "which, as bitstrings, represent the integers $0,1,2,\\cdots, 7$. Again, Qiskit uses a representation in which the first qubit is on the right-most side of the tensor product and the third qubit is on the left-most side:\n",
- "\n",
- "$$\\left|abc\\right\\rangle : \\underset{\\text{qubit 2}}{\\left|a\\right\\rangle}\\otimes \\underset{\\text{qubit 1}}{\\left|b\\right\\rangle}\\otimes \\underset{\\text{qubit 0}}{\\left|c\\right\\rangle}.$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### Toffoli gate ($ccx$ gate)\n",
- "\n",
- "The [Toffoli gate](https://en.wikipedia.org/wiki/Quantum_logic_gate#Toffoli_(CCNOT)_gate) flips the third qubit if the first two qubits (LSB) are both $\\left|1\\right\\rangle$:\n",
- "\n",
- "$$\\left|abc\\right\\rangle \\rightarrow \\left|bc\\oplus a\\right\\rangle \\otimes \\left|b\\right\\rangle \\otimes \\left|c\\right\\rangle.$$\n",
- "\n",
- "In matrix form, the Toffoli gate is\n",
- "$$\n",
- "C_{CX} = \n",
- "\\begin{pmatrix}\n",
- "1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
- "0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
- "0 & 0 & 1 & 0 & 0 & 0 & 0 & 0\\\\\n",
- "0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\\\\n",
- "0 & 0 & 0 & 0 & 1 & 0 & 0 & 0\\\\\n",
- "0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\\\\n",
- "0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\\\\\n",
- "0 & 0 & 0 & 1 & 0 & 0 & 0 & 0\n",
- "\\end{pmatrix}.\n",
- "$$"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 53,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:54.132975Z",
- "start_time": "2018-09-29T00:15:54.127056Z"
- }
- },
- "outputs": [],
- "source": [
- "q = QuantumRegister(3)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 54,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:55.291905Z",
- "start_time": "2018-09-29T00:15:54.136934Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 54,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "qc = QuantumCircuit(q)\n",
- "qc.ccx(q[0], q[1], q[2])\n",
- "qc.draw()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 55,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:55.321561Z",
- "start_time": "2018-09-29T00:15:55.294193Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- "array([[1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n",
- " [0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n",
- " [0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n",
- " [0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j],\n",
- " [0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n",
- " [0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j],\n",
- " [0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],\n",
- " [0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j]])"
- ]
- },
- "execution_count": 55,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "job = execute(qc, backend)\n",
- "job.result().get_unitary(qc, decimals=3)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### Controlled swap gate (Fredkin Gate)\n",
- "\n",
- "The [Fredkin gate](https://en.wikipedia.org/wiki/Quantum_logic_gate#Fredkin_(CSWAP)_gate), or the _controlled swap gate_, exchanges the second and third qubits if the first qubit (LSB) is $\\left|1\\right\\rangle$:\n",
- "\n",
- "$$ \\left|abc\\right\\rangle \\rightarrow \\begin{cases} \\left|bac\\right\\rangle~~\\text{if}~c=1 \\cr \\left|abc\\right\\rangle~~\\text{if}~c=0 \\end{cases}.$$\n",
- "\n",
- "In matrix form, the Fredkin gate is\n",
- "\n",
- "$$\n",
- "C_{\\mathrm{SWAP}} = \n",
- "\\begin{pmatrix}\n",
- "1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
- "0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
- "0 & 0 & 1 & 0 & 0 & 0 & 0 & 0\\\\\n",
- "0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\\\\n",
- "0 & 0 & 0 & 0 & 1 & 0 & 0 & 0\\\\\n",
- "0 & 0 & 0 & 1 & 0 & 0 & 0 & 0\\\\\n",
- "0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\\\\\n",
- "0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\n",
- "\\end{pmatrix}.\n",
- "$$"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 56,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:56.767060Z",
- "start_time": "2018-09-29T00:15:55.324346Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 56,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "qc = QuantumCircuit(q)\n",
- "qc.cswap(q[0], q[1], q[2])\n",
- "qc.draw()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 57,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:56.852089Z",
- "start_time": "2018-09-29T00:15:56.774963Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- "array([[1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n",
- " [0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n",
- " [0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n",
- " [0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j],\n",
- " [0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n",
- " [0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n",
- " [0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],\n",
- " [0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j]])"
- ]
- },
- "execution_count": 57,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "job = execute(qc, backend)\n",
- "job.result().get_unitary(qc, decimals=3)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Non unitary operations\n",
- "\n",
- "Now we have gone through all the unitary operations in quantum circuits we also have access to non-unitary operations. These include measurements, reset of qubits, and classical conditional operations."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 58,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:56.861132Z",
- "start_time": "2018-09-29T00:15:56.856547Z"
- }
- },
- "outputs": [],
- "source": [
- "q = QuantumRegister(1)\n",
- "c = ClassicalRegister(1)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### Measurements\n",
- "\n",
- "We don't have access to all the information when we make a measurement in a quantum computer. The quantum state is projected onto the standard basis. Below are two examples showing a circuit that is prepared in a basis state and the quantum computer prepared in a superposition state."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 59,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:58.079872Z",
- "start_time": "2018-09-29T00:15:56.865487Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 59,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "qc = QuantumCircuit(q, c)\n",
- "qc.measure(q, c)\n",
- "qc.draw()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 60,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:58.124389Z",
- "start_time": "2018-09-29T00:15:58.081861Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- "{'0': 1024}"
- ]
- },
- "execution_count": 60,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "backend = BasicAer.get_backend('qasm_simulator')\n",
- "job = execute(qc, backend, shots=1024)\n",
- "job.result().get_counts(qc)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- " The simulator predicts that 100 percent of the time the classical register returns 0. "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 61,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:59.283582Z",
- "start_time": "2018-09-29T00:15:58.128814Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 61,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "qc = QuantumCircuit(q, c)\n",
- "qc.h(q)\n",
- "qc.measure(q, c)\n",
- "qc.draw()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 62,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:59.318065Z",
- "start_time": "2018-09-29T00:15:59.286200Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- "{'0': 513, '1': 511}"
- ]
- },
- "execution_count": 62,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "job = execute(qc, backend, shots=1024)\n",
- "job.result().get_counts(qc)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- " The simulator predicts that 50 percent of the time the classical register returns 0 or 1. "
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### Reset\n",
- "It is also possible to `reset` qubits to the $\\left|0\\right\\rangle$ state in the middle of computation. Note that `reset` is not a Gate operation, since it is irreversible."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 63,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:16:00.676218Z",
- "start_time": "2018-09-29T00:15:59.322345Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 63,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "qc = QuantumCircuit(q, c)\n",
- "qc.reset(q[0])\n",
- "qc.measure(q, c)\n",
- "qc.draw()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 64,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:16:00.760611Z",
- "start_time": "2018-09-29T00:16:00.681669Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- "{'0': 1024}"
- ]
- },
- "execution_count": 64,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "job = execute(qc, backend, shots=1024)\n",
- "job.result().get_counts(qc)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 65,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:16:02.094104Z",
- "start_time": "2018-09-29T00:16:00.775977Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 65,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "qc = QuantumCircuit(q, c)\n",
- "qc.h(q)\n",
- "qc.reset(q[0])\n",
- "qc.measure(q, c)\n",
- "qc.draw()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 66,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:16:02.129340Z",
- "start_time": "2018-09-29T00:16:02.096088Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- "{'0': 1024}"
- ]
- },
- "execution_count": 66,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "job = execute(qc, backend, shots=1024)\n",
- "job.result().get_counts(qc)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Here we see that for both of these circuits the simulator always predicts that the output is 100 percent in the 0 state."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### Conditional operations\n",
- "It is also possible to do operations conditioned on the state of the classical register"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 67,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:16:03.290081Z",
- "start_time": "2018-09-29T00:16:02.133254Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 67,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "qc = QuantumCircuit(q, c)\n",
- "qc.x(q[0]).c_if(c, 0)\n",
- "qc.measure(q,c)\n",
- "qc.draw()"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Here the classical bit always takes the value 0 so the qubit state is always flipped. "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 68,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "{'1': 1024}"
- ]
- },
- "execution_count": 68,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "job = execute(qc, backend, shots=1024)\n",
- "job.result().get_counts(qc)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 69,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:16:04.406486Z",
- "start_time": "2018-09-29T00:16:03.323686Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 69,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "qc = QuantumCircuit(q, c)\n",
- "qc.h(q)\n",
- "qc.measure(q,c)\n",
- "qc.x(q[0]).c_if(c, 0)\n",
- "qc.measure(q,c)\n",
- "qc.draw()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 70,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:16:04.433578Z",
- "start_time": "2018-09-29T00:16:04.408345Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- "{'1': 1024}"
- ]
- },
- "execution_count": 70,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "job = execute(qc, backend, shots=1024)\n",
- "job.result().get_counts(qc)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Here the classical bit by the first measurement is random but the conditional operation results in the qubit being deterministically put into $\\left|1\\right\\rangle$."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### Arbitrary initialization\n",
- "What if we want to initialize a qubit register to an arbitrary state? An arbitrary state for $n$ qubits may be specified by a vector of $2^n$ amplitudes, where the sum of amplitude-norms-squared equals 1. For example, the following three-qubit state can be prepared:\n",
- "\n",
- "$$\\left|\\psi\\right\\rangle = \\frac{i}{4}\\left|000\\right\\rangle + \\frac{1}{\\sqrt{8}}\\left|001\\right\\rangle + \\frac{1+i}{4}\\left|010\\right\\rangle + \\frac{1+2i}{\\sqrt{8}}\\left|101\\right\\rangle + \\frac{1}{4}\\left|110\\right\\rangle$$"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 71,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:16:04.467773Z",
- "start_time": "2018-09-29T00:16:04.437893Z"
- }
- },
- "outputs": [
- {
- "data": {
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- "text/plain": [
- ""
- ]
- },
- "execution_count": 71,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "# Initializing a three-qubit quantum state\n",
- "import math\n",
- "desired_vector = [\n",
- " 1 / math.sqrt(16) * complex(0, 1),\n",
- " 1 / math.sqrt(8) * complex(1, 0),\n",
- " 1 / math.sqrt(16) * complex(1, 1),\n",
- " 0,\n",
- " 0,\n",
- " 1 / math.sqrt(8) * complex(1, 2),\n",
- " 1 / math.sqrt(16) * complex(1, 0),\n",
- " 0]\n",
- "\n",
- "\n",
- "q = QuantumRegister(3)\n",
- "\n",
- "qc = QuantumCircuit(q)\n",
- "\n",
- "qc.initialize(desired_vector, [q[0],q[1],q[2]])\n",
- "qc.draw(output='latex')"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 72,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:16:04.575688Z",
- "start_time": "2018-09-29T00:16:04.476846Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- "array([0.25 +0.j , 0. -0.35355339j,\n",
- " 0.25 -0.25j , 0. +0.j ,\n",
- " 0. +0.j , 0.70710678-0.35355339j,\n",
- " 0. -0.25j , 0. +0.j ])"
- ]
- },
- "execution_count": 72,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "backend = BasicAer.get_backend('statevector_simulator')\n",
- "job = execute(qc, backend)\n",
- "qc_state = job.result().get_statevector(qc)\n",
- "qc_state "
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "[Fidelity](https://en.wikipedia.org/wiki/Fidelity_of_quantum_states) is useful to check whether two states are same or not.\n",
- "For quantum (pure) states $\\left|\\psi_1\\right\\rangle$ and $\\left|\\psi_2\\right\\rangle$, the fidelity is\n",
- "\n",
- "$$\n",
- "F\\left(\\left|\\psi_1\\right\\rangle,\\left|\\psi_2\\right\\rangle\\right) = \\left|\\left\\langle\\psi_1\\middle|\\psi_2\\right\\rangle\\right|^2.\n",
- "$$\n",
- "\n",
- "The fidelity is equal to $1$ if and only if two states are same."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 73,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:16:04.607616Z",
- "start_time": "2018-09-29T00:16:04.580046Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- "1.0"
- ]
- },
- "execution_count": 73,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "state_fidelity(desired_vector,qc_state)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "#### Further details:\n",
- "\n",
- "How does the desired state get generated behind the scenes? There are multiple methods for doing this. Qiskit uses a [method proposed by Shende et al](https://arxiv.org/abs/quant-ph/0406176). Here, the idea is to assume the quantum register to have started from our desired state, and construct a circuit that takes it to the $\\left|00..0\\right\\rangle$ state. The initialization circuit is then the reverse of such circuit.\n",
- "\n",
- "To take an arbitrary quantum state to the zero state in the computational basis, we perform an iterative procedure that disentangles qubits from the register one-by-one. We know that any arbitrary single-qubit state $\\left|\\rho\\right\\rangle$ can be taken to the $\\left|0\\right\\rangle$ state using a $\\phi$-degree rotation about the Z axis followed by a $\\theta$-degree rotation about the Y axis:\n",
- "\n",
- "$$R_y(-\\theta)R_z(-\\phi)\\left|\\rho\\right\\rangle = re^{it}\\left|0\\right\\rangle$$\n",
- "\n",
- "Since now we are dealing with $n$ qubits instead of just 1, we must factorize the state vector to separate the Least Significant Bit (LSB):\n",
- "\n",
- "$$\\begin{align*}\n",
- " \\left|\\psi\\right\\rangle =& \\alpha_{0_0}\\left|00..00\\right\\rangle + \\alpha_{0_1}\\left|00..01\\right\\rangle + \\alpha_{1_0}\\left|00..10\\right\\rangle + \\alpha_{1_1}\\left|00..11\\right\\rangle + ... \\\\&+ \\alpha_{(2^{n-1}-1)_0}\\left|11..10\\right\\rangle + \\alpha_{(2^{n-1}-1)_1}\\left|11..11\\right\\rangle \\\\\n",
- "=& \\left|00..0\\right\\rangle (\\alpha_{0_0}\\left|0\\right\\rangle + \\alpha_{0_1}\\left|1\\right\\rangle) + \\left|00..1\\right\\rangle (\\alpha_{1_0}\\left|0\\right\\rangle + \\alpha_{1_1}\\left|1\\right\\rangle) + ... \\\\&+ \\left|11..1\\right\\rangle (\\alpha_{(2^{n-1}-1)_0}(\\left|0\\right\\rangle + \\alpha_{(2^{n-1}-1)_1}\\left|1\\right\\rangle) \\\\\n",
- "=& \\left|00..0\\right\\rangle\\left|\\rho_0\\right\\rangle + \\left|00..1\\right\\rangle\\left|\\rho_1\\right\\rangle + ... + \\left|11..1\\right\\rangle\\left|\\rho_{2^{n-1}-1}\\right\\rangle\n",
- "\\end{align*}$$\n",
- "\n",
- "Now each of the single-qubit states $\\left|\\rho_0\\right\\rangle, ..., \\left|\\rho_{2^{n-1}-1}\\right\\rangle$ can be taken to $\\left|0\\right\\rangle$ by finding appropriate $\\phi$ and $\\theta$ angles per the equation above. Doing this simultaneously on all states amounts to the following unitary, which disentangles the LSB:\n",
- "\n",
- "$$U = \\begin{pmatrix} \n",
- "R_{y}(-\\theta_0)R_{z}(-\\phi_0) & & & &\\\\ \n",
- "& R_{y}(-\\theta_1)R_{z}(-\\phi_1) & & &\\\\\n",
- "& . & & &\\\\\n",
- "& & . & &\\\\\n",
- "& & & & R_y(-\\theta_{2^{n-1}-1})R_z(-\\phi_{2^{n-1}-1})\n",
- "\\end{pmatrix} $$\n",
- "\n",
- "Hence,\n",
- "\n",
- "$$U\\left|\\psi\\right\\rangle = \\begin{pmatrix} r_0e^{it_0}\\\\ r_1e^{it_1}\\\\ . \\\\ . \\\\ r_{2^{n-1}-1}e^{it_{2^{n-1}-1}} \\end{pmatrix}\\otimes\\left|0\\right\\rangle$$\n",
- "\n",
- "\n",
- "U can be implemented as a \"quantum multiplexor\" gate, since it is a block diagonal matrix. In the quantum multiplexor formalism, a block diagonal matrix of size $2^n \\times 2^n$, and consisting of $2^s$ blocks, is equivalent to a multiplexor with $s$ select qubits and $n-s$ data qubits. Depending on the state of the select qubits, the corresponding blocks are applied to the data qubits. A multiplexor of this kind can be implemented after recursive decomposition to primitive gates of cx, rz and ry."
- ]
- }
- ],
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diff --git a/qiskit/advanced/terra/terra_parallel_tools.ipynb b/qiskit/advanced/terra/terra_parallel_tools.ipynb
deleted file mode 100644
index 5aa19f26f..000000000
--- a/qiskit/advanced/terra/terra_parallel_tools.ipynb
+++ /dev/null
@@ -1,336 +0,0 @@
-{
- "cells": [
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- " Trusted Notebook\" align=\"middle\">"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "# Using the Qiskit Terra parallel tools"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "In this tutorial we will see how to leverage the `parallel_map` routine in Qiskit Terra to execute functions in parallel, and track the progress of these parallel tasks using progress bars."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-12-18T18:59:57.469931Z",
- "start_time": "2018-12-18T18:59:57.465314Z"
- }
- },
- "outputs": [],
- "source": [
- "from qiskit import *\n",
- "from qiskit.tools.parallel import parallel_map\n",
- "from qiskit.tools.events import TextProgressBar\n",
- "from qiskit.tools.jupyter import * # Needed to load the Jupyter HTMLProgressBar"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Define a function that builds a single Quantum Volume circuit"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Here we will construct a set of 1000 Quantum Volume circuits of width and depth 4. For a technical discussion of Quantum Volume, see https://arxiv.org/abs/1811.12926."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-12-18T18:59:58.031719Z",
- "start_time": "2018-12-18T18:59:58.028761Z"
- }
- },
- "outputs": [],
- "source": [
- "num_circuits = 1000\n",
- "width = 4\n",
- "depth = 4"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-12-18T18:59:58.194568Z",
- "start_time": "2018-12-18T18:59:58.190192Z"
- }
- },
- "outputs": [],
- "source": [
- "import copy\n",
- "import math\n",
- "import numpy as np\n",
- "from qiskit.quantum_info.random import random_unitary \n",
- "from qiskit.quantum_info.synthesis import two_qubit_cnot_decompose"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "In preparation for executing in parallel, the code below takes an index value, an array of random number seeds, and the width and depth of the circuit as inputs."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-12-18T18:59:58.369775Z",
- "start_time": "2018-12-18T18:59:58.352565Z"
- }
- },
- "outputs": [],
- "source": [
- "def build_qv_circuit(idx, seeds, width, depth):\n",
- " \"\"\"Builds a single Quantum Volume circuit. Two circuits,\n",
- " one with measurements, and one without, are returned.\n",
- "\n",
- " The model circuits consist of layers of Haar random\n",
- " elements of SU(4) applied between corresponding pairs\n",
- " of qubits in a random bipartition.\n",
- " \n",
- " See: https://arxiv.org/abs/1811.12926\n",
- " \"\"\"\n",
- " np.random.seed(seeds[idx])\n",
- " q = QuantumRegister(width, \"q\")\n",
- " c = ClassicalRegister(width, \"c\")\n",
- " # Create measurement subcircuit\n",
- " qc = QuantumCircuit(q,c)\n",
- " # For each layer\n",
- " for j in range(depth):\n",
- " # Generate uniformly random permutation Pj of [0...n-1]\n",
- " perm = np.random.permutation(width)\n",
- " # For each pair p in Pj, generate Haar random SU(4)\n",
- " # Decompose each SU(4) into CNOT + SU(2) and add to Ci\n",
- " for k in range(math.floor(width/2)):\n",
- " qubits = [int(perm[2*k]), int(perm[2*k+1])]\n",
- " U = random_unitary(4) \n",
- " for gate in two_qubit_cnot_decompose(U):\n",
- " gate_name = gate[0].name\n",
- " gate_params = gate[0].params\n",
- " # The first qubit argument used in gate\n",
- " i0 = qubits[gate[1][0].index]\n",
- " if gate_name == \"cx\":\n",
- " # The second qubit argument used in gate\n",
- " i1 = qubits[gate[1][1].index]\n",
- " qc.cx(q[i0], q[i1])\n",
- " elif gate_name == \"u1\":\n",
- " qc.u1(gate_params[2], q[i0])\n",
- " elif gate_name == \"u2\":\n",
- " qc.u2(gate_params[1], gate_params[2], q[i0])\n",
- " elif gate_name == \"u3\":\n",
- " qc.u3(gate_params[0], gate_params[1], gate_params[2], q[i0])\n",
- " elif gate_name == \"id\":\n",
- " pass # do nothing\n",
- " qc_no_meas = copy.deepcopy(qc)\n",
- " # Create circuit with final measurement\n",
- " qc.measure(q,c)\n",
- " return qc, qc_no_meas"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Generate 1000 circuits in parallel and track progress"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Because Quantum Volume circuits are generated randomly for the NumPy random number generator, we must be careful when running in parallel. If the random number generator is not explicitly seeded, the computer uses the current time as a seed value. When running in parallel, this can result in each process starting with the same seed value, and thus not giving random results. Here we generate all the random seed values needed, and pass this into `parallel_map` as an extra argument in `task_args`, along with `width` and `depth`. The main function argument passed in `parallel_map` is just an array that indexes the processes and seed value."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-12-18T19:09:08.823589Z",
- "start_time": "2018-12-18T19:08:50.977782Z"
- }
- },
- "outputs": [],
- "source": [
- "num_circuits = 1000\n",
- "seeds = np.random.randint(np.iinfo(np.int32).max, size=num_circuits)\n",
- "TextProgressBar()\n",
- "parallel_map(build_qv_circuit, np.arange(num_circuits), task_args=(seeds, width, depth));"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Use a Jupyter progress bar"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-12-18T19:09:28.110746Z",
- "start_time": "2018-12-18T19:09:08.827393Z"
- }
- },
- "outputs": [],
- "source": [
- "seeds = np.random.randint(np.iinfo(np.int32).max, size=num_circuits)\n",
- "HTMLProgressBar()\n",
- "parallel_map(build_qv_circuit, np.arange(num_circuits), task_args=(seeds, width, depth));"
- ]
- }
- ],
- "metadata": {
- "hide_input": false,
- "kernelspec": {
- "display_name": "Python 3",
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- "name": "python3"
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diff --git a/qiskit/advanced/terra/using_the_transpiler.ipynb b/qiskit/advanced/terra/using_the_transpiler.ipynb
deleted file mode 100644
index 5be970627..000000000
--- a/qiskit/advanced/terra/using_the_transpiler.ipynb
+++ /dev/null
@@ -1,608 +0,0 @@
-{
- "cells": [
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- " Trusted Notebook\" align=\"middle\">"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "# Introducing the Qiskit Transpiler"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Introduction"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "In this notebook we introduce the Qiskit transpiler and walk through some examples of circuit transformations using **transpiler passes**.\n",
- "\n",
- "The transpiler is Qiskit's circuit-rewriting framework. We intentionally do not call it a \"compiler\", since we use compiler in the context of a larger translation from high-level applications (potentially many circuits, with classical control flow between them) down to the level of machine pulses. The transpiler, in contrast, is responsible only for circuit-level analysis and transformations.\n",
- "\n",
- "Circuits are a fundamental and universal model of computation on quantum computers. In the Noisy Intermediate-Scale Quantum (NISQ) regime, we are always limited by the scarcity of quantum resources. The transpiler is a tool that helps us reduce the number of gates and qubits, in order to increase the fidelity of executions.\n",
- "\n",
- "Circuit optimization is a difficult task (in general QMA-complete). To make it approachable, we break it down. Each transpiler pass is thus responsible for doing one small, well-defined task. Through this \"separation of responsibilities\", we are able to chain together different passes to achieve an aggressive optimization goal.\n",
- "\n",
- "Which passes are chained together and in which order has a major effect on the final outcome. This pipeline is determined by a **pass manager**, which schedules the passes and also allows passes to communicate with each other by providing a shared space."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Transpiler API"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "There are two main ways to use the transpiler:\n",
- "1. Use the ``transpile()`` function, and specify some desired transpilation options, like ``basis_gates``, ``coupling_map``, ``initial_layout`` of qubits, or ``optimization_level``.\n",
- "\n",
- "2. Create your own custom pass manager."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 58,
- "metadata": {
- "collapsed": true
- },
- "outputs": [],
- "source": [
- "from qiskit.compiler import transpile\n",
- "from qiskit.transpiler import PassManager"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Let's start with a very simple transpilation task. Suppose we have a single Toffoli gate that we want to unroll to a more fundamental basis."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 60,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 60,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "from qiskit import QuantumRegister, QuantumCircuit\n",
- "q = QuantumRegister(3, 'q')\n",
- "circ = QuantumCircuit(q)\n",
- "circ.ccx(q[0], q[1], q[2])\n",
- "circ.draw()"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### *transpile( ) function*"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "This function is a convenience function, allowing the user to quickly transpile a circuit with minimal effort. Refer to the function documentation for more info."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 65,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "image/png": 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2Fpo3N0X/Vz0xYcIEvPbaa/VuzrpFM13sXfjk1J5zSbmVxmEbyyaVHn/4bc+B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\nO0kNM9eadGwU83ERqJtxXp8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- "text/plain": [
- ""
- ]
- },
- "execution_count": 65,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "new_circ = transpile(circ, basis_gates=['u1', 'u3', 'u2', 'cx'])\n",
- "new_circ.draw(output='mpl')"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### *PassManager object*"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "This lets you specify the passes you want."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 66,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "image/png": 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2Fpo3N0X/Vz0xYcIEvPbaa/VuzrpFM13sXfjk1J5zSbmVxmEbyyaVHn/4bc+B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\nZgAAAABJRU5ErkJggg==\n",
- "text/plain": [
- ""
- ]
- },
- "execution_count": 66,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "from qiskit.transpiler.passes import Unroller\n",
- "pass_ = Unroller(['u1', 'u2', 'u3', 'cx'])\n",
- "pm = PassManager(pass_)\n",
- "new_circ = pm.run(circ)\n",
- "new_circ.draw(output='mpl')"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "All of Qiskit's transpiler passes are accessible from ``qiskit.transpiler.passes``."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 56,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "['BarrierBeforeFinalMeasurements',\n",
- " 'BasicSwap',\n",
- " 'CXCancellation',\n",
- " 'CXDirection',\n",
- " 'CheckCXDirection',\n",
- " 'CheckMap',\n",
- " 'Collect2qBlocks',\n",
- " 'CommutationAnalysis',\n",
- " 'CommutativeCancellation',\n",
- " 'ConsolidateBlocks',\n",
- " 'CountOps',\n",
- " 'DAGFixedPoint',\n",
- " 'Decompose',\n",
- " 'DenseLayout',\n",
- " 'Depth',\n",
- " 'EnlargeWithAncilla',\n",
- " 'FixedPoint',\n",
- " 'FullAncillaAllocation',\n",
- " 'LegacySwap',\n",
- " 'LookaheadSwap',\n",
- " 'MergeAdjacentBarriers',\n",
- " 'NoiseAdaptiveLayout',\n",
- " 'NumTensorFactors',\n",
- " 'Optimize1qGates',\n",
- " 'OptimizeSwapBeforeMeasure',\n",
- " 'RemoveDiagonalGatesBeforeMeasure',\n",
- " 'RemoveResetInZeroState',\n",
- " 'ResourceEstimation',\n",
- " 'SetLayout',\n",
- " 'Size',\n",
- " 'StochasticSwap',\n",
- " 'TrivialLayout',\n",
- " 'Unroll3qOrMore',\n",
- " 'Unroller',\n",
- " 'Width']"
- ]
- },
- "execution_count": 56,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "from qiskit.transpiler import passes\n",
- "[pass_ for pass_ in dir(passes) if pass_[0].isupper()]"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Different Variants of the Same Pass"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "There can be passes that do the same job, but in different ways. For example, the ``TrivialLayout``, ``DenseLayout`` and ``NoiseAdaptiveLayout`` all choose a layout (binding of virtual qubits to physical qubits), but use different algorithms and objectives. Similarly, the ``BasicSwap``, ``LookaheadSwap`` and ``StochasticSwap`` all insert swaps to make the circuit compatible with the coupling map. The modularity of the transpiler allows plug-and-play replacements for each pass.\n",
- "\n",
- "Below, we show the swapper passes all applied to the same circuit, to transform it to match a linear chain topology. You can see differences in performance, where the StochasticSwap is clearly the best. However, this can vary depending on the input circuit."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 21,
- "metadata": {},
- "outputs": [],
- "source": [
- "from qiskit.transpiler import CouplingMap, Layout\n",
- "from qiskit.transpiler.passes import BasicSwap, LookaheadSwap, StochasticSwap\n",
- "\n",
- "coupling = [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6]]\n",
- "\n",
- "qr = QuantumRegister(7, 'q')\n",
- "circuit = QuantumCircuit(qr)\n",
- "circuit.h(qr[3])\n",
- "circuit.cx(qr[0], qr[6])\n",
- "circuit.cx(qr[6], qr[0])\n",
- "circuit.cx(qr[0], qr[1])\n",
- "circuit.cx(qr[3], qr[1])\n",
- "circuit.cx(qr[3], qr[0])\n",
- "\n",
- "coupling_map = CouplingMap(couplinglist=coupling)\n",
- "layout = Layout({qr[i]: i for i in range(coupling_map.size())})\n",
- "\n",
- "bs = BasicSwap(coupling_map=coupling_map, initial_layout=layout)\n",
- "pass_manager = PassManager(bs)\n",
- "basic_circ = pass_manager.run(circuit)\n",
- "\n",
- "ls = LookaheadSwap(coupling_map=coupling_map, initial_layout=layout)\n",
- "pass_manager = PassManager(ls)\n",
- "lookahead_circ = pass_manager.run(circuit)\n",
- "\n",
- "ss = StochasticSwap(coupling_map=coupling_map, initial_layout=layout)\n",
- "pass_manager = PassManager(ss)\n",
- "stochastic_circ = pass_manager.run(circuit)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 22,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "image/png": 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2qZCIiOh6GFxERCQUBhcREQmFwUVEREJhcBERkVAYXEREJBQGFxERCYXBRURE\nQmFwERGRUBhcREQkFAYXEREJhcFFRERCYXAREZFQGFxERCQUBhcREQmFwUVEREJhcBERkVAYXERE\nJBQGFxERCYXBRUREQmFwERGRUBhcREQklG6WLoCovZ555hmUlJSYfd6AgACsWbPG7PMSdXUMLhJe\nSUkJvtt/AE5eQ8w2Z9XJQ2abi4gMMbioU3DyGoL4lTlmm++j52LMNhcRGeI5LiIiEgqDi4iIhMLg\nIiIioTC4iIhIKAwuIiISCoOLiIiEwuAiIiKhdNngSk9PR1hYmNH9g4KCsG3bto4riIiIjNJlg+ta\nOp0OixcvhpOTE+zs7BAXF4fq6mr99piYGOTm5lqwQjKl9ZOH4NDW9w3aJEnC2tjbUP5tnoWqIjm4\ncuUKMjMzcffdd8POzg4A8Pjjj+O7776zcGU39uOPP2LevHlwcXEBAPj5+eHNN9/EpUuXLFyZ6TG4\n/kulUiEnJweFhYWoqKgAAEyZMkW/ncHVedRX/4pLF87DyWuoQXvdr6fR+Fs9XO4IsExhZHGNjY14\n6KGHMHnyZHz//feor68HAGzevBmhoaF44403LFzh9eXm5sLf3x9r165FZWUlAODw4cOYP38+QkND\nDd6EdwayC66srCz4+PjA1tYW48ePR2JiIuLj4zt83rS0NCQlJcHLywsODg5YuXIltm7dCrVaDQDw\n9/eHUqlEUVFRh9dCHevcsQNQWCnRz/Mug/bqU4fRq48T7JxcLVQZWdoLL7yAvLw/jribm5v17Vf/\nnZCQgG+++cYitbXk9OnTeOSRR9DU1ARJkvTtV2s+ePAgpk6daqHqOoasgmvjxo1ITExERkYGtFot\noqOjkZKSgsDAwFaNo1Kp4OfnZ3T/2tpanDlzBkFBQfo2b29v2Nvbo7S0VN8WExODnBzzfR4edYzz\nxw6gj6s3uvWwMWivOnkYLrfzaKurunTpEt5+++0b9rGyspLdXwRITU3F5cuXDULrzyRJQl5eHo4d\nO2bmyjqObIKroaEBCQkJSEtLQ0hICBQKBWbOnAmdTofAwECcP38eoaGhCAsLQ0hICHbs2NHiWMnJ\nySgrKzN6bq1WCwBwcHAwaHd0dIRGo9E/joqK0r8bI3GdP1aC2l9PIfXROw2+9n/0b7jc0bo3SdR5\n7NmzR7802JLm5mZ88cUXBkdjlmbsKYzO9Nolm0+HLygoQHNzMyIjI/VtVVVVAIDAwED0798fu3fv\nhlKpxMmTJ/Hoo49i3759Jpn76gnYuro6g/ba2lrY29vrH6vVari7u5tkzptRKBRmmcfULFW369BQ\no/ueP16CkZMXY9B9jxq0b3oaZqyWAAAUf0lEQVR6DFxu9zd6nIKCAov+nkR9johOp9NBqVRauoxW\nS0hIQEJCgqXLuKGWjhqvJZsjrsrKSjg7Oxu0ZWZmwsXFBQMGDIBSqdQ/WWpra1u1FHgzjo6OcHd3\nR3Fxsb7t5MmT0Gg0BvPk5uYiJsY8f85CkiThvixV99ixY43er7W/nMTl+lp4BN0LO6db9F+6pt9x\nub6uVUdcY8eO7XL7ujN/HT169Ka/c4VCAQ8PD4vX+uevqKgoo4J0y5YtFq/1Zl/Gkk1wDR48GOXl\n5SgoKEBjYyMyMzOhUqkMzm+dOnUKo0ePRnh4OCZNmmTS+WfNmoUVK1bg1KlT0Gg0SEpKQnh4ODw9\nPQH8sf6dn5+P6Ohok85L5nXuWAm6WfeCk5evQfsvR/bBzskVvRydLFQZWdpdd92FMWPGwMqq5ZdF\nSZLw9NNPm7Gqm5s9ezZ0Ol2L2xUKBVxcXDrVa5dsgis4OBhLly5FbGws3NzcUFhYiJCQEIPguu22\n27Bnzx4UFhZi3rx5LY61fPly+Pr6trj9epKTkzFx4kQEBwfD1dUVOp0OmzZt0m/fvn27fsmSxHX+\n2AG43BEAK6XhKvmvR/fDmRdmdHlvvPEGrK2trxteCoUCfn5+mDNnjgUqa9mECRNaXAm6upy8du1a\ndO/e3ZxldSjZBBcALFu2DDU1NaisrERKSgqOHTumD67Lly/r+9nb28PW1rbFcZYsWYLDhw+3am6l\nUonVq1ejuroaWq0WW7ZsMQgpcy4TUscZO+uV6/6l5Pvmr8LEF9PNXxDJyrBhw7Br1y4EBBi+ibGy\nssIjjzyCnTt36s+Jy4VSqURWVhYWLlwIa2trg22enp749NNPERsba6HqOoZsLs64lkajgVqt1gfX\nvn37sGTJEiiVSjQ1NSElJcWs9Xh4eJjlfjIisqzhw4ejqKgI+/fvR1lZGbp3745x48bBzc3N0qW1\nqEePHlizZg3+8Y9/YPv27aivr4eXlxfGjh17w6VPUck2uA4dOgQ7Ozt4e3sDAEaPHo1du3aZbPyA\ngIBW3ZT38ssvm2xuIpK/4cOHY/jw4ZYuo1X69OmDRx999OYdBSfb4AoNDTW4h8rUAgIC/rIcQERE\n8tf5jiGJiKhTY3AREZFQGFxERCQUBhcREQmFwUVEREJhcBERkVBkezk8UWtUnTyEj54z3yebVJ08\nBJ++/BMoRJbA4CLhWeJ+PJ++gbwPkMhCFFJrPkue6AYUCkWr/jQBtR33NXVlPMdFRERCYXAREZFQ\nGFxERCQUBhcREQmFwUVEREJhcBERkVAYXEREJBQGFxERCYXBRUREQmFwERGRUBhcREQkFAYXEREJ\nhcFFRERCYXAREZFQGFxERCQUBhcREQmFwUVEREJhcBERkVAYXEREJBQGFxERCYXBRUREQmFwERGR\nULpscKWnpyMsLMzo/kFBQdi2bVvHFUREREbpssF1LZ1Oh8WLF8PJyQl2dnaIi4tDdXW1fntMTAxy\nc3MtWCEREQEMLj2VSoWcnBwUFhaioqICADBlyhT9dgYXEZE8yC64srKy4OPjA1tbW4wfPx6JiYmI\nj4/v8HnT0tKQlJQELy8vODg4YOXKldi6dSvUajUAwN/fH0qlEkVFRR1eCxERtUxWwbVx40YkJiYi\nIyMDWq0W0dHRSElJQWBgYKvGUalU8PPzM7p/bW0tzpw5g6CgIH2bt7c37O3tUVpaqm+LiYlBTk5O\nq2ohIiLTkk1wNTQ0ICEhAWlpaQgJCYFCocDMmTOh0+kMgqumpgZ9+vTBpk2bWhwrOTkZZWVlRs+t\n1WoBAA4ODgbtjo6O0Gg0+sdRUVHIy8szelwiIjI92QRXQUEBmpubERkZqW+rqqoCAIPgevXVVzF6\n9GiTzm1nZwcAqKurM2ivra2Fvb29/rFarYa7u7tJ5yYiotbpZukCrqqsrISzs7NBW2ZmJlxcXDBg\nwAAAQHl5OWpqagyW9EzB0dER7u7uKC4uRkBAAADg5MmT0Gg0BkuOubm5iIuLM+ncLVEoFGaZx9RE\nrVtE3NfU2UiSZFQ/2QTX4MGDUV5ejoKCAowaNQrZ2dlQqVQIDQ3V93nppZfwyiuv4P333zf5/LNm\nzcKKFSswbtw49OvXD0lJSQgPD4enpycA4NKlS8jPz8eGDRtMPvf1GPsLlBOFQiFk3SLivqauTDZL\nhcHBwVi6dCliY2Ph5uaGwsJChISE6JcJ9+7di379+sHb2/umYy1fvhy+vr6tmj85ORkTJ05EcHAw\nXF1dodPpDM6jbd++HYGBgejfv3/rfjAiIjIphSTjt22enp5YtWoV4uPj8a9//Qsff/wxevbsifLy\ncvTu3RupqakYNWpUm8ZOT09Heno6du7caVT/adOmwdfXF4sWLWrTfF0BjwLMh/uaujLZLBVeS6PR\nQK1W64+4FixYgAULFgAAXn75Zfj4+LQ5tNrCw8PDLPeTERHRjcn2iGvv3r2IiIhAXV1dh5yELikp\nQUlJCaZOnWrysbsqHgWYD/c1dWWyDS4SD19MzYf7mroy2VycQUREZAwGFxERCYXBRUREQmFwERGR\nUBhcREQkFAYXEREJhcFFRERCYXAREZFQGFxERCQUBhcREQmFwUVEREJhcBERkVAYXEREJBQGFxER\nCYXBRUREQmFwERGRUBhcREQkFAYXEREJhcFFRERCYXAREZFQGFxERCQUBhcREQmFwUVEREJhcBER\nkVAYXEREJBQGFxERCYXBRUREQmFwERGRUBhcREQkFAYXEREJhcFFRERCYXAREZFQumxwpaenIyws\nzOj+QUFB2LZtW8cVRERERumywXUtnU6HxYsXw8nJCXZ2doiLi0N1dbV+e0xMDHJzcy1YIRERAQwu\nPZVKhZycHBQWFqKiogIAMGXKFP12BhcRkTzILriysrLg4+MDW1tbjB8/HomJiYiPj+/wedPS0pCU\nlAQvLy84ODhg5cqV2Lp1K9RqNQDA398fSqUSRUVFHV4LERG1TFbBtXHjRiQmJiIjIwNarRbR0dFI\nSUlBYGBgq8ZRqVTw8/Mzun9tbS3OnDmDoKAgfZu3tzfs7e1RWlqqb4uJiUFOTk6raiEiItOSTXA1\nNDQgISEBaWlpCAkJgUKhwMyZM6HT6fTB1bNnT4SFhSEsLAxpaWktjpWcnIyysjKj59ZqtQAABwcH\ng3ZHR0doNBr946ioKOTl5bXmxyIiIhPrZukCriooKEBzczMiIyP1bVVVVQCgDy5XV1fs3LnT5HPb\n2dkBAOrq6gzaa2trYW9vr3+sVqvh7u5u8vmvR6FQmGUeUxO1bhFxX1NnI0mSUf1kE1yVlZVwdnY2\naMvMzISLiwsGDBgAADh37hzGjh2LPn364H//93/h5eVlkrkdHR3h7u6O4uJiBAQEAABOnjwJjUZj\nsOSYm5uLuLg4k8x5M8b+AuVEoVAIWbeIuK+pK5PNUuHgwYNRXl6OgoICNDY2IjMzEyqVyuD81unT\np1FQUID58+dj+vTpJp1/1qxZWLFiBU6dOgWNRoOkpCSEh4fD09MTAHDp0iXk5+cjOjrapPMSEVHr\nyCa4goODsXTpUsTGxsLNzQ2FhYUICQkxCK7+/fsDAO677z79JevXs3z5cvj6+rZq/uTkZEycOBHB\nwcFwdXWFTqfDpk2b9Nu3b9+OwMBAfQ1ERGQZCknG6w2enp5YtWoV4uPjUV9fj549e0KpVOLQoUOY\nPn06fvjhhzaPnZ6ejvT0dKPPmU2bNg2+vr5YtGhRm+fs7Lh8ZT7c19SVyeYc17U0Gg3UarX+iOvI\nkSOYPXu2/kKKdevWmbUeDw8Ps9xPRkRENybbI669e/ciIiICdXV1HXL1VElJCUpKSjB16lSTj91V\n8SjAfLivqSuTbXCRePhiaj7c19SVyebiDCIiImMwuIiISCgMLiIiEgqDi4iIhMLgIiIioTC4iIhI\nKAwuIiISCoOLiIiEwuAiIiKhMLiIiEgoDC4iIhIKg4uIiITC4CIiIqEwuIiISCgMLiIiEgqDi4iI\nhMLgIiIioTC4iIhIKAwuIiISCoOLiIiEwuAiIiKhMLiIiEgoDC4iIhIKg4uIiITC4CIiIqEwuIiI\nSCjdLF0AiaupqQkHDx5EUVERzp49CwBYu3YtgoKC4O/vDxsbGwtXSESdkUKSJMnSRZBYzp8/jzff\nfBNpaetRWXn+un0c+/TBtKlTsXDhQnh4eJi5ws5PoVCA/3Wpq2JwkdEkScKHH36IufPmofbiRXgG\nP4A7x8VhwB2BcBjggZQoF0zfeACVx0twbFcOyr/9HDY21li5YgXmzJkDKyuuTJsKg4u6Mi4VklEk\nSUJSUhJWrVqFgYOGY8rrKejrfsdf+tk7u8He2Q0+d0dDU1mBHf9KwLx581BYWIgNGzZAqVRaoHoi\n6kwYXGSU1157DatWrYJf1DSEzXkdVkYEkL2zGx56ZTN++OB/8f77KvTu3Rtvv/22Gaolos6sy67d\npKenIywszOj+QUFB2LZtW8cVJGP79u3DP/7xD9wZFodxc1cYFVpXKRQKhDyeiGGxTyM1NRV5eXkd\nWCkRdQVdNriupdPpsHjxYjg5OcHOzg5xcXGorq7Wb4+JiUFubq4FK7QMSZIwe/ZT6N3XBePmroBC\noWjTOKFPLoGT5yDMnv0UmpqaTFxl1/Dbb79h48aNmDt3LgAgKyuL+5K6JAbXf6lUKuTk5KCwsBAV\nFRUAgClTpui3d9Xg2rt3Lw4cKMaIvy2Cja1Dm8fp1sMao6a+gLNnK/Dpp5+asMKu4YsvvsAtt9yC\nqVOnIjU1FQDw6KOP4tZbb8W3335r4eqIzEt2wZWVlQUfHx/Y2tpi/PjxSExMRHx8fIfPm5aWhqSk\nJHh5ecHBwQErV67E1q1boVarAQD+/v5QKpUoKirq8Frk5L333oN1L1vcdW9cu8fyHH4fHFxuxcaN\nG01QWdexZ88exMTEQKPRAACam5v126qqqjB+/HgcOnTIUuURmZ2sgmvjxo1ITExERkYGtFotoqOj\nkZKSgsDAwFaNo1Kp4OfnZ3T/2tpanDlzBkFBQfo2b29v2Nvbo7S0VN8WExODnJycVtUiuu+/L8SA\nu4aju03vdo9lpVTC1W80Cgt/4KXcrfDSSy+hubnZILCuam5uxu+//w6VSmWByogsQzbB1dDQgISE\nBKSlpSEkJAQKhQIzZ86ETqfTB1dpaSkiIiJw7733Ytq0aS2OlZycjLKyMqPn1mq1AAAHB8OlMEdH\nR/27XACIiorqUhcXNDc348iRw+jvNdRkYzp7D0V1dRUqKytNNmZndubMGeTn5183tK5qbm5GVlYW\n6uvrzVgZkeXI5nL4goICNDc3IzIyUt9WVVUFAAgMDERjYyMWLVqE7OzsvwRMe9nZ2QEA6urqDNpr\na2thb2+vf6xWq+Hu7m7SueWssbERV65cgbWt/c07G6lH7z/Gqq+vh4uLi8nG7ax+/fVXo/o1NTWh\npqYGtra2HVwRkeXJJrgqKyvh7Oxs0JaZmQkXFxcMGDAAu3btgp2dHZ544gnU1dVh0aJFiI6ONsnc\njo6OcHd3R3FxMQICAgAAJ0+ehEajMVhyzM3NRVxc+8/1GKOtV+91hL3pr2Fv+mtG9V0T6WRUPx8f\nn/aURNfh6elp6RKI2sXYUwiyCa7BgwejvLwcBQUFGDVqFLKzs6FSqRAaGgoAOHv2LIqLi1FSUgJJ\nknD33XdjzJgxBkdE7TFr1iysWLEC48aNQ79+/ZCUlITw8HD9i8GlS5eQn5+PDRs2mGS+m5HLOaA7\n7rwLuj6eePDlTTftuybSCc98WXXDPt+8+RxO7f4YtRcv8iOgjCBJEoKCglBaWtricqFSqUR4eHiX\nWsamrk02rxzBwcFYunQpYmNj4ebmhsLCQoSEhOjPb/Xt2xcjR46Eo6Mj+vTpAz8/P5SXl193rOXL\nl8PX17dV8ycnJ2PixIkIDg6Gq6srdDodNm36vxfr7du3IzAwEP3792/7DymgkBHBOPfjfuiutP9+\nIUmS8MuhvRgeFMTQMpJCocCLL77YYmhd/czC5ORkM1dGZDmyevVYtmwZampqUFlZiZSUFBw7dkwf\nXCNHjkR5eTmamprQ2NiIo0ePtvip40uWLMHhw4dbNbdSqcTq1atRXV0NrVaLLVu2GIRUbm4uYmJi\n2v7DCeqxxx5DQ10NTnz3RbvH+vXID6hW/4S//e1vJqis65g0aRLeeustfdgrFAr9UnK3bt2QkZGB\ne+65x5IlEpmVbJYKr6XRaKBWq/XB5eDggEWLFmHcuHFobGzEggUL0K9fP7PV4+HhYZb7yeQmIiIC\nnp634YfM1fAKiUC3HtZtGkdqbsZ376vg4OiIxx9/3MRVdn5PP/00oqOjsW7dOuzbtw8KhQJjxozB\nzJkzeZELdTmy/bMme/fuRUREBOrq6jrkQoWSkhKUlJRg6tSpJh+7s8nLy0N0dDSCHp6Pe2a81GK/\nG53jOpCThoLUpVi/fj1mzpzZUaUSURcg2+AieZk1axbWr1+PMbNewbBJT123T0vB9ePOLdi2ag4i\nIyLx+eefyeqKSSISj2yXCkle3nrrLVTX1OCTtBdReawEY+csR0/7vjf8nsbf6vHthldR+tk7uGfM\nGGze/CFDi4jajcFFRunevTuyNm/G8uXL8corr+D0/q8x6IG/4a5xD6O/5yAou/cAADTrruDCmWM4\ntjsHR7ZuwqXaKixcuBCvv/46evbsaeGfgog6Ay4VUquVlZVh+fLl+Pjjj3HlyhUou/eAvZMrLv5y\nCt2te6Lp8m9QKBSYEBWF55OTcffdd1u6ZCLqRBhc1Gbnz5/Hzp07UVRUhLNnzyIzMxMLFy7E8OHD\nMWbMmC718VhEZD4MLiIiEoqsbkAmIiK6GQYXEREJhcFFRERCYXAREZFQGFxERCQUBhcREQmFwUVE\nREJhcBERkVAYXEREJBQGFxERCYXBRUREQmFwERGRUBhcREQkFAYXEREJhcFFRERCYXAREZFQGFxE\nRCQUBhcREQmFwUVEREJhcBERkVAYXEREJJT/D0zFCoU0Ts8rAAAAAElFTkSuQmCC\n",
- "text/plain": [
- ""
- ]
- },
- "execution_count": 22,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "circuit.draw(output='mpl')"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 23,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "image/png": 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xx1xQ6X81bNhQGzZs0D333FNqQLIGo27dumnNmjWqW7eukyutfIwxevvtmQpo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\ncuVKu9t15w9IxX0J4izXrl0zd911V4n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llVdo0aIF0dHRjB49mvPnz1fsT0lJITMzsxYr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\nRK5CYII=\n",
- "text/plain": [
- ""
- ]
- },
- "execution_count": 23,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "basic_circ.draw(output='mpl')"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 24,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "image/png": 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XvU+ePInRo0cjLy+vUUaaJyUlISkpCTNnztT7uUlafv75ZwwaNEinKd0qlQq+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\n",
- "text/plain": [
- ""
- ]
- },
- "execution_count": 24,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "lookahead_circ.draw(output='mpl')"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 25,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "image/png": 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UlIQxY8YYtB4nJyeD7Ncgddrsg8CgcO+QyWR48803cOlkAX7b8Z9m9bU/eQGuV1Vi5syZ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\nAhEREYliSCAiIiJRDAlEREQkiiGBiIi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- "text/plain": [
- ""
- ]
- },
- "execution_count": 25,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "stochastic_circ.draw(output='mpl')"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Preset Pass Managers"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Qiskit comes with several pre-defined pass managers, corresponding to various levels of optimization achieved through different pipelines of passes. Currently ``optimization_level`` 0 through 3 are supported; the higher the number, the more optimized it is, at the expense of more time. Choosing a good pass manager may take trial and error, as it depends heavily on the circuit being transpiled and the backend being targeted.\n",
- "\n",
- "Here we illustrate the different levels by looking at a state synthesis circuit. We initialize four qubits to an arbitrary state, and then try to optimize the circuit that achieves this.\n",
- "\n",
- "- ``optimization_level=0``: just maps the circuit to the backend, with no explicit optimization (except whatever optimizations the mapper does).\n",
- "\n",
- "- ``optimization_level=1``: maps the circuit, but also does light-weight optimizations by collapsing adjacent gates.\n",
- "\n",
- "- ``optimization_level=2``: medium-weight optimization, including a noise-adaptive layout and a gate-cancellation procedure based on gate commutation relationships.\n",
- "\n",
- "- ``optimization_level=3``: heavy-weight optimization, which in addition to previous steps, does resynthesis of two-qubit blocks of gates in the circuit."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 29,
- "metadata": {
- "collapsed": true
- },
- "outputs": [],
- "source": [
- "import math\n",
- "from qiskit.test.mock import FakeTokyo\n",
- "\n",
- "qr = QuantumRegister(10)\n",
- "qc = QuantumCircuit(qr)\n",
- "\n",
- "backend = FakeTokyo() # mimics the tokyo device in terms of coupling map and basis gates\n",
- "backend.properties = {} # remove fake properties"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 30,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "image/png": 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Rl8sFn8+Xtr1uFW+88QZ/asgWpFrgN27cQHd3NwYGBmCz2aDRaNDV1QVZlpMK/L/+67/w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\nwBg4kcAYOJHAGDiRwBg4kcD+HwDY0hui12lqAAAAAElFTkSuQmCC\n",
- "text/plain": [
- ""
- ]
- },
- "execution_count": 30,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "random_state = [\n",
- " 1 / math.sqrt(4) * complex(0, 1),\n",
- " 1 / math.sqrt(8) * complex(1, 0),\n",
- " 0,\n",
- " 0,\n",
- " 0,\n",
- " 0,\n",
- " 0,\n",
- " 0,\n",
- " 1 / math.sqrt(8) * complex(1, 0),\n",
- " 1 / math.sqrt(8) * complex(0, 1),\n",
- " 0,\n",
- " 0,\n",
- " 0,\n",
- " 0,\n",
- " 1 / math.sqrt(4) * complex(1, 0),\n",
- " 1 / math.sqrt(8) * complex(1, 0)]\n",
- "\n",
- "qc.initialize(random_state, qr[0:4])\n",
- "qc.draw(output='mpl')"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Now map this to the 20-qubit Tokyo device, with different optimization levels:"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 46,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "gates = {'u3': 15, 'u1': 15, 'cx': 107}\n",
- "depth = 125\n"
- ]
- }
- ],
- "source": [
- "optimized_0 = transpile(qc, backend=backend, seed_transpiler=11, optimization_level=0)\n",
- "print('gates = ', optimized_0.count_ops())\n",
- "print('depth = ', optimized_0.depth())"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 47,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "gates = {'u3': 15, 'cx': 95, 'u1': 10}\n",
- "depth = 108\n"
- ]
- }
- ],
- "source": [
- "optimized_1 = transpile(qc, backend=backend, seed_transpiler=11, optimization_level=1)\n",
- "print('gates = ', optimized_1.count_ops())\n",
- "print('depth = ', optimized_1.depth())"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 48,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "gates = {'u3': 15, 'cx': 40, 'u1': 6}\n",
- "depth = 49\n"
- ]
- }
- ],
- "source": [
- "optimized_2 = transpile(qc, backend=backend, seed_transpiler=11, optimization_level=2)\n",
- "print('gates = ', optimized_2.count_ops())\n",
- "print('depth = ', optimized_2.depth())"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 49,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "gates = {'u3': 50, 'cx': 26, 'u2': 8}\n",
- "depth = 45\n"
- ]
- }
- ],
- "source": [
- "optimized_3 = transpile(qc, backend=backend, seed_transpiler=11, optimization_level=3)\n",
- "print('gates = ', optimized_3.count_ops())\n",
- "print('depth = ', optimized_3.depth())"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "You can see that the circuit gets progressively better (both in terms of depth and the number of expensive cx gates)."
- ]
- }
- ],
- "metadata": {
- "kernelspec": {
- "display_name": "Python 3",
- "language": "python",
- "name": "python3"
- },
- "language_info": {
- "codemirror_mode": {
- "name": "ipython",
- "version": 3
- },
- "file_extension": ".py",
- "mimetype": "text/x-python",
- "name": "python",
- "nbconvert_exporter": "python",
- "pygments_lexer": "ipython3",
- "version": "3.7.3"
- },
- "varInspector": {
- "cols": {
- "lenName": 16,
- "lenType": 16,
- "lenVar": 40
- },
- "kernels_config": {
- "python": {
- "delete_cmd_postfix": "",
- "delete_cmd_prefix": "del ",
- "library": "var_list.py",
- "varRefreshCmd": "print(var_dic_list())"
- },
- "r": {
- "delete_cmd_postfix": ") ",
- "delete_cmd_prefix": "rm(",
- "library": "var_list.r",
- "varRefreshCmd": "cat(var_dic_list()) "
- }
- },
- "types_to_exclude": [
- "module",
- "function",
- "builtin_function_or_method",
- "instance",
- "_Feature"
- ],
- "window_display": false
- }
- },
- "nbformat": 4,
- "nbformat_minor": 2
-}
diff --git a/qiskit/advanced/terra/visualizing_a_quantum_circuit.ipynb b/qiskit/advanced/terra/visualizing_a_quantum_circuit.ipynb
deleted file mode 100644
index 454fd8412..000000000
--- a/qiskit/advanced/terra/visualizing_a_quantum_circuit.ipynb
+++ /dev/null
@@ -1,749 +0,0 @@
-{
- "cells": [
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- " Trusted Notebook\" align=\"middle\">"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "# Visualizing a Quantum Circuit"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 1,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:16:38.758552Z",
- "start_time": "2018-09-29T00:16:37.828380Z"
- }
- },
- "outputs": [],
- "source": [
- "from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Drawing a Quantum Circuit\n",
- "\n",
- "When building a quantum circuit, it often helps to draw the circuit. This is supported natively by a `QuantumCircuit` object. You can either call `print()` on the circuit, or call the `draw()` method on the object. This will render a [ASCII art version](https://en.wikipedia.org/wiki/ASCII_art) of the circuit diagram."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 2,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:17:28.150946Z",
- "start_time": "2018-09-29T00:17:27.979866Z"
- }
- },
- "outputs": [],
- "source": [
- "# Build a quantum circuit\n",
- "\n",
- "n = 3 # number of qubits \n",
- "q = QuantumRegister(n)\n",
- "c = ClassicalRegister(n)\n",
- "\n",
- "circuit = QuantumCircuit(q, c)\n",
- "\n",
- "circuit.x(q[1])\n",
- "circuit.h(q)\n",
- "circuit.cx(q[0], q[1])\n",
- "circuit.measure(q, c);"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 3,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:17:29.971852Z",
- "start_time": "2018-09-29T00:17:29.703427Z"
- }
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- " ┌───┐ ┌─┐\n",
- "q0_0: |0>──────────────────┤ H ├──■─────┤M├\n",
- " ┌───┐┌───┐└───┘┌─┴─┐┌─┐└╥┘\n",
- "q0_1: |0>────────┤ X ├┤ H ├─────┤ X ├┤M├─╫─\n",
- " ┌───┐┌─┐└───┘└───┘ └───┘└╥┘ ║ \n",
- "q0_2: |0>┤ H ├┤M├─────────────────────╫──╫─\n",
- " └───┘└╥┘ ║ ║ \n",
- " c0_0: 0 ══════╬══════════════════════╬══╩═\n",
- " ║ ║ \n",
- " c0_1: 0 ══════╬══════════════════════╩════\n",
- " ║ \n",
- " c0_2: 0 ══════╩═══════════════════════════\n",
- " \n"
- ]
- }
- ],
- "source": [
- "print(circuit)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 4,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 4,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "circuit.draw()"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Alternative Renderers for Circuits\n",
- "\n",
- "A text output is useful for quickly seeing the output while developing a circuit, but it doesn't provide the most flexibility in its output. There are two alternative output renderers for the quantum circuit. One uses [matplotlib](https://matplotlib.org/), and the other uses [LaTeX](https://www.latex-project.org/), which leverages the [qcircuit package](https://github.com/CQuIC/qcircuit). These can be specified by using `mpl` and `latex` values for the `output` kwarg on the draw() method."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 5,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:17:51.417854Z",
- "start_time": "2018-09-29T00:17:51.290944Z"
- }
- },
- "outputs": [
- {
- "data": {
- "image/png": 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\n",
- "text/plain": [
- "
Trusted Notebook\" width=\"500 px\" align=\"left\">"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "# Quantum Circuits\n",
- "\n",
- "The `QuantumCircuit`, `QuantumRegister`, and `ClassicalRegister` are the main objects for Qiskit Terra. Most users will be able to do all they want with these objects. "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 1,
- "metadata": {},
- "outputs": [],
- "source": [
- "import numpy as np\n",
- "from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister\n",
- "from qiskit import BasicAer, execute\n",
- "from qiskit.quantum_info import Pauli, state_fidelity, basis_state, process_fidelity "
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Quantum and Classical Registers\n",
- "\n",
- "Quantum and Classical Registers are declared using the following:"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 2,
- "metadata": {},
- "outputs": [],
- "source": [
- "q0 = QuantumRegister(2, 'q0')\n",
- "c0 = ClassicalRegister(2, 'c0')\n",
- "q1 = QuantumRegister(2, 'q1')\n",
- "c1 = ClassicalRegister(2, 'c1')\n",
- "q_test = QuantumRegister(2, 'q0')"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "The name is optional. If not given, Qiskit will name it $qi$, where $i$ is an interger which will count from 0. The name and size can be returned using the following:"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 3,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "q0\n",
- "2\n"
- ]
- }
- ],
- "source": [
- "print(q0.name)\n",
- "print(q0.size)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "You can test if the registers are the same or different. "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 4,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "True"
- ]
- },
- "execution_count": 4,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "q0==q0"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 5,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "True"
- ]
- },
- "execution_count": 5,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "q0==q_test"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 6,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "False"
- ]
- },
- "execution_count": 6,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "q0==q1"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Quantum Circuits\n",
- "\n",
- "Quantum Circuits are made using registers, which are created either when initiated or by using the `add_register` command. "
- ]
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\n",
- "Note: The registers are listed in the order they are initiated or added (**not** the tensor product for quantum registers).\n",
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\n",
- "Note: The circuit drawer has the last register added at the bottom. If we add a new register it will add it to the bottom of the circuit. \n",
- "
"
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- "### Extending a circuit\n",
- "\n",
- "In many situations you may have two circuits that you want to concatenate to form a new circuit. This is very useful when one circuit has no measurements, and the final circuit represents a measurement. "
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\n",
- "Note: The tensor order in Qiskit goes as $Q_n \\otimes .. Q_1 \\otimes Q_0$\n",
- "
\n",
- "\n",
- "That is the four-qubit statevector of length 16, with the sixth element (`int('0110',2)=6`) being one. Note the element count starts from zero."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 17,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "[0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 1.+0.j 0.+0.j 0.+0.j 0.+0.j\n",
- " 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j]\n"
- ]
- }
- ],
- "source": [
- "backend_sim = BasicAer.get_backend('statevector_simulator')\n",
- "result = execute(circ, backend_sim).result()\n",
- "state = result.get_statevector(circ)\n",
- "print(state)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "To check the fidelity of this state with the `basis_state` in Qiskit Terra, use:"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 18,
- "metadata": {},
- "outputs": [
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- "data": {
- "text/plain": [
- "1.0"
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- "execution_count": 18,
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- ],
- "source": [
- "state_fidelity(basis_state('0110', 4), state)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "We can also use Qiskit Terra to make the unitary operator representing the circuit (provided there are no measurements). This will be a $16\\otimes16$ matrix equal to $I\\otimes X\\otimes X\\otimes I$. To check this is correct, we can use the `Pauli` class and the `process_fidelity` function. "
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- "execution_count": 19,
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- "execution_count": 19,
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- "source": [
- "backend_sim = BasicAer.get_backend('unitary_simulator')\n",
- "result = execute(circ, backend_sim).result()\n",
- "unitary = result.get_unitary(circ)\n",
- "process_fidelity(Pauli(label='IXXI').to_matrix(), unitary)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "To map the information of the quantum state to the classial world, we use the example with measurements `qc`:"
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Trusted Notebook\" align=\"middle\">"
- ]
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- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "# Summary of Quantum Operations "
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- " In this section we will go into the different operations that are available in Qiskit Terra. These are:\n",
- "- Single-qubit quantum gates\n",
- "- Multi-qubit quantum gates\n",
- "- Measurements\n",
- "- Reset\n",
- "- Conditionals\n",
- "- State initialization\n",
- "\n",
- "We will also show you how to use the three different simulators:\n",
- "- unitary_simulator\n",
- "- qasm_simulator\n",
- "- statevector_simulator"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 1,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:22.356783Z",
- "start_time": "2018-09-29T00:15:22.017905Z"
- }
- },
- "outputs": [],
- "source": [
- "# Useful additional packages \n",
- "import matplotlib.pyplot as plt\n",
- "%matplotlib inline\n",
- "import numpy as np\n",
- "from math import pi"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 2,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:24.371649Z",
- "start_time": "2018-09-29T00:15:22.358409Z"
- }
- },
- "outputs": [],
- "source": [
- "from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister, execute\n",
- "from qiskit.tools.visualization import circuit_drawer\n",
- "from qiskit.quantum_info import state_fidelity\n",
- "from qiskit import BasicAer\n",
- "\n",
- "backend = BasicAer.get_backend('unitary_simulator')"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Single Qubit Quantum states\n",
- "\n",
- "A single qubit quantum state can be written as\n",
- "\n",
- "$$\\left|\\psi\\right\\rangle = \\alpha\\left|0\\right\\rangle + \\beta \\left|1\\right\\rangle$$\n",
- "\n",
- "\n",
- "where $\\alpha$ and $\\beta$ are complex numbers. In a measurement the probability of the bit being in $\\left|0\\right\\rangle$ is $|\\alpha|^2$ and $\\left|1\\right\\rangle$ is $|\\beta|^2$. As a vector this is\n",
- "\n",
- "$$\n",
- "\\left|\\psi\\right\\rangle = \n",
- "\\begin{pmatrix}\n",
- "\\alpha \\\\\n",
- "\\beta\n",
- "\\end{pmatrix}.\n",
- "$$\n",
- "\n",
- "Note due to conservation probability $|\\alpha|^2+ |\\beta|^2 = 1$ and since global phase is undetectable $\\left|\\psi\\right\\rangle := e^{i\\delta} \\left|\\psi\\right\\rangle$ we only requires two real numbers to describe a single qubit quantum state.\n",
- "\n",
- "A convenient representation is\n",
- "\n",
- "$$\\left|\\psi\\right\\rangle = \\cos(\\theta/2)\\left|0\\right\\rangle + \\sin(\\theta/2)e^{i\\phi}\\left|1\\right\\rangle$$\n",
- "\n",
- "where $0\\leq \\phi < 2\\pi$, and $0\\leq \\theta \\leq \\pi$. From this it is clear that there is a one-to-one correspondence between qubit states ($\\mathbb{C}^2$) and the points on the surface of a unit sphere ($\\mathbb{R}^3$). This is called the Bloch sphere representation of a qubit state.\n",
- "\n",
- "Quantum gates/operations are usually represented as matrices. A gate which acts on a qubit is represented by a $2\\times 2$ unitary matrix $U$. The action of the quantum gate is found by multiplying the matrix representing the gate with the vector which represents the quantum state.\n",
- "\n",
- "$$\\left|\\psi'\\right\\rangle = U\\left|\\psi\\right\\rangle$$\n",
- "\n",
- "A general unitary must be able to take the $\\left|0\\right\\rangle$ to the above state. That is \n",
- "\n",
- "$$\n",
- "U = \\begin{pmatrix}\n",
- "\\cos(\\theta/2) & a \\\\\n",
- "e^{i\\phi}\\sin(\\theta/2) & b \n",
- "\\end{pmatrix}\n",
- "$$ \n",
- "\n",
- "where $a$ and $b$ are complex numbers constrained such that $U^\\dagger U = I$ for all $0\\leq\\theta\\leq\\pi$ and $0\\leq \\phi<2\\pi$. This gives 3 constraints and as such $a\\rightarrow -e^{i\\lambda}\\sin(\\theta/2)$ and $b\\rightarrow e^{i\\lambda+i\\phi}\\cos(\\theta/2)$ where $0\\leq \\lambda<2\\pi$ giving \n",
- "\n",
- "$$\n",
- "U = \\begin{pmatrix}\n",
- "\\cos(\\theta/2) & -e^{i\\lambda}\\sin(\\theta/2) \\\\\n",
- "e^{i\\phi}\\sin(\\theta/2) & e^{i\\lambda+i\\phi}\\cos(\\theta/2) \n",
- "\\end{pmatrix}.\n",
- "$$\n",
- "\n",
- "This is the most general form of a single qubit unitary."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Single-Qubit Gates\n",
- "\n",
- "The single-qubit gates available are:\n",
- "- u gates\n",
- "- Identity gate\n",
- "- Pauli gates\n",
- "- Clifford gates\n",
- "- $C3$ gates\n",
- "- Standard rotation gates \n",
- "\n",
- "We have provided a backend: `unitary_simulator` to allow you to calculate the unitary matrices. "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 3,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:24.381507Z",
- "start_time": "2018-09-29T00:15:24.373378Z"
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- "source": [
- "q = QuantumRegister(1)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### u gates\n",
- "\n",
- "In Qiskit we give you access to the general unitary using the $u3$ gate\n",
- "\n",
- "$$\n",
- "u3(\\theta, \\phi, \\lambda) = U(\\theta, \\phi, \\lambda) \n",
- "$$\n"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 4,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:15:25.666961Z",
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┌─────┐┌─┐\n", - "q3_0: |0>┤ X ├┤M├\n", - " ├──┴──┤└╥┘\n", - " c0_0: 0 ╡ = 0 ╞═╩═\n", - " └─────┘" - ], - "text/plain": [ - "
┌───┐┌─┐┌─────┐┌─┐\n", - "q3_0: |0>┤ H ├┤M├┤ X ├┤M├\n", - " └───┘└╥┘├──┴──┤└╥┘\n", - " c0_0: 0 ══════╩═╡ = 0 ╞═╩═\n", - " └─────┘" - ], - "text/plain": [ - "
Trusted Notebook\" align=\"middle\">"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "# Using the Qiskit Terra parallel tools"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "In this tutorial we will see how to leverage the `parallel_map` routine in Qiskit Terra to execute functions in parallel, and track the progress of these parallel tasks using progress bars."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-12-18T18:59:57.469931Z",
- "start_time": "2018-12-18T18:59:57.465314Z"
- }
- },
- "outputs": [],
- "source": [
- "from qiskit import *\n",
- "from qiskit.tools.parallel import parallel_map\n",
- "from qiskit.tools.events import TextProgressBar\n",
- "from qiskit.tools.jupyter import * # Needed to load the Jupyter HTMLProgressBar"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Define a function that builds a single Quantum Volume circuit"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Here we will construct a set of 1000 Quantum Volume circuits of width and depth 4. For a technical discussion of Quantum Volume, see https://arxiv.org/abs/1811.12926."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-12-18T18:59:58.031719Z",
- "start_time": "2018-12-18T18:59:58.028761Z"
- }
- },
- "outputs": [],
- "source": [
- "num_circuits = 1000\n",
- "width = 4\n",
- "depth = 4"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-12-18T18:59:58.194568Z",
- "start_time": "2018-12-18T18:59:58.190192Z"
- }
- },
- "outputs": [],
- "source": [
- "import copy\n",
- "import math\n",
- "import numpy as np\n",
- "from qiskit.quantum_info.random import random_unitary \n",
- "from qiskit.quantum_info.synthesis import two_qubit_cnot_decompose"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "In preparation for executing in parallel, the code below takes an index value, an array of random number seeds, and the width and depth of the circuit as inputs."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-12-18T18:59:58.369775Z",
- "start_time": "2018-12-18T18:59:58.352565Z"
- }
- },
- "outputs": [],
- "source": [
- "def build_qv_circuit(idx, seeds, width, depth):\n",
- " \"\"\"Builds a single Quantum Volume circuit. Two circuits,\n",
- " one with measurements, and one without, are returned.\n",
- "\n",
- " The model circuits consist of layers of Haar random\n",
- " elements of SU(4) applied between corresponding pairs\n",
- " of qubits in a random bipartition.\n",
- " \n",
- " See: https://arxiv.org/abs/1811.12926\n",
- " \"\"\"\n",
- " np.random.seed(seeds[idx])\n",
- " q = QuantumRegister(width, \"q\")\n",
- " c = ClassicalRegister(width, \"c\")\n",
- " # Create measurement subcircuit\n",
- " qc = QuantumCircuit(q,c)\n",
- " # For each layer\n",
- " for j in range(depth):\n",
- " # Generate uniformly random permutation Pj of [0...n-1]\n",
- " perm = np.random.permutation(width)\n",
- " # For each pair p in Pj, generate Haar random SU(4)\n",
- " # Decompose each SU(4) into CNOT + SU(2) and add to Ci\n",
- " for k in range(math.floor(width/2)):\n",
- " qubits = [int(perm[2*k]), int(perm[2*k+1])]\n",
- " U = random_unitary(4) \n",
- " for gate in two_qubit_cnot_decompose(U):\n",
- " gate_name = gate[0].name\n",
- " gate_params = gate[0].params\n",
- " # The first qubit argument used in gate\n",
- " i0 = qubits[gate[1][0].index]\n",
- " if gate_name == \"cx\":\n",
- " # The second qubit argument used in gate\n",
- " i1 = qubits[gate[1][1].index]\n",
- " qc.cx(q[i0], q[i1])\n",
- " elif gate_name == \"u1\":\n",
- " qc.u1(gate_params[2], q[i0])\n",
- " elif gate_name == \"u2\":\n",
- " qc.u2(gate_params[1], gate_params[2], q[i0])\n",
- " elif gate_name == \"u3\":\n",
- " qc.u3(gate_params[0], gate_params[1], gate_params[2], q[i0])\n",
- " elif gate_name == \"id\":\n",
- " pass # do nothing\n",
- " qc_no_meas = copy.deepcopy(qc)\n",
- " # Create circuit with final measurement\n",
- " qc.measure(q,c)\n",
- " return qc, qc_no_meas"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Generate 1000 circuits in parallel and track progress"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Because Quantum Volume circuits are generated randomly for the NumPy random number generator, we must be careful when running in parallel. If the random number generator is not explicitly seeded, the computer uses the current time as a seed value. When running in parallel, this can result in each process starting with the same seed value, and thus not giving random results. Here we generate all the random seed values needed, and pass this into `parallel_map` as an extra argument in `task_args`, along with `width` and `depth`. The main function argument passed in `parallel_map` is just an array that indexes the processes and seed value."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-12-18T19:09:08.823589Z",
- "start_time": "2018-12-18T19:08:50.977782Z"
- }
- },
- "outputs": [],
- "source": [
- "num_circuits = 1000\n",
- "seeds = np.random.randint(np.iinfo(np.int32).max, size=num_circuits)\n",
- "TextProgressBar()\n",
- "parallel_map(build_qv_circuit, np.arange(num_circuits), task_args=(seeds, width, depth));"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Use a Jupyter progress bar"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-12-18T19:09:28.110746Z",
- "start_time": "2018-12-18T19:09:08.827393Z"
- }
- },
- "outputs": [],
- "source": [
- "seeds = np.random.randint(np.iinfo(np.int32).max, size=num_circuits)\n",
- "HTMLProgressBar()\n",
- "parallel_map(build_qv_circuit, np.arange(num_circuits), task_args=(seeds, width, depth));"
- ]
- }
- ],
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diff --git a/qiskit/advanced/terra/using_the_transpiler.ipynb b/qiskit/advanced/terra/using_the_transpiler.ipynb
deleted file mode 100644
index 5be970627..000000000
--- a/qiskit/advanced/terra/using_the_transpiler.ipynb
+++ /dev/null
@@ -1,608 +0,0 @@
-{
- "cells": [
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- " Trusted Notebook\" align=\"middle\">"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "# Introducing the Qiskit Transpiler"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Introduction"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "In this notebook we introduce the Qiskit transpiler and walk through some examples of circuit transformations using **transpiler passes**.\n",
- "\n",
- "The transpiler is Qiskit's circuit-rewriting framework. We intentionally do not call it a \"compiler\", since we use compiler in the context of a larger translation from high-level applications (potentially many circuits, with classical control flow between them) down to the level of machine pulses. The transpiler, in contrast, is responsible only for circuit-level analysis and transformations.\n",
- "\n",
- "Circuits are a fundamental and universal model of computation on quantum computers. In the Noisy Intermediate-Scale Quantum (NISQ) regime, we are always limited by the scarcity of quantum resources. The transpiler is a tool that helps us reduce the number of gates and qubits, in order to increase the fidelity of executions.\n",
- "\n",
- "Circuit optimization is a difficult task (in general QMA-complete). To make it approachable, we break it down. Each transpiler pass is thus responsible for doing one small, well-defined task. Through this \"separation of responsibilities\", we are able to chain together different passes to achieve an aggressive optimization goal.\n",
- "\n",
- "Which passes are chained together and in which order has a major effect on the final outcome. This pipeline is determined by a **pass manager**, which schedules the passes and also allows passes to communicate with each other by providing a shared space."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Transpiler API"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "There are two main ways to use the transpiler:\n",
- "1. Use the ``transpile()`` function, and specify some desired transpilation options, like ``basis_gates``, ``coupling_map``, ``initial_layout`` of qubits, or ``optimization_level``.\n",
- "\n",
- "2. Create your own custom pass manager."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 58,
- "metadata": {
- "collapsed": true
- },
- "outputs": [],
- "source": [
- "from qiskit.compiler import transpile\n",
- "from qiskit.transpiler import PassManager"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Let's start with a very simple transpilation task. Suppose we have a single Toffoli gate that we want to unroll to a more fundamental basis."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 60,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/html": [
- "\n", - "q_0: |0>──■──\n", - " │ \n", - "q_1: |0>──■──\n", - " ┌─┴─┐\n", - "q_2: |0>┤ X ├\n", - " └───┘" - ], - "text/plain": [ - "
Trusted Notebook\" align=\"middle\">"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "# Visualizing a Quantum Circuit"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 1,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:16:38.758552Z",
- "start_time": "2018-09-29T00:16:37.828380Z"
- }
- },
- "outputs": [],
- "source": [
- "from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Drawing a Quantum Circuit\n",
- "\n",
- "When building a quantum circuit, it often helps to draw the circuit. This is supported natively by a `QuantumCircuit` object. You can either call `print()` on the circuit, or call the `draw()` method on the object. This will render a [ASCII art version](https://en.wikipedia.org/wiki/ASCII_art) of the circuit diagram."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 2,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:17:28.150946Z",
- "start_time": "2018-09-29T00:17:27.979866Z"
- }
- },
- "outputs": [],
- "source": [
- "# Build a quantum circuit\n",
- "\n",
- "n = 3 # number of qubits \n",
- "q = QuantumRegister(n)\n",
- "c = ClassicalRegister(n)\n",
- "\n",
- "circuit = QuantumCircuit(q, c)\n",
- "\n",
- "circuit.x(q[1])\n",
- "circuit.h(q)\n",
- "circuit.cx(q[0], q[1])\n",
- "circuit.measure(q, c);"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 3,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:17:29.971852Z",
- "start_time": "2018-09-29T00:17:29.703427Z"
- }
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- " ┌───┐ ┌─┐\n",
- "q0_0: |0>──────────────────┤ H ├──■─────┤M├\n",
- " ┌───┐┌───┐└───┘┌─┴─┐┌─┐└╥┘\n",
- "q0_1: |0>────────┤ X ├┤ H ├─────┤ X ├┤M├─╫─\n",
- " ┌───┐┌─┐└───┘└───┘ └───┘└╥┘ ║ \n",
- "q0_2: |0>┤ H ├┤M├─────────────────────╫──╫─\n",
- " └───┘└╥┘ ║ ║ \n",
- " c0_0: 0 ══════╬══════════════════════╬══╩═\n",
- " ║ ║ \n",
- " c0_1: 0 ══════╬══════════════════════╩════\n",
- " ║ \n",
- " c0_2: 0 ══════╩═══════════════════════════\n",
- " \n"
- ]
- }
- ],
- "source": [
- "print(circuit)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 4,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/html": [
- "┌───┐ ┌─┐\n", - "q0_0: |0>──────────────────┤ H ├──■─────┤M├\n", - " ┌───┐┌───┐└───┘┌─┴─┐┌─┐└╥┘\n", - "q0_1: |0>────────┤ X ├┤ H ├─────┤ X ├┤M├─╫─\n", - " ┌───┐┌─┐└───┘└───┘ └───┘└╥┘ ║ \n", - "q0_2: |0>┤ H ├┤M├─────────────────────╫──╫─\n", - " └───┘└╥┘ ║ ║ \n", - " c0_0: 0 ══════╬══════════════════════╬══╩═\n", - " ║ ║ \n", - " c0_1: 0 ══════╬══════════════════════╩════\n", - " ║ \n", - " c0_2: 0 ══════╩═══════════════════════════\n", - "" - ], - "text/plain": [ - "
"
- ]
- },
- "execution_count": 5,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "# Matplotlib Drawing\n",
- "circuit.draw(output='mpl')"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 6,
- "metadata": {},
- "outputs": [
- {
- "data": {
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\n",
- "text/plain": [
- ""
- ]
- },
- "execution_count": 6,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "# Latex Drawing\n",
- "circuit.draw(output='latex')"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Controlling output from circuit.draw()\n",
- "\n",
- "By default, the draw method returns the rendered image as an object and does not output anything. The exact class returned depends on the output specified: `'text'`(the default) returns a `TextDrawer` object, `'mpl'` returns a `matplotlib.Figure` object, and `latex` returns a `PIL.Image` object. Having the return types enables modifying or directly interacting with the rendered output from the drawers. Jupyter notebooks understand these return types and render them for us in this tutorial, but when running outside of Jupyter, you do not have this feature automatically. However, the `draw()` method has optional arguments to display or save the output. When specified, the `filename` kwarg takes a path to which it saves the rendered output. Alternatively, if you're using the `mpl` or `latex` outputs, you can leverage the `interactive` kwarg to open the image in a new window (this will not always work from within a notebook but will be demonstrated anyway)."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Customizing the output\n",
- "\n",
- "Depending on the output, there are also options to customize the circuit diagram rendered by the circuit.\n",
- "\n",
- "### Disable Plot Barriers and Reversing Bit Order\n",
- "The first two options are shared among all three backends. They allow you to configure both the bit orders and whether or not you draw barriers. These can be set by the `reverse_bits` kwarg and `plot_barriers` kwarg, respectively. The examples below will work with any output backend; `latex` is used here for brevity."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 7,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:17:56.930280Z",
- "start_time": "2018-09-29T00:17:56.926191Z"
- }
- },
- "outputs": [],
- "source": [
- "# Draw a new circuit with barriers and more registers\n",
- "\n",
- "q_a = QuantumRegister(3, name='qa')\n",
- "q_b = QuantumRegister(5, name='qb')\n",
- "c_a = ClassicalRegister(3)\n",
- "c_b = ClassicalRegister(5)\n",
- "\n",
- "circuit = QuantumCircuit(q_a, q_b, c_a, c_b)\n",
- "\n",
- "circuit.x(q_a[1])\n",
- "circuit.x(q_b[1])\n",
- "circuit.x(q_b[2])\n",
- "circuit.x(q_b[4])\n",
- "circuit.barrier()\n",
- "circuit.h(q_a)\n",
- "circuit.barrier(q_a)\n",
- "circuit.h(q_b)\n",
- "circuit.cswap(q_b[0], q_b[1], q_b[2])\n",
- "circuit.cswap(q_b[2], q_b[3], q_b[4])\n",
- "circuit.cswap(q_b[3], q_b[4], q_b[0])\n",
- "circuit.barrier(q_b)\n",
- "circuit.measure(q_a, c_a)\n",
- "circuit.measure(q_b, c_b);"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 8,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:17:57.325792Z",
- "start_time": "2018-09-29T00:17:57.309795Z"
- }
- },
- "outputs": [
- {
- "data": {
- "image/png": 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\n",
- "text/plain": [
- ""
- ]
- },
- "execution_count": 8,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "# Draw the circuit\n",
- "circuit.draw(output='latex')"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 9,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "image/png": 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\n",
- "text/plain": [
- ""
- ]
- },
- "execution_count": 9,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "# Draw the circuit with reversed bit order\n",
- "circuit.draw(output='latex', reverse_bits=True)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 10,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "image/png": 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\n",
- "text/plain": [
- ""
- ]
- },
- "execution_count": 10,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "# Draw the circuit without barriers\n",
- "circuit.draw(output='latex', plot_barriers=False)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 11,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "image/png": 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\n",
- "text/plain": [
- ""
- ]
- },
- "execution_count": 11,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "# Draw the circuit without barriers and reverse bit order\n",
- "circuit.draw(output='latex', plot_barriers=False, reverse_bits=True)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### Backend-specific customizations\n",
- "\n",
- "Some available customizing options are specific to a backend. The `line_length` kwarg for the `text` backend can be used to set a maximum width for the output. When a diagram is wider than the maximum, it will wrap the diagram below. The `mpl` backend has the `style` kwarg, which is used to customize the output. The `scale` option is used by the `mpl` and `latex` backends to scale the size of the output image with a multiplicative adjustment factor. The `style` kwarg takes in a `dict` with multiple options, providing a high level of flexibility for changing colors, changing rendered text for different types of gates, different line styles, etc. Available options are:\n",
- "\n",
- "- **textcolor** (str): The color code to use for text. Defaults to `'#000000'`\n",
- "- **subtextcolor** (str): The color code to use for subtext. Defaults to `'#000000'`\n",
- "- **linecolor** (str): The color code to use for lines. Defaults to `'#000000'`\n",
- "- **creglinecolor** (str): The color code to use for classical register lines `'#778899'`\n",
- "- **gatetextcolor** (str): The color code to use for gate text `'#000000'`\n",
- "- **gatefacecolor** (str): The color code to use for gates. Defaults to `'#ffffff'`\n",
- "- **barrierfacecolor** (str): The color code to use for barriers. Defaults to `'#bdbdbd'`\n",
- "- **backgroundcolor** (str): The color code to use for the background. Defaults to `'#ffffff'`\n",
- "- **fontsize** (int): The font size to use for text. Defaults to 13\n",
- "- **subfontsize** (int): The font size to use for subtext. Defaults to 8\n",
- "- **displaytext** (dict): A dictionary of the text to use for each element\n",
- " type in the output visualization. The default values are:\n",
- " \n",
- " \n",
- " 'id': 'id',\n",
- " 'u0': 'U_0',\n",
- " 'u1': 'U_1',\n",
- " 'u2': 'U_2',\n",
- " 'u3': 'U_3',\n",
- " 'x': 'X',\n",
- " 'y': 'Y',\n",
- " 'z': 'Z',\n",
- " 'h': 'H',\n",
- " 's': 'S',\n",
- " 'sdg': 'S^\\\\dagger',\n",
- " 't': 'T',\n",
- " 'tdg': 'T^\\\\dagger',\n",
- " 'rx': 'R_x',\n",
- " 'ry': 'R_y',\n",
- " 'rz': 'R_z',\n",
- " 'reset': '\\\\left|0\\\\right\\\\rangle'\n",
- " \n",
- " \n",
- " You must specify all the necessary values if using this. There is\n",
- " no provision for an incomplete dict passed in.\n",
- "- **displaycolor** (dict): The color codes to use for each circuit element.\n",
- " By default, all values default to the value of `gatefacecolor` and\n",
- " the keys are the same as `displaytext`. Also, just like\n",
- " `displaytext`, there is no provision for an incomplete dict passed\n",
- " in.\n",
- "- **latexdrawerstyle** (bool): When set to True, enable LaTeX mode, which will\n",
- " draw gates like the `latex` output modes.\n",
- "- **usepiformat** (bool): When set to True, use radians for output.\n",
- "- **fold** (int): The number of circuit elements at which to fold the circuit.\n",
- " Defaults to 20\n",
- "- **cregbundle** (bool): If set True, bundle classical registers.\n",
- "- **showindex** (bool): If set True, draw an index.\n",
- "- **compress** (bool): If set True, draw a compressed circuit.\n",
- "- **figwidth** (int): The maximum width (in inches) for the output figure.\n",
- "- **dpi** (int): The DPI to use for the output image. Defaults to 150.\n",
- "- **creglinestyle** (str): The style of line to use for classical registers.\n",
- " Choices are `'solid'`, `'doublet'`, or any valid matplotlib\n",
- " `linestyle` kwarg value. Defaults to `doublet`."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 12,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:18:01.113112Z",
- "start_time": "2018-09-29T00:18:01.108121Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 12,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "# Set line length to 80 for above circuit\n",
- "circuit.draw(output='text', line_length=80)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 13,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-09-29T00:18:03.374646Z",
- "start_time": "2018-09-29T00:18:03.105372Z"
- }
- },
- "outputs": [
- {
- "data": {
- "image/png": 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\n",
- "text/plain": [
- "
░ »\n", - "qa_0: |0>─────────────────────░───────────────────────────────────────────────»\n", - " ┌───┐ ░ »\n", - "qa_1: |0>───────────────┤ X ├─░───────────────────────────────────────────────»\n", - " └───┘ ░ »\n", - "qa_2: |0>─────────────────────░───────────────────────────────────────────────»\n", - " ░ ┌───┐ ░ »\n", - "qb_0: |0>─────────────────────░─────────────────────┤ H ├─■─────X──░──────────»\n", - " ┌───┐ ░ ┌───┐└───┘ │ │ ░ »\n", - "qb_1: |0>──────────┤ X ├──────░────────────────┤ H ├──────X─────┼──░──────────»\n", - " ┌───┐└───┘ ░ ┌───┐└───┘ │ │ ░ ┌─┐»\n", - "qb_2: |0>─────┤ X ├───────────░───────────┤ H ├───────────X──■──┼──░───────┤M├»\n", - " └───┘ ░ ┌───┐└───┘ │ │ ░ ┌─┐└╥┘»\n", - "qb_3: |0>─────────────────────░──────┤ H ├───────────────────X──■──░────┤M├─╫─»\n", - " ┌───┐ ░ ┌───┐└───┘ │ │ ░ ┌─┐└╥┘ ║ »\n", - "qb_4: |0>┤ X ├────────────────░─┤ H ├────────────────────────X──X──░─┤M├─╫──╫─»\n", - " └───┘ ░ └───┘ ░ └╥┘ ║ ║ »\n", - " c1_0: 0 ═════════════════════════════════════════════════════════════╬══╬══╬═»\n", - " ║ ║ ║ »\n", - " c1_1: 0 ═════════════════════════════════════════════════════════════╬══╬══╬═»\n", - " ║ ║ ║ »\n", - " c1_2: 0 ═════════════════════════════════════════════════════════════╬══╬══╬═»\n", - " ║ ║ ║ »\n", - " c2_0: 0 ═════════════════════════════════════════════════════════════╬══╬══╬═»\n", - " ║ ║ ║ »\n", - " c2_1: 0 ═════════════════════════════════════════════════════════════╬══╬══╬═»\n", - " ║ ║ ║ »\n", - " c2_2: 0 ═════════════════════════════════════════════════════════════╬══╬══╩═»\n", - " ║ ║ »\n", - " c2_3: 0 ═════════════════════════════════════════════════════════════╬══╩════»\n", - " ║ »\n", - " c2_4: 0 ═════════════════════════════════════════════════════════════╩═══════»\n", - " »\n", - "« ┌───┐ ░ ┌─┐\n", - "«qa_0: ────────────────┤ H ├─░───────┤M├\n", - "« ┌───┐└───┘ ░ ┌─┐└╥┘\n", - "«qa_1: ───────────┤ H ├──────░────┤M├─╫─\n", - "« ┌───┐└───┘ ░ ┌─┐└╥┘ ║ \n", - "«qa_2: ──────┤ H ├───────────░─┤M├─╫──╫─\n", - "« ┌─┐└───┘ ░ └╥┘ ║ ║ \n", - "«qb_0: ───┤M├───────────────────╫──╫──╫─\n", - "« ┌─┐└╥┘ ║ ║ ║ \n", - "«qb_1: ┤M├─╫────────────────────╫──╫──╫─\n", - "« └╥┘ ║ ║ ║ ║ \n", - "«qb_2: ─╫──╫────────────────────╫──╫──╫─\n", - "« ║ ║ ║ ║ ║ \n", - "«qb_3: ─╫──╫────────────────────╫──╫──╫─\n", - "« ║ ║ ║ ║ ║ \n", - "«qb_4: ─╫──╫────────────────────╫──╫──╫─\n", - "« ║ ║ ║ ║ ║ \n", - "«c1_0: ═╬══╬════════════════════╬══╬══╩═\n", - "« ║ ║ ║ ║ \n", - "«c1_1: ═╬══╬════════════════════╬══╩════\n", - "« ║ ║ ║ \n", - "«c1_2: ═╬══╬════════════════════╩═══════\n", - "« ║ ║ \n", - "«c2_0: ═╬══╩════════════════════════════\n", - "« ║ \n", - "«c2_1: ═╩═══════════════════════════════\n", - "« \n", - "«c2_2: ═════════════════════════════════\n", - "« \n", - "«c2_3: ═════════════════════════════════\n", - "« \n", - "«c2_4: ═════════════════════════════════\n", - "«" - ], - "text/plain": [ - "
"
- ]
- },
- "execution_count": 13,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "# Change the background color in mpl\n",
- "\n",
- "style = {'backgroundcolor': 'lightgreen'}\n",
- "\n",
- "circuit.draw(output='mpl', style=style)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 14,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "image/png": 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\n",
- "text/plain": [
- "
"
- ]
- },
- "execution_count": 14,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "# Scale the mpl output to 1/2 the normal size\n",
- "circuit.draw(output='mpl', scale=0.5)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 15,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "image/png": 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\n",
- "text/plain": [
- ""
- ]
- },
- "execution_count": 15,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "# Scale the latex output to 1/2 the normal size\n",
- "circuit.draw(output='latex', scale=0.5)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "\n",
- "## LaTeX Source\n",
- "\n",
- "One additional option available with the `latex` output type is to return the raw LaTeX source code instead of rendering an image for it. This enables easy integration with a separate LaTeX document. To use this, set the `output` kwarg to `'latex_source'`. You can also use the `filename` kwarg to write this output directly to a file (and still return the string) instead of returning just a string."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 16,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "% \\documentclass[preview]{standalone}\n",
- "% If the image is too large to fit on this documentclass use\n",
- "\\documentclass[draft]{beamer}\n",
- "% img_width = 16, img_depth = 17\n",
- "\\usepackage[size=custom,height=24,width=28,scale=0.7]{beamerposter}\n",
- "% instead and customize the height and width (in cm) to fit.\n",
- "% Large images may run out of memory quickly.\n",
- "% To fix this use the LuaLaTeX compiler, which dynamically\n",
- "% allocates memory.\n",
- "\\usepackage[braket, qm]{qcircuit}\n",
- "\\usepackage{amsmath}\n",
- "\\pdfmapfile{+sansmathaccent.map}\n",
- "% \\usepackage[landscape]{geometry}\n",
- "% Comment out the above line if using the beamer documentclass.\n",
- "\\begin{document}\n",
- "\\begin{equation*}\n",
- " \\Qcircuit @C=0.5em @R=0.0em @!R {\n",
- "\t \t\\lstick{qa_{0}: \\ket{0}} & \\qw & \\qw \\barrier{7} & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\gate{H} & \\qw \\barrier[-1.15em]{2} & \\qw & \\qw & \\meter & \\qw & \\qw\\\\\n",
- "\t \t\\lstick{qa_{1}: \\ket{0}} & \\gate{X} & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\gate{H} & \\qw & \\qw & \\meter & \\qw & \\qw & \\qw\\\\\n",
- "\t \t\\lstick{qa_{2}: \\ket{0}} & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\gate{H} & \\qw & \\meter & \\qw & \\qw & \\qw & \\qw\\\\\n",
- "\t \t\\lstick{qb_{0}: \\ket{0}} & \\qw & \\qw & \\gate{H} & \\ctrl{1} & \\qw & \\qswap \\qwx[4] & \\qw \\barrier[-1.15em]{4} & \\qw & \\qw & \\qw & \\meter & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw\\\\\n",
- "\t \t\\lstick{qb_{1}: \\ket{0}} & \\gate{X} & \\qw & \\gate{H} & \\qswap & \\qw & \\qw & \\qw & \\qw & \\qw & \\meter & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw\\\\\n",
- "\t \t\\lstick{qb_{2}: \\ket{0}} & \\gate{X} & \\qw & \\gate{H} & \\qswap \\qwx[-1] & \\ctrl{1} & \\qw & \\qw & \\qw & \\meter & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw\\\\\n",
- "\t \t\\lstick{qb_{3}: \\ket{0}} & \\qw & \\qw & \\gate{H} & \\qw & \\qswap & \\ctrl{1} & \\qw & \\meter & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw\\\\\n",
- "\t \t\\lstick{qb_{4}: \\ket{0}} & \\gate{X} & \\qw & \\gate{H} & \\qw & \\qswap \\qwx[-1] & \\qswap & \\meter & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw\\\\\n",
- "\t \t\\lstick{c1_{0}: 0} & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw \\cwx[-8] & \\cw & \\cw\\\\\n",
- "\t \t\\lstick{c1_{1}: 0} & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw \\cwx[-8] & \\cw & \\cw & \\cw\\\\\n",
- "\t \t\\lstick{c1_{2}: 0} & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw \\cwx[-8] & \\cw & \\cw & \\cw & \\cw\\\\\n",
- "\t \t\\lstick{c2_{0}: 0} & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw \\cwx[-8] & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw\\\\\n",
- "\t \t\\lstick{c2_{1}: 0} & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw \\cwx[-8] & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw\\\\\n",
- "\t \t\\lstick{c2_{2}: 0} & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw \\cwx[-8] & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw\\\\\n",
- "\t \t\\lstick{c2_{3}: 0} & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw \\cwx[-8] & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw\\\\\n",
- "\t \t\\lstick{c2_{4}: 0} & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw \\cwx[-8] & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw & \\cw\\\\\n",
- "\t }\n",
- "\\end{equation*}\n",
- "\n",
- "\\end{document}\n"
- ]
- }
- ],
- "source": [
- "# Print the latex source for the visualization\n",
- "print(circuit.draw(output='latex_source'))"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 17,
- "metadata": {},
- "outputs": [],
- "source": [
- "# Save the latex source to a file\n",
- "circuit.draw(output='latex_source', filename='/tmp/circuit.tex');"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## circuit_drawer() as function\n",
- "\n",
- "If you have an application where you prefer to draw a circuit with a self-contained function instead of as a method of a circuit object, you can directly use the `circuit_drawer()` function, which is part of the public stable interface from `qiskit.tools.visualization`. The function behaves identically to the `circuit.draw()` method, except that it takes in a circuit object as required argument.\n",
- "\n",
- "
\n",
- "Note: In Qiskit Terra <= 0.7, the default behavior for the circuit_drawer() function is to use the latex output backend, and in 0.6.x that includes a fallback to mpl if latex fails for any reason. Starting with release > 0.7, the default changes to the text output.\n",
- "
"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 18,
- "metadata": {},
- "outputs": [],
- "source": [
- "from qiskit.tools.visualization import circuit_drawer"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 19,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "image/png": 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ESdOnT9c333yj//7v/1afPn1cXu/cMRJJSUmaP3++bDabZs+e7cZKIbk5TJw+fVrPPfecsrOz1b9/f/n5+emxxx6T3W53hInQ0FCNHDlSwcHB8vf318MPP6wzZ844TuN1zz33KCwsTK+++mqdY6WmpqqoqMjl2qqqqiRJwcHBTv0hISGqrKx03B88eLDWrVvn8vM2J6dOnVJqaqrCw8O9XQoAAF5hs9lUXFysdu3aObWMjAzFxMR4u7xG5/Dhw5o9e7bGjBmjhIQEl9c7P0isXLlSo0aN0h//+Ee9+uqrOnnypBsrhgw3Wr9+vRESEuLUt3fvXkOSUVZWZhiGYWzcuNG49957jQ4dOhhBQUFGQECAce211zqW379/v7FgwQLjlVdeuex6FixYYMTFxRmGYRjl5eWGJCM/P99pmaCgICMnJ8dxPzs72xgyZMhlj30pkrzWzr0nrlqyZIkRGhpqjB071ujZs6dRU1NTr/Xj4uK8+nppNBqNRqur1edzMTQ01HjttdeM/fv3O7WQkBDj448/5rOxnu/1a6+9Zkgyvv32W5ffu3feeceQZCQlJRk///yzo3/btm2GJCMrK4v3+jJbXdw6M3HkyJFap+Javny5wsPDdc011+irr77SiBEj9PTTT+u7777TiRMnlJKS4jQt2LFjR7fUFhISos6dO2vHjh2OvpKSElVWVjrtLrVmzRolJye7pYbzGYbhlRYXF1evOtevX6+JEyfqo48+0ptvvqkjR45o5cqV9X69cXFxXnvNNBqNRqNdrNXnc7G4uFjl5eVKSEhQx44dHe3nn39WRUVFvWcmmttn44Xe67Vr1+qWW27RDTfc4NJ79tsZifOP37zlllvUvXt3ffzxxz7xXqekv3vB242h1cWtYaJHjx4qLi7W1q1bVV1dreXLlys9Pd2xi1N+fr5CQ0MVGxsri8WihQsXaubMmR7bx3D8+PHKyMjQnj17VFlZqZSUFCUkJKhr166Szu7Gs3nzZiUmJnqkHl+3bds2jRgxQosXL9aAAQMcx06kpaVxSlgAQLNjs9nUpk2bWvv1b9u2TZ06deLaBvX066+/qrCwULfccotLy9cVJKSzB2TfcsstnEjHzdwaJmJiYvTiiy9q6NCh6tixo/Ly8tS/f39HmHjwwQcVFRWliIgI9ejRQ+Xl5QoNDTUVJmbMmKGePXvWa53U1FQlJSUpJiZGHTp0kN1u19KlSx2Pb9y4UdHR0WrXrl2962lqdu7cqcTERM2ePVtDhgxx9D/xxBP68ccfTc1OAADQmNlsNsXExKhFixZO/V9++SUHX5tw+PBh/fTTTy7NSlwqSJxzww036NChQ/rpp58aulz8R4tLL3J50tLSlJaW5rjftWtXjRs3TtLZXY1yc3Odln/22WdNjTNt2jRNmzatXutYLBZlZmYqMzPzgo97ahenxqBXr146fvx4rf42bdro8OHDXqgIAADvutiZgrKysjxcSdMQFham/Px8dejQoc7l7Ha7Vq5c6dIF6R555BH94Q9/UMuWLRu6XPyH28PE+SorK1VaWuqYmXDF2LFjlZeXpzNnzigvL09r1651Y4XOunTp4rgeBgAAANynZcuWtS7+dyEWi0Vr165VixYtLnmNq2uvvVbXXnttQ5WIC/BomNi5c6cCAwMVGRnp8jrz589vsPGtVqvGjBnj8vLTp09vsLEBAADQMK666ipvl4D/8GiYiI2NdbqGg6dZrVaXEi8AAACAS3P7FbABAAAANE2ECQAAAACmECYAAAAAmEKYAAAAAGAKYQIAAACAKYQJAAAAAKZ49NSw8E0FBQWKj4/36HicohcA4Ks8/bl4bszm+NnIe934ESaaOW/8MnG9DwCAr/LW51Nz/Gw0+3pL9pWpW+dra92uz7jN7b12J8JEMzdnzhxvlwAAgM/gc9FzzL7XqRnZSk8ZX+s2vINjJgAAAACYQpgAAAAAYAphAgAAAIAphAkAAAAAphAmAAAAAJhCmAAAAABgCmECAAAAgCmECQAAAACmECYAAAAAmEKYAAAAAGAKYQIAAACAKYQJAAAAAKa08HYBAAAAvmLSpEkqKCjwythWq1Vz5swxta636r6cmtE0MDMBAADwHwUFBV75Un6543qjbm+9V/AtzEwAAACcx2q1asuWLR4dMz4+/rKfw9N1N0TNaPyYmQAAAABgCmECAAAAgCmECQAAAACmECYAAAAAmEKYAAAAAGAKYQIAAACAKZwaFgAAoJk5efKkCgoKtGvXLp0+fVpXXnmlevbsqejoaAUEBFxwnffee099+/aV1Wr1cLXwZc1qZmLhwoX1Oidy3759tWHDBvcVBAAA4EGfffaZhg8frtDQUN1xxx2aMGGCnnvuOT3++OMaMGCAQkJCNGzYMG3evNlpvaysLD322GP629/+5qXK4auaVZj4LbvdrqlTpyosLEyBgYEaNmyYjh496ng8OTlZa9as8WKFAADA10VERGjevHlOfYZhKCgoSKtXr/ZSVc6OHz+uUaNGKS4uTps2bdKTTz6pNWvWqLS0VOXl5dq3b5/Wrl2rSZMmaevWrbrrrrs0cuRIHT16VFlZWZo4caKSkpKUnZ3t7ZcCH9Osw0R6erpycnKUl5enAwcOSJJGjRrleJwwAQAA6nLw4EGVlZXV2vWnpKREVVVV6tevn5cq+392796tvn376v3339fLL7+sgwcP6m9/+5uSkpLUuXNnhYSEqFOnTkpMTFRmZqYOHDigV155RatWrVL37t0dQWLlypVq1aqVt18OfIxHwsSKFSsUFRWlgIAADRo0SJMnT9bw4cMlSTU1NRo9erS6dOmigIAARUVF6f333/dEWcrOzlZKSoq6deum4OBgzZo1S7m5uSotLZUk9enTRxaLRdu3b/dIPQAAoHGx2WyyWCzq1auXU39hYaHCw8PVqVMnL1V21uHDh3X33XerqqpK//u//6vp06fryiuvrHOd1q1b67/+6780efJklZeXq3Xr1pozZw5BAhfk9jCxaNEiTZ48WcuWLVNVVZUSExM1d+5cRUdHS5JOnDih++67T0VFRaqsrNSzzz6rMWPGqLq6ul7jpKenq3fv3i4vX1FRoX379qlv376OvsjISAUFBamwsNDRl5ycrJycnHrVAgAAmgebzabu3burdevWTv2FhYVen5UwDEMTJkzQoUOHtGHDBvXv39/ldbOyspSenq64uDhJ0lNPPSXDMNxVKhoxt4aJ06dP67nnnlN2drb69+8vPz8/PfbYY7Lb7Y4wERoaqpEjRyo4OFj+/v56+OGHdebMGZ06dUq7d+/WgAEDdMcdd+j222/X119/fdGxUlNTVVRU5HJtVVVVkqTg4GCn/pCQEFVWVjruDx48WOvWravPywYAAM2EzWZTcXGx2rVr59QyMjIUExPj1drWrl2rjz76SK+88orTH08v5fxjJDZs2KCMjAytX79eH3zwgRurRaNluNH69euNkJAQp769e/cakoyysjLDMAxj48aNxr333mt06NDBCAoKMgICAoxrr73WMAzDOHr0qHH06FHDMAxj165dxu23335Z9SxYsMCIi4szDMMwysvLDUlGfn6+0zJBQUFGTk6O4352drYxZMiQyxrXFZJoNBqNRqP5QDv3XcEVoaGhxmuvvWbs37/fqYWEhBgff/yxy88TFxfX4HXfeeedRufOnY1ffvnF5TreeecdQ5KRlJRk/Pzzz4ZhGIbdbjeioqKM2267rcFrpjWOVhe3zkwcOXJE7du3d+pbvny5wsPDdc011+irr77SiBEj9PTTT+u7777TiRMnlJKS4pgWbNu2rdq2bStJatWqlSwWS4PVFhISos6dO2vHjh2OvpKSElVWVjrtLrVmzRolJyc32LgXYxgGjUaj0Wg0L7dzu/W4ori4WOXl5UpISFDHjh0d7eeff1ZFRUW9Zybi4uIarO69e/dq8+bN+stf/qIWLVy7rNj5MxLnH2zt7++vCRMm6IsvvtB3333XYDWbbSnp717wtq+3xlq3YRh1/ty4NUz06NFDxcXF2rp1q6qrq7V8+XKlp6c7dnHKz89XaGioYmNjZbFYtHDhQs2cObPWPoZ2u11PP/20UlNTG7S+8ePHKyMjQ3v27FFlZaVSUlKUkJCgrl27SpJOnTqlzZs3KzExsUHHBQAAjZ/NZlObNm3Up08fp/5t27apU6dOtf6g6klfffWVJCkhIcGl5S8WJM459zznnhc4x61hIiYmRi+++KKGDh2qjh07Ki8vT/3793eEiQcffFBRUVGKiIhQjx49VF5ertDQUKcwYRiGxo4dq8TERN17770XHWvGjBnq2bNnvepLTU1VUlKSYmJi1KFDB9ntdi1dutTx+MaNGxUdHa127drV85UDAICmzmazKSYmptZf/r/88kuvH3xdVFR0wbNMXcilgoQk/e53v1Pr1q2dTlIDSJJr816XIS0tTWlpaY77Xbt21bhx4ySd3dUoNzfXaflnn33W6f5TTz2lqKgoPf7443WOM23aNE2bNq1etVksFmVmZiozM/OCj3tqFycAAND4zJ49+4L9WVlZHq6kthtvvFFjxoy55Olcc3NzXbqORIsWLfTwww/X+w+3aPrcHibOV1lZqdLSUsfMxKVs2bJF2dnZio2N1aZNm3T11Vfrww8/dHOV/0+XLl0c18MAAABoLB566CE99NBDl1zu7rvv1uuvv66nnnrqksHjH//4R0OVhybEo2Fi586dCgwMVGRkpEvLx8fH1/t6E3WxWq0aM2aMy8tPnz69wcYGAADwNVdccYWmTJni7TLQiHk0TMTGxjpdw8HTrFZrrcvdAwAAADDH7VfABgAAANA0ESYAAAAAmEKYAAAAAGAKYQIAAACAKYQJAAAAAKYQJgAAAACY4tFTwwIAAPi6goICxcfHe3zMyz19vafrboia0fgRJgAAAP7DW1+OL/daWGbXLdlXpm6dr61129UxCRMgTAAAAPzHnDlzvF2CKWbrTs3IVnrK+Fq3AVdxzAQAAAAAUwgTAAAAAEwhTAAAAAAwhTABAAAAwBTCBAAAAABTCBMAAAAATCFMAAAAADCFMAEAAADAFMIEAAAAAFMIEwAAAABMIUwAAAAAMIUwAQAAAMAUwgQAAAAAU1p4uwCgviZNmqSCggKvjG21WjVnzhyvjA0AjY23ttdsqwHPYWYCjU5BQYFXPpy8NS4ANFbe2G6yrQY8i5kJNEpWq1Vbtmzx6Jjx8fEeHQ8AmgJPb6/ZVgOexcwEAAAAAFMIEwAAAABMIUwAAAAAMIUwAQAAAMAUwgQAAAAAUwgTAJqlsrIyl5c1DKNeywPwnIqKCv3000/eLgNotnwiTAwePFgzZ850+zgLFy6s1ynj+vbtqw0bNrivIABe8dFHHykyMlLr16+/5LKGYej555+X1WrVwYMHPVAd0Dz9+9//1pQpU3THHXcoODhY/v7+uvLKKxUdHa1x48bp008/lWEYTuuUl5dr4MCBeuCBB2o9BsAzfCJM5Ofnq3fv3h4f1263a+rUqQoLC1NgYKCGDRumo0ePOh5PTk7WmjVrPF4XGl5ERITmzZvn1GcYhoKCgrR69WovVXVpZWVlevPNN/Xyyy8rKytLx44d83ZJTcKAAQN044036k9/+lOdgeJckMjMzNT999+viIgID1YJNA/ffvut7rrrLvXu3Vt///vfVVNToz//+c+aNm2aJk6cqLCwMK1cuVIDBw7UjTfeqI0bN0o6GyQGDRqkoqIi/eUvf5Gfn5+XXwnQPHk9TBw+fFhlZWVeCRPp6enKyclRXl6eDhw4IEkaNWqU43HCRNNw8OBBlZWVyWq1OvWXlJSoqqpK/fr181JlF1ddXa2JEyeqU6dOeuaZZ5SWlqaJEycqIiJC06ZNU01NjbdLbNSuvvpq/c///I969ep10UBxfpCYOHGi3nrrLb6sAA0sKytLVqtVhYWFev311/XDDz/oiy++0Ntvv61XX31Vb7zxhjZu3KhDhw5pyZIl8vPzU0JCgh599FENHDhQRUVFWrVqlRITE739UoBmyyNhYsWKFYqKilJAQIAGDRqkyZMna/jw4ZLOzkqEhIRo3bp1uv766xUcHKxHHnlEv/zyi9vrys7OVkpKirp166b2XFWWAAAgAElEQVTg4GDNmjVLubm5Ki0tlST16dNHFotF27dvd3stcB+bzSaLxaJevXo59RcWFio8PFydOnXyUmUXN3bsWGVlZclutzv1V1dXa+bMmZo6daqXKms66goUBAnA/TIyMjRx4kTdfffd2rVrl6ZMmaK2bdtecNnWrVvrz3/+s/Lz8/XEE09o/vz5ys/P14oVKwgSgJe5PUwsWrRIkydP1rJly1RVVaXExETNnTtX0dHRks6GiZMnT+rIkSPatWuXduzYodzcXM2fP79e46Snp9drdqOiokL79u1T3759HX2RkZEKCgpSYWGhoy85OVk5OTn1qgW+xWazqXv37mrdurVTf2FhoU/OSnz99ddatmxZncvMmTPHEXph3oUCBUECcL9PPvlEqampGjFihHJycnTNNde4tN5PP/2kvLw8WSwW1dTU8Mc+wAe4NUycPn1azz33nLKzs9W/f3/5+fnpsccek91ud4SJHTt2KCEhQS+99JJatmypyMhIJSYmqqCgQJK0dOlS3Xrrrbr11lu1efPmi46VmpqqoqIil2urqqqSJAUHBzv1h4SEqLKy0nF/8ODBWrduncvPC99js9lUXFysdu3aObWMjAzFxMR4u7xa3nvvPfn71/2rWVNTo4ULF3qmoCbut4Hi/vvvJ0gAbnTixAmNGzdOPXr00MKFC9WiRQuX1jv/GImPPvpIo0aN0syZM5Wfn+/migHUxa1hYuvWraqpqdF9993n6Pvxxx8lyWlm4qGHHnJa78iRI2rfvr0qKiqUmZmpzZs3a+3atXr22WcbbF/xwMBASWc3auerqKhQUFCQ435paak6d+7cIGPCO77++mtNnz5dBQUFTu3KK6/0yZkJV2YcLBaL9u7d6/5imomrr75aGzduVGhoqD788EMNHjyYIAG4SXZ2tg4ePKj58+erVatWLq1zfpA4d4zEnDlzFBQUpFdffdXNFQOok+FGCxcuNLp37+7UN2PGDCM8PNwwDMM4ceKE4efnZ2zatMnx+KFDh4yAgABj+/btRm5urvH00087HrvvvvuM3bt3m65nwYIFRlxcnON+586djffee89xf/fu3YYkY8+ePY6+xMREY8GCBabHdJUkWj3a+f+Pdfn+++8NScbXX399wf7Dhw+7/H8UFxfn9ddNo9Foja2dv7222+3GddddZwwYMMDlbe/x48eNfv36GS1btjTWrl3r9Njzzz9vWCwW48CBA2yraTQ3trq4dWaiR48eKi4u1tatW1VdXa3ly5crPT3dMStRUFAgi8WiJUuW6Ndff9WBAwc0YsQIjRgxQjfffLOOHTum0NBQx/OFhoY26Kkxx48fr4yMDO3Zs0eVlZVKSUlRQkKCunbtKkk6deqUNm/e7JGDuwzDoLnY4uLiXH5fbTab2rRpoz59+jj1b9u2TZ06dVL79u3r9f8UFxfn9tf3z3/+06VaPvvsM6//XzSFVlNToylTpkiSJk6cKEm6+eab1bJlS61bt87r9dFojbn9dntdXFysPXv21Noj4WIuNCNxvlGjRslut2vTpk0e31Y3lZaS/u4Fb/tya4w1N+a6DcOo8/fUrWEiJiZGL774ooYOHaqOHTsqLy9P/fv3d9rF6a677lJERITCw8N12223acCAAcrKypIktW3bVuXl5Y7nq6iouOiZHmbMmKGePXvWq77U1FQlJSUpJiZGHTp0kN1u19KlSx2Pb9y4UdHR0WrXrl19Xzp8hM1mU0xMTK19cr/88kuf3MVJkv70pz+pW7duFz1uwt/fX7///e91++23e7iypscwah9sLemSp40FYM65A6Z///vfX3LZSwUJSbrxxht11VVXcSA24EVuP5tTWlqajh07piNHjmju3Ln67rvvHGHimWee0YYNG/Taa6/p2LFjKi0t1V//+lfHF7/+/fvr888/15kzZ3T8+HEdPHjQMWvwW9OmTdOuXbvqVZvFYlFmZqaOHj2qqqoqffjhh07BYc2aNUpOTjb3wuETZs+erS1bttTqz8rK0ocffuj5glxwxRVXaOPGjerYsaMkOULFuX979OihnJwc9ue/TBcKEufeU1euQwGg/vbv3y9JioqKqnM5V4KEdPZzvFu3btq3b1+D1wrANR69aF1lZaVKS0sdYeJSQkJCNGnSJMXHx2vw4MF64403LnmWm4bUpUsXx/UwAE+KjIzUrl279O677+q2226TJMXHx2vx4sWy2Wwun0YRF1ZXkDiHQAE0vCeffFI//PCDrrrqqjqXO3bsmI4ePerSBek+/fRTzm4HeJFr52NrIDt37lRgYKAiIyNdXmf06NEaPXp0g4xvtVo1ZswYl5efPn16g4wLmBEQEKDx48dr/Pjx8vPzq7VPMMxbtmyZS6d/PRcoBg4cqKFDh6q4uNgxYwSg/tq0aaM2bdpccrmoqCh9++23Lp3tqb7HvgFoWB4NE7GxsU7XcPA0q9Uqq9XqtfEB+IYHH3xQ1dXVeuSRRy65u9i5QPHpp58SJAAPcvW0sQC8y6NhAgB8wRVXXKGxY8e6vPzVV1+tBx54wI0VAQDQOHn0mAkAAAAATQdhAgAAAIAphAkAAAAAphAmAAAAAJhCmAAAAABgCmdzQqNUUFCg+Ph4j4/JqYUBoH48vb1mWw14FmECjY63PiS4TgkA1I/ZbWbJvjJ163xtrduujsm2GvAcwgQanTlz5ni7BACAC8xur1MzspWeMr7WbQC+h2MmAAAAAJhCmAAAAABgCmECAAAAgCmECQAAAACmECYAAAAAmEKYAAAAAGAKYQIAAACAKYQJAAAAAKYQJgAAAACYQpgAAAAAYAphAgAAAIAphAkAAAAAphAmAAAAAJjSwtsFwLsmTZqkgoICj49rtVo1Z84cU+t6q2bp8uoGALPY7gHwVcxMNHMFBQUe/4C63DG9UbM3xwUAtnsAfBUzE5DVatWWLVs8Nl58fPxlP4ena5Yapm4AMIvtHgBfxMwEAAAAAFMIEwAAAABMIUwAAAAAMIUwAQAAAMAUwgQAAAAAUwgTAAAAAEwhTAA+oqqqSuPGjdOPP/7o0vJ79+7V448/rjNnzri5MgCNzS+//KKvv/5a7777rl544QWlpKTo9ddf16effqoTJ05ccJ3y8nKNGzdO5eXlHq4WQGPmE2Fi8ODBmjlzptvHWbhwYb3Omd23b19t2LDBfQUB59m1a5eWLVumu+6665KBYu/evbrzzjv1/vvva8+ePR6qEICvO378uP7617+qa9euiomJ0YQJE5SZmak5c+bo+eef18CBAxUeHq6HH35YhYWFjvXKy8s1aNAgLV68mIvUAagXnwgT+fn56t27t8fHtdvtmjp1qsLCwhQYGKhhw4bp6NGjjseTk5O1Zs0aj9fly06ePKmwsDB98MEHjr6ffvpJsbGxuv/++1VTU+PF6i4uIiJC8+bNc+ozDENBQUFavXq1l6pydsstt2jt2rXavXt3nYHiXJCoqKjQp59+qt/97ncerhSAL8rJyVGPHj00ffp09e7dW8uXL9fu3btVXV2tM2fO6OjRo9q4caMeffRRffjhh+rbt6+mTZumQ4cOadCgQSoqKtKqVat05513evulAGhEvB4mDh8+rLKyMq+EifT0dOXk5CgvL08HDhyQJI0aNcrxOGGitoCAAE2ZMkVpaWkyDEN2u10PPPCAWrVqpWXLlsnf3+s/UrUcPHhQZWVlslqtTv0lJSWqqqpSv379vFRZbXfffXedgeK3QaJv375eqhSAL8nIyNCQIUN0zTXXaMeOHfrkk080cuRIdevWTX5+fpKktm3bauDAgXr77be1b98+jR49WjNnzlT37t0dQSIxMdHLrwRAY+ORb34rVqxQVFSUAgICNGjQIE2ePFnDhw+XdHZWIiQkROvWrdP111+v4OBgPfLII/rll1/cXld2drZSUlLUrVs3BQcHa9asWcrNzVVpaakkqU+fPrJYLNq+fbvba2lMnnzySR06dEirVq3S+PHjdeDAAeXk5KhVq1beLu2CbDabLBaLevXq5dRfWFio8PBwderUyUuVXdjFAgVBAsCFZGdnKzU1VSNHjtRXX32l6OjoS64TGhqqN954Q9ddd52qqqp000036Q9/+IMHqgXQ1Lg9TCxatEiTJ0/WsmXLVFVVpcTERM2dO9exscvPz9fJkyd15MgR7dq1Szt27FBubq7mz59fr3HS09PrNbtRUVGhffv2OX0hi4yMVFBQkNN+pMnJycrJyalXLU3dVVddpalTp2rMmDHasmWLcnNzFRQU5O2yLspms6l79+5q3bq1U39hYaFPzUqc77eBQhJBAkAt33//vSZNmqSEhAQtXrxYLVu2dGm9c8dIHDx4UBMmTND27duVlZXl5moBNEVuDROnT5/Wc889p+zsbPXv319+fn567LHHZLfbHWFix44dSkhI0EsvvaSWLVsqMjJSiYmJjgPA7rnnHoWFhenVV1+tc6zU1FQVFRW5XFtVVZUkKTg42Kk/JCRElZWVjvuDBw/WunXrXH7e5uTUqVNKTU1VeHi4t0upk81mU3Fxsdq1a+fUMjIyFBMT4+3yLupcoCguLpZ09sBKggSA802aNEktW7bUe++9pxYtWri0zrkgcW7XpnfeeUcJCQlKSUnRsWPH3FwxgCbHcKP169cbISEhTn179+41JBllZWWGYRhGZGSksXz5cqdl/vjHPxovvfSSYRiGsX//fmPBggXGK6+8ctn1LFiwwIiLizMMwzDKy8sNSUZ+fr7TMkFBQUZOTo7jfnZ2tjFkyJDLHvtSJHmtnXtPXLVkyRIjNDTUGDt2rNGzZ0+jpqamXuvHxcV5tObQ0FDjtddeM/bv3+/UQkJCjI8//tijddNoNJrZ9tvt3vfff29IMqZPn+7yduz48eNGv379jJYtWxpr16519BcVFRmSjMzMTLZ7NBqtVquLW2cmjhw5ovbt2zv1LV++XOHh4brmmmtUWVmpkpISp79sHz58WP/617+UnJwsSerYsaNbagsJCVHnzp21Y8cOR19JSYkqKyuddpdas2aNoxZ3MgzDKy0uLq5eda5fv14TJ07URx99pDfffFNHjhzRypUr6/164+LiPFJzcXGxysvLlZCQoI4dOzrazz//rIqKinrPTFxO3fVte/bsUdeuXRUSEiJJuvLKK9WrVy8dOXLEaz8vzaFJ3vt9pNEu1i603Vu6dKn8/f01btw4l7Zfv52ROP9g65tuukm33XabFi9e7NXt3rmWkv7uBW/TeK8ba82NuW7DMOrctrg1TPTo0UPFxcXaunWrqqurtXz5cqWnpzt2cSooKJDFYtGSJUv066+/6sCBAxoxYoRGjBihm2++2Z2lSZLGjx+vjIwM7dmzR5WVlUpJSVFCQoK6du0q6exuPJs3b+bsFv+xbds2jRgxQosXL9aAAQMcx06kpaX57ClhbTab2rRpoz59+jj1b9u2TZ06daoVdn3Fbw+2luTSaWMBNB82m009evRQRETEJZetK0icc9ddd2nnzp06deqUO8oF0ES5NUzExMToxRdf1NChQ9WxY0fl5eWpf//+Tgdf33XXXYqIiFB4eLhuu+02DRgwwNRBYDNmzFDPnj3rtU5qaqqSkpIUExOjDh06yG63a+nSpY7HN27cqOjoaLVr167e9TQ1O3fuVGJiombPnq0hQ4Y4+p944gn9+OOPpmYnPMFmsykmJqbWvsRffvmlzx58fbGzNl3qtLEAmpedO3fWOuX1hbgSJCTJarWqpqZG//d//9fQpQJowlw7WusypKWlKS0tzXG/a9eujinZZ555Rs8884wk6bXXXruscaZNm6Zp06bVax2LxaLMzExlZmZe8HFP7eLUGPTq1UvHjx+v1d+mTRsdPnzYCxW5Zvbs2Rfs99Wzllzq9K/nAkVSUpLuuusu/etf/1JYWJiXqgXgTWPHjq11yusLeeKJJ1y6jkSvXr00ZcoUtW3btiHLBNDEuT1MnK+yslKlpaUunQP7nLFjxyovL09nzpxRXl6e1q5d68YKnXXp0sVxPQzA3Vy9jgSBAoAkvfzyyy4tl5mZqUceeUQDBw6sc7nu3bvr9ddfb4jSADQjHg0TO3fuVGBgoCIjI11ep77Xm6iL1WrVmDFjXF5++vTpDTY2cCnV1dW66qqr9MEHH1zy9K/nAsWUKVM8coFHAI1XRESES8dVAIAZHg0TsbGxTtdw8DSr1erS/qWAN3Tv3l1FRUXy93ftUKa7775b27dvd3l5AACAhsa3EMCH1DcYECQAAIA38U0EAAAAgCmECQAAAACmECYAAAAAmEKYAAAAAGAKYQIAAACAKR49NSx8U0FBgeLj4z063uWeotfTNZ8bk1MLA/AWtnsAfBFhopnzxofE5V7vw1sfbFynBIC3XM62p2Rfmbp1vrbWbVfHZbsHoC6EiWZuzpw53i6h3hpjzQBwOS5nu5eaka30lPG1bgNAQ+CYCQAAAACmECYAAAAAmEKYAAAAAGAKYQIAAACAKYQJAAAAAKYQJgAAAACYQpgAAAAAYAphAgAAAIAphAkAAAAAphAmAAAAAJhCmAAAAABgCmECAAAAgCmECQAAAACmtPB2AfCuSZMmqaCgwOPjWq1WzZkzx9S63qpZury6AfiGxrjdAwBfxcxEM1dQUODxD9XLHdMbNXtzXAANqzFu9wDAVzEzAVmtVm3ZssVj48XHx1/2c3i6Zqlh6gbgGxrjdg8AfBEzEwAAAABMIUwAAAAAMIUwAQAAAMAUwgQAAAAAUwgTAAAAAEwhTAA+ZNeuXS4vaxhGvZYHcHlOnz6tI0eO6Pjx4zIMo85ly8vL9cMPP3ioMgDwHp8IE4MHD9bMmTPdPs7ChQvrdXq+vn37asOGDe4rCDjP5s2bddNNN+n111+/5LKGYej5559XdHS0ioqKPFAd0PwYhqEvvvhCY8eO1Y033qiAgACFh4erbdu2CgsLU0JCgt59912dPHnSab3y8nINGjRICQkJ+vXXX71UPQB4hk+Eifz8fPXu3dvj49rtdk2dOlVhYWEKDAzUsGHDdPToUcfjycnJWrNmjcfr8mUnT55UWFiYPvjgA0ffTz/9pNjYWN1///2qqanxYnUXFxERoXnz5jn1GYahoKAgrV692ktVObvjjjs0fPhwPf/883UGinNBIjMzU+PGjdNNN93kwSov7eTJk8rOztaECRP0xBNPaNWqVfrll1+8XRZQL0VFRbrlllt0++23a9WqVerevbtefvllvfXWW3rjjTc0ZMgQ7d+/XxMmTFCHDh00d+5c1dTUOIJEUVGRZs6cqRYtuJwTgKbN61u5w4cPq6yszCthIj09XTk5OcrLy1Pbtm01duxYjRo1Sp988omks2EiMTFRb7/9tsdr81UBAQGaMmWK0tLSNGzYMNXU1OiBBx5Qq1attGzZMvn7+0Q+dXLw4EGVlZXJarU69ZeUlKiqqkr9+vXzUmXOWrRooWXLlkmSnn/+eUnS1KlTnZY5P0hMnDhRb731lvz8/Dxe68WsWLFCjz76qE6ePCmLxSLDMPTOO+8oIiJCH330kWJiYrxdInBJb775pqZMmaLQ0FC9++67euihh3TVVVfVWs4wDOXl5SktLU2TJk3SihUrdPr0aX3zzTdatWqVEhMTvVA9AHiWR775rVixQlFRUQoICNCgQYM0efJkDR8+XNLZWYmQkBCtW7dO119/vYKDg/XII4945C+Z2dnZSklJUbdu3RQcHKxZs2YpNzdXpaWlkqQ+ffrIYrFo+/btbq+lMXnyySd16NAhrVq1SuPHj9eBAweUk5OjVq1aebu0C7LZbLJYLOrVq5dTf2FhocLDw9WpUycvVVbbuUDxwAMP1Jqh8PUgsWHDBo0cOVKnTp2SdHbm79xM1aFDh3TPPfeouLjYmyUCl/T666/rmWee0R/+8Ad98803Gj9+/AWDhCT5+fnplltu0bp16/TWW2/pyy+/VGFhoRYtWkSQANBsuD1MLFq0SJMnT9ayZctUVVWlxMREzZ07V9HR0ZLOhomTJ0/qyJEj2rVrl3bs2KHc3FzNnz+/XuOkp6fXa3ajoqJC+/btU9++fR19kZGRCgoKUmFhoaMvOTlZOTk59aqlqbvqqqs0depUjRkzRlu2bFFubq6CgoK8XdZF2Ww2de/eXa1bt3bqLyws9JlZifNdLFD4cpCQpBdffFGSLnhgak1NjU6ePOnS8SCAt/zrX//S888/rwcffFCrVq1S27ZtXVqvoqJCCxcuVIsWLeTv769Vq1a5uVIA8B1uDROnT5/Wc889p+zsbPXv319+fn567LHHZLfbHWFix44dSkhI0EsvvaSWLVsqMjJSiYmJKigo0O7duzVgwADdcccduv322/X1119fdKzU1NR6HYhaVVUlSQoODnbqDwkJUWVlpeP+4MGDtW7duvq87Gbj1KlTSk1NVXh4uLdLqZPNZlNxcbHatWvn1DIyMnx2t5vfBgpJPh0kvvnmG23fvr3OY2Zqamq0ePFijp+ATzp9+rQeffRRXX/99Zo/f74sFotL651/jMSHH36oV199VR988IHTcWUA0JS5NUxs3bpVNTU1uu+++xx9P/74oyQ5zUw89NBDTusdOXJE7du3V0hIiFavXq3PP/9c2dnZevbZZxustsDAQEnSiRMnnPorKiqc/speWlqqzp07N9i4TcHSpUs1c+ZMjR07VnPnzr3kKRK97euvv9b06dNVUFDg1K688kqfnJk4p0WLFlq6dKluuOEGSdKtt97qk0FCksrKylxa7ueff3YK64CvWLZsmfbu3at//OMfatOmjUvrnB8kzh0jMWXKFPXq1UuvvPKKz28bAaBBGG60cOFCo3v37k59M2bMMMLDww3DMIwTJ04Yfn5+xqZNmxyPHzp0yAgICDC2b9/utF5xcbERFxd3WfUsWLDA6Tk6d+5svPfee477u3fvNiQZe/bscfQlJiYaCxYsuKxxXSHJa60+7+u6deuMwMBAY+vWrcbJkyeNsLAw45///Ge9XmtcXJzHav7+++8NScbXX399wf7Dhw97tG4ajeYb7bfbkOjoaKNPnz5GTU2NS9uD48ePG/369TNatmxprF271umx7OxsQ5Kxbds2th80Gq1JtLq4dWaiR48eKi4u1tatW1VdXa3ly5crPT3dMStRUFAgi8WiJUuW6Ndff9WBAwc0YsQIjRgxQjfffLPjeex2u55++mmlpqY2aH3jx49XRkaG9uzZo8rKSqWkpCghIUFdu3aVdHY3ns2bN3vkQDrDMLzS4uLiXK5x27ZtGjFihBYvXqwBAwY4jp1IS0ur9ylh4+LiPFKzzWZTmzZt1KdPn1qvpVOnTmrfvr3H6q5Pq6mp0ZQpUyRJEydOVHV1tR544AFJ0qxZs7z281JXvddff32dsyb+/v4aOXKk12u9VJO89/tI80z77Tbk2LFjys/P14gRI1ya+bvQjMT5zv2ubtq0ySvbj9+2lPR3L3jbl1tjrLmxtsb4XjfGmhtz3YZh1LlNdGuYiImJ0YsvvqihQ4eqY8eOysvLU//+/Z12cbrrrrsUERGh8PBw3XbbbRowYICysrIcz2EYhsaOHavExETde++9Fx1rxowZ6tmzZ73qS01NVVJSkmJiYtShQwfZ7XYtXbrU8fjGjRsVHR2tdu3a1fOVNz07d+5UYmKiZs+erSFDhjj6n3jiCf34449auXKlF6u7OJvNppiYmFrnev/yyy99dhcnw6h91qYrrrjiomd58gV+fn56+eWXL7rB8ff3l8VicQQkwJfs2LFDklzaJlwqSEhnj8W74YYbOBMggGbB7deZSEtLU1pamuN+165dNW7cOEnSM888o2eeeUaS9Nprr11w/aeeekpRUVF6/PHH6xxn2rRpmjZtWr1qs1gsyszMVGZm5gUfX7NmjZKTk+v1nE1Vr169dPz48Vr9bdq00eHDh71QkWtmz559wf7zA6svuVCQOPeXUleuQ+FNDz30kA4dOuRU07lw0bJlS61cudJpxhHwFee2YedmpS/GlSBxTteuXX162wgADcWjVxirrKxUaWmpY2biUrZs2aLs7Gxt2rRJ8fHxGjp0qJsrdNalSxfH9TAAd6srSJxT13UofMHkyZO1e/dupaSkaODAgZLOnrf/wIEDnHcfPuvPf/6z7Ha7IiMj61zOz89PrVu3dumCdOvXr9e2bdsaskwA8EkevQL2zp07FRgYeMkN9jnx8fGqrq5usPGtVqvGjBnj8vLTp09vsLGBS9m0aZNLp3/97QzFoEGDah0T4k3XXXedZs6cKensly92bUJj4O9/6b+thYSE6LPPPnPpuApXng8AmgKPhonY2FivnhbSarXKarV6bXygLvfcc4/Wr1+ve++995JfVs4FikcffdSnggTQ1PniqZkBwJs8GiYA1O38a7JcSosWLTRo0CA3VgMAAFA35mEBAAAAmEKYAAAAAGAKYQIAAACAKYQJAAAAAKYQJgAAAACYwtmcoIKCAsXHx3t0vMs9Ra+naz43JqcWBpqGxrjdAwBfRJho5rzx4Xa51/vw1gcy1ykBmgazv8cl+8rUrfO1tW67OibbDwBNEWGimZszZ463S6i3xlgzAN9hdhuSmpGt9JTxtW4DQHPGMRMAAAAATCFMAAAAADCFMAEAAADAFMIEAAAAAFMIEwAAAABMIUwAAAAAMIUwAQAAAMAUwgQAAAAAUwgTAAAAAEwhTAAAAAAwhTABAAAAwBTCBAAAAABTCBMAAAAATGnh7QKA+po0aZIKCgq8MrbVatWcOXO8Mjbga/hdBAAwM4FGp6CgwCtfYLw1LuCr+F0EADAzgUbJarVqy5YtHh0zPj7eo+MBjQG/iwDQvDEzAQAAAMAUwgQAAAAAUwgTAAAAAEwhTAAAAAAwhTABAAAAwBTCBAAAAABTODUsgMsya9Ys+fv7a8qUKZdc1m63a8KECUpOTlZiYqIHqoMvOX36tM2ELM0AACAASURBVD777DNt375du3fv1i+//KLQ0FBZrVbFxsbqd7/7Xa11ysvL9fDDD+v111/XDTfc4IWqAQB18YmZicGDB2vmzJluH2fhwoX1Oj953759tWHDBvcVBDRyhmFox44dmjp1qjIzM+tc1m63a+zYsZo3b57+/e9/e6jC+ikrK5MknThxwsuVNC2HDx/Wc889pw4dOui+++7Tf/3Xf2njxo364osvtHDhQj366KO68cYbddttt2nVqlUyDEPS2SAxaNAgbdiwQSUlJV5+FQCAC/GJMJGfn6/evXt7fFy73a6pU6cqLCxMgYGBGjZsmI4ePep4PDk5WWvWrPF4XWh4ERERmjdvnlOfYRgKCgrS6tWrvVRV4+fn56elS5fqwQcfrDNQnAsSixcv1iuvvKIXXnjBw5XWbe3atYqNjVVERIQkqV27dnrooYf07bffermyxm/lypXq2bOn/v73vzuCQUVFhQ4cOKCSkhJVVFTo//v/2bv7sKjuA/3/NwwKURmGANEYAwjGJmoEUWp8ivgQadRoCDEbd2M0xujWtpqNocPafE02DRStSaPdtslciQ/xoWlcsktsLHZrNUk1ZU1V/Gp+TVdBBWslqHSQVA1wfn/4deqEB+E4nJnB9+u6znXNfM6Z+dwgIDfn6bPP9PLLL6uqqkoPP/ywHnroIX322WeaNGmSDh48qMLCQt1///3+/lAAAM3we5k4ffq0Tp065ZcyUVBQoKKiIpWUlKiyslKSNGvWLM96ykTncPLkSZ06dUqpqale42VlZaqtrdWwYcP8lKxzCAsLa7VQfLVIPPfcc35K2rzVq1dr2rRpKikp8YzV19fr7bff1te//nX94Q9/8GO64LZ8+XI98sgjSkpKUmlpqX7xi19o0qRJioqK8mwTGhqq/v3765lnntEf//hHrVixQtu2bVNKSoqnSHBIHAAELkvKxDvvvKN+/fqpR48emjRpkpYsWaIZM2ZIurxXwuFw6P3339cdd9yhqKgoPfHEE/ryyy87PJfL5ZLT6VRSUpKioqK0YsUKFRcX6/jx45KklJQU2Ww2fpkIcnv37pXNZtOgQYO8xktLS9WzZ0/dfvvtfkrWebRWKAK5SPzxj3/U008/LUlqbGz0WtfY2Ki6ujrNmDGjyTpc29q1a5Wbm6uZM2dq9+7dGjBgwDVfY7PZNG/ePCUnJ+vixYuKjY1t16GpAADrdXiZWL9+vZYsWaJNmzaptrZWU6dO1apVqzRkyBBJl8vE+fPnVVVVpcOHD2vfvn0qLi7WmjVr2jVPQUFBu/Zu1NTU6MSJExo6dKhnLDk5WXa7XaWlpZ6x6dOnq6ioqF1ZEFj27t2r/v37KyIiwmu8tLSUvRI+9NVCsWLFCkkK2CIhST/72c9aXd/Y2Kjy8nL993//t0WJOodjx45p0aJFGjdunN566y116dKlTa+7co7E0aNHlZ+fr1OnTsnpdHZwWgDA9ejQMvHFF1/omWeekcvl0vDhwxUSEqJ58+apoaHBUyb27dunzMxMLVu2TF27dlVycrKmTp2qAwcO6PTp0xo5cqQyMjI0fPhw7dixo8W5cnNzdfDgwTZnq62tlSSv3e2S5HA45Ha7Pc+nTJmi999/vz0fNgLM3r17deTIEcXGxnoty5cvV3p6ur/jdSpXCsUjjzzi+SUwUIuEJP3ud7/znOzbmj179liQpvNwOp0yDENr1qxRWFjbLhp4pUhcObTpX//1X7V48WL99Kc/bdfPdgCAxYwOtG3bNsPhcHiNHTt2zJBknDp1yjAMw0hOTjY2b97stc20adOMZcuWGfX19UZ9fb1hGIZx9OhRY9iwYdeVZ+3atcbYsWMNwzCMc+fOGZKM/fv3e21jt9uNoqIiz3OXy2U8+OCD1zVvW0hiacdy5d+xLaKjo428vDyjoqLCa3E4HMYvf/nLNr/P2LFj/f5xs7AE2vLV78WTJ08aYWFhxjPPPNPm762zZ88aw4YNM7p27Wps3brVM15dXW1EREQY//zP/8z3IgsLC4sfl9Z06J6Jqqoq3XLLLV5jmzdvVs+ePdWrVy+53W6VlZWpZ8+envWnT5/Wb3/7W02fPl02m002m03S5cOSfHmStsPhUHx8vPbt2+cZKysrk9vt9prnvffe0/Tp0302b0sMw2Bp4zJ27Ng2f16PHDmic+fOKTMzU3369PEsFy5cUE1NTbv3TIwdO9bvH38gL/X19Xr88cclSS+88ILn8/bDH/7Q79maW771rW8pJCTkmv/u77//vt+zBuLS3PdiYWGh6uvrtWDBgjZ9T311j8TVJ1vHxMRoxowZ+vnPf97kvBV/fC86C15v9nGgL8GYOxgzB+sSjJ/rYMwczLkNw2j153iHlokBAwboyJEj+uCDD3Tp0iVt3rxZBQUFnkOcDhw4IJvNpg0bNqi+vl6VlZV69NFH9eijjyotLU2SVF5ertGjRyszM1NZWVk+zTd//nwtX75c5eXlcrvdcjqdyszMVGJioiSprq5OO3fu5EoiQWzv3r3q1q2bUlJSvMb37Nmj22+/vUnZhXlfvWrT888/L0nXvGysP33zm99s9YdkaGio4uPjlZmZaWGq4PbJJ5+oV69e6t+//zW3ba1IXDF27Fj99a9/1dGjRzsiLgDgOnVomUhPT9f3vvc9PfTQQ+rTp49KSko0fPhwr5Ovx48fr969e6tnz54aNWqU7r33Xq+TIvv27avf/e53Kikp0be//e0W58rPz9fAgQPblS83N1cPPPCA0tPTddttt6mhoUEbN270rP/1r3+tIUOGKDY2tp0fOQLF3r17lZ6e3uS47Y8//piTr32otcu/tuU+FP4ycOBAz4nioaHePw5DQ0MVERGhX/ziF549pLi2Tz/9tE17kdtSJCR53uvTTz/1aU4AgG+07cy46/Diiy/qxRdf9DxPTEzUU089JUlavHixFi9eLEnKy8tr8tqLFy8qPDxckmS329WjR48W51m6dKmWLl3armw2m00rV65s8Rccqw5xQsd55ZVXmh2/1lV80HbXuo/ElZOyJSknJ0eS9Oyzz1qesyU5OTnq27evfvCDH3gOewwNDVVWVpaef/553X333X5OGFwWLVqkyMjIa2730ksvtek+En379tXKlSt11113+TImAMBHOrxMXM3tduv48eOePRPXsnfvXi1dulQ2m01ffvmlVq1a1cEJvSUkJHjuhwGgKcMw2nQfia8WitDQUD3zzDNWRm3Vww8/rIcffljHjh1T3759dfr0afZImnT1jT9bk5eXp4ceekijRo1qdbvY2FgtWbLEF9EAAB3A0jJx6NAhRUZGKjk5uU3bjx49Wh9++KHP5k9NTdWcOXPavP3VJ5ACaCokJETJycltuvzrlULRpUsXJSQkWJSwfa6cL0WR6HgRERHXLBIAgMBnaZkYOXKk1z0crJaamqrU1FS/zQ90RsuWLWvztmFhYdqwYUMHpgEAAFbq8DtgAwAAAOicKBMAAAAATKFMAAAAADCFMgEAAADAFMoEAAAAAFMoEwAAAABMsfTSsICvHDhwQBkZGZbPyaWFAW98LwLAjY0ygaDjr18iuE8J4O16vh/KTpxSUvytTR63dV6+FwEgMFAmEHReffVVf0cAoOv7Xsxd7lKBc36TxwCA4MI5EwAAAABMoUwAAAAAMIUyAQAAAMAUygQAAAAAUygTAAAAAEyhTAAAAAAwhTIBAAAAwBTKBAAAAABTKBMAAAAATKFMAAAAADCFMgEAAADAFMoEAAAAAFMoEwAAAABMCfN3APjX008/rQMHDlg+b2pqql599VVTr/VXZun6cgOt4esaABCM2DNxgztw4IDlv8Bc75z+yOzPeXFj4OsaABCM2DMBpaamateuXZbNl5GRcd3vYXVmyTe5gdbwdQ0ACDbsmQAAAABgCmUCAAAAgCmUCQAAAACmUCYAAAAAmEKZAAAAAGAKZQLAdSkrK9OxY8favP0nn3yi2trajgvUBoZhaOfOnW3e/sKFC9qzZ08HJjLHMAxVVFSotLRUhw4duubn9dy5c9q/f79F6QAAN4KAKBNTpkzRD37wgw6fZ926de26DOLQoUO1ffv2jgsEBLnGxkZlZ2crIyOjTYXio48+UkZGhr7zne90fLhWbNy4UePHj9cPf/jDa2574cIFPfTQQxo/frwqKystSNe6xsZG/epXv1JWVpZuueUWxcfHKzU1VXfffbeioqJ05513KicnR0ePHvV63blz5zRp0iRlZmaqrq7OT+kBAJ1NQJSJ/fv3a/DgwZbP29DQoJycHMXFxSkyMlLZ2dmqrq72rJ8+fbree+89y3MFsvPnzysuLk7/8R//4Rn729/+ppEjR+rhhx9WY2OjH9O1rHfv3nrjjTe8xgzDkN1u13/+53/6KVXwCw0N1Ztvvim3233NQvHRRx/p/vvv1+23327JHw9aM3PmTD3yyCP67ne/22qhuFIkfvWrX+nHP/6x+vTpY2HKpj755BOlpKRo8uTJ+v3vf69p06bp3//931VYWKi3335bL7zwgpKSkvSjH/1I/fr104IFC+R2uz1F4uDBg1qzZo26d+/u148DANB5+P2mdadPn9apU6f8UiYKCgpUVFSkkpISxcTEaO7cuZo1a5Z+9atfSbpcJqZOnaqf/OQnlmcLVD169NCzzz6rF198UdnZ2WpsbNQjjzyi8PBwbdq0SaGhAdFPvZw8eVKnTp1Samqq13hZWZlqa2s1bNgwPyXrHNLS0vSb3/xGEydOVEZGhnbt2qXExESvba4uEr/97W916623+ifs/xMWFqZNmzZJkr773e9KknJycry2ubpIuFwuPfXUU5bnvNqPfvQj5eTkqFevXtq8ebOys7PVtWvXZrc9efKkXn75Za1atUrbtm1TVFSU/vd//1eFhYWaOnWqxckBAJ2ZJb/5vfPOO+rXr5969OihSZMmacmSJZoxY4aky3slHA6H3n//fd1xxx2KiorSE088oS+//LLDc7lcLjmdTiUlJSkqKkorVqxQcXGxjh8/LklKSUmRzWbTH/7whw7PEky+/e1v6y9/+YsKCws1f/58VVZWqqioSOHh4f6O1qy9e/fKZrNp0KBBXuOlpaXq2bOnbr/9dj8l6zyuFIrm9lAEWpG44kqhaG4PRaAViZdfflnPPPOMpk+frkOHDmnmzJktFglJuu222/TKK69o27Zt+stf/qLDhw9r1apVFAkAgM91eJlYv369lixZok2bNqm2tlZTp07VqlWrNGTIEEmXy8T58+dVVVWlw4cPa9++fSouLtaaNWvaNU9BQUG79m7U1NToxIkTGjp0qGcsOTlZdrtdpaWlnrHp06erqKioXVk6u+7duysnJ0dz5szRrl27VFxcLLvd7u9YLdq7d6/69++viIgIr/HS0lL2SvhQS4UiEIvEFS0VikAqErt371ZOTo5mzJihd955Rw6Ho02vO3funJ577jmFhITIbrfrtdde06VLlzo4LQDgRtOhZeKLL77QM888I5fLpeHDhyskJETz5s1TQ0ODp0zs27dPmZmZWrZsmbp27ark5GRNnTpVBw4c8LzPmTNnFB0drY0bN7Y4V25urg4ePNjmbFeuehIVFeU17nA45Ha7Pc+nTJmi999/v83veyOpq6tTbm6uevbs6e8ordq7d6+OHDmi2NhYr2X58uVKT0/3d7xO5epCMWLECEkK2CJxxVcLhaSAKRKXLl3S3LlzlZCQoDVr1shms7XpdVefI/Huu+9qw4YNKi0t1YoVKzo4MQDghmN0oG3bthkOh8Nr7NixY4Yk49SpU4ZhGEZycrKxefNmr22mTZtmLFu2zPP86aefNqZOnWps2LDhuvKsXbvWGDt2rGEYhnHu3DlDkrF//36vbex2u1FUVOR57nK5jAcffPC65m0LSX5brnxO2mrDhg1GdHS0MXfuXGPgwIFGY2Nju14/duxYSzNHR0cbeXl5RkVFhdficDiMX/7yl5bmZmFpbfnq1/Xbb79tSPL6mXQtZ8+eNYYNG2Z07drV2Lp1q2d8+vTpxs0332x88cUXfF2zsLCwsLRraU2H7pmoqqrSLbfc4jW2efNm9ezZU7169ZLb7VZZWZnXX7ZPnz6t3/72t5o+fbok6ciRIzpz5ozX4Ui+4HA4FB8fr3379nnGysrK5Ha7vQ6Xeu+99zxZOpJhGH5Zxo4d266c27Zt08KFC/Vf//VfWr16taqqqrRly5Z2f7xjx461JPORI0d07tw5ZWZmqk+fPp7lwoULqqmpafeeievJfaMsH374obp3767ExEQ5HA4lJCSovLzc77laW/72t7/p/vvvlyTPoW8rVqywNENzX9evv/66kpKS2nyuw9V7JL56svWiRYt09uxZFRYWBsTXtbPg9WYfB/ISjJmDNXcwZg7WJRg/18GYOZhzG4bR6v89HVomBgwYoCNHjuiDDz7QpUuXtHnzZhUUFHgOcTpw4IBsNps2bNig+vp6VVZW6tFHH9Wjjz6qtLQ0SdKyZcv0/PPPd0i++fPna/ny5SovL5fb7ZbT6VRmZqbnSjR1dXXauXMnJy3+P3v27NGjjz6qt956S/fee6/n3IkXX3wxYC8Ju3fvXnXr1k0pKSle43v27NHtt9/epOzi+lx9svWePXu0Y8eONl021p++erL1xx9/3KbLxna0S5cuaffu3crKymrTVdJaKxKSNG7cON1888364IMPOioyAOAG1KFlIj09Xd/73vf00EMPqU+fPiopKdHw4cO9Tr4eP368evfurZ49e2rUqFG699579bOf/UzS5V/4YmJilJycfM258vPzNXDgwHbly83N1QMPPKD09HTddtttamho8Dov49e//rWGDBmi2NjYdr1vZ3To0CFNnTpVr7zyih588EHP+Le+9S19/vnnpvZOWGHv3r1KT09XWJj3VZA//vhjTr72seau2tTaVZ4CQXNXbWrtKk9W+vTTT3Xp0qU2fZ1eq0hIUkhIiNLS0rg6HQDApzr8PhMvvviiXnzxRc/zxMREz0mNixcv1uLFiyVJeXl5TV77ySef6ODBg/rGN76hI0eOqHv37kpOTvac2Hm1pUuXaunSpe3KZrPZtHLlSq1cubLZ9VYd4hQMBg0apLNnzzYZ79atm06fPu2HRG3zyiuvNDt+pbDCN1q7/Gtb7kPhD61d/rUt96HoaLW1tbr11lvVt2/fVrdzu93XLBJXDBgwQL///e99HRUAcAOz9KZ1brdbx48f9+yZuJZFixZp0aJFkqQXXnhB/fr1a7ZIdJSEhATP/TAANK8t95EItELRlvtI+LtQjBkzRn/+85+vuV337t01ePBgPf/889c8JHPVqlW+igcAgCSLy8ShQ4cUGRnZpsOWvuqFF1647vlTU1M1Z84cS+cEOjPDMPQv//Ivbbr869WF4qWXXtIbb7xhYVJv7777bpsu/3p1oXjhhRc0c+ZM9enTx6qYbWKz2fTmm2/6OwYA4AZlaZkYOXKk1z0crJaamqrU1FS/zQ90NiEhIdq6dasktek+Emlpadq9e/c1D93paP/4j/+ou+66q017Sa8Uik8//TTgigQAAP5maZkA0Pm092Z0d911VwclaZ+2Hm4pXS4UV18yGgAAXNahV3MCAAAA0HlRJgAAAACYQpkAAAAAYAplAgAAAIAplAkAAAAApnA1J+jAgQPKyMiwdL7rvUSv1ZmvzMmlhdGR+LoGAAQbysQNzh+/RFzv/T789YsP9ylBRzL7tVV24pSS4m9t8rg98/J1DQAwizJxg3v11Vf9HaHdgjEzcC1mv65zl7tU4Jzf5DEAAFbgnAkAAAAAplAmAAAAAJhCmQAAAABgCmUCAAAAgCmUCQAAAACmUCYAAAAAmEKZAAAAAGAKZQIAAACAKZQJAAAAAKZQJgAAAACYQpkAAAAAYAplAgAAAIAplAkAAAAAplAmAAAAAJhCmQAAAABgCmUCAAAAgCmUCQAAAACmUCYAAAAAmBLm7wAAAABAZ1JVfU5Hjp9sMr7nD4eafTz4zmT16H6TJdl8jTIBAAAA+JA9srt27Nmnui8ueI2/95s9TR73uTVO96QNtDSfL3GYEwAAAOBDEeFdNWlMepu2fWD8CIWGhHRwoo5DmQAAAAB8LH3w19Qr7uZWt0m5K1kJfXpZlKhjUCYAAAAAHwsNDdUDE0a2uD4szKb7M4ZbmKhjBFyZePvttzVmzBjZ7XaFhVl7SkdDQ4NycnIUFxenyMhIZWdnq7q62tIMAAAA6BySE3prwB2Jza679+spcth7WBuoAwRcmYiOjtbChQv16quvWj53QUGBioqKVFJSosrKSknSrFmzLM8BAACAzmHyuOGyhXr/ym3v0U1jh6f4KZFv+a1M7N69WxMmTJDdbpfD4dCMGTMkSZmZmZo5c6aSkpIsz+RyueR0OpWUlKSoqCitWLFCxcXFOn78uOVZAAAAEPxio6M0atggr7HMsV9XeNcufkrkW34pE4WFhcrKytLChQtVVVWliooKzZs3z6dzFBQUaPDgwW3evqamRidOnNDQoUM9Y8nJybLb7SotLfVpNgAAANw4xo9MU/duEZIuXwp2yMA7/JzId0IMwzCsnLCurk4JCQl644039OCDD7a43a5duzRx4kTV19d7jW/cuFE/+clPJEn5+fkaN26cT3JVVFQoPj5eZWVl6tu3r2c8ISFBeXl5euyxx3wyT0tyl7s69P0BAAAAMwqc81teaVjs/fffN2JjY43GxsZWt9u5c6dhs9m8xs6dO2ekpKQYf/vb34zPP//cSElJMRoaGnyS69y5c4YkY//+/V7jdrvdKCoq8skcAOBrzoLXm30c6IIxdzBmNozgzB2MmYNVMH6ugzGzYRhGQ0OD8ds9+/wdw+csP8ypurpa0dHRCjFxc46SkhKNHTtWERERio2NVe/evXXs2DGf5HI4HIqPj9e+ffs8Y2VlZXK73e06XAoAAAD4qtDQUI0bMcTfMXzO8sOcDh06pCFDhujdd9/VlClT5Ha7VVJSoszMTEmXL8/65Zdf6sMPP9TkyZN1/vx5SVJ4eLh+/vOf609/+pNeeOEFSdI//dM/6emnn1Z6etvuMHgteXl5euutt1RcXKyYmBg9+eSTqq2tVXFxsU/evzUc5gQAAIBAFFCHORmGYaxbt87o37+/0b17d6NXr17G0qVLPevWrl1rSGqylJeXG8XFxcaiRYs8206ePNk4evRos3Pk5eUZAwYMaFeu+vp6Y8mSJUZMTIzRo0cPIysry/j888/NfZAAYIFg3d0fjLmDMbNhBGfuYMwcrILxcx2MmTszv1zNafbs2frss890/vx5nTp1Snl5eZ51c+bMkWEYTZbExEQNHz5cH330kS5evKizZ8/q5MmTSkxMbHaOpUuX6vDhw+3KZbPZtHLlSlVXV6u2tlbvvvuuYmNjr+dDBQAAADota28xfZ0cDoeefvppZWRkSJJefvllhYYG3H33AAAAgBtCUJUJSXr88cf1+OOP+zsGAAAAcMPjz/oAAAAATKFMAAAAADCFMgEAAADAFMoEAAAAAFMoEwAAAABMoUwAAAAAMIUyAQAAAMAUygQAAAAAUygTAAAAAEyhTAAAAAAwhTIBAAAAwBTKBAAAAABTKBMAAAAATKFMAAAAADCFMgEAAADAFMoEAAAAAFMoEwAAAABMoUwAAAAAMIUyAQAAAMAUygQAAAAAUygTAAAAAEyhTAAAAAAwhTIBAAAAwBTKBAAAAABTKBMAAAAATKFMAAAAADCFMgEAAADAFMoEAAAAAFMoEwAAAABMCfN3AAAAAKAlP39vhw79qdxr7Hsr32j2cfrgO/XgpNGWZQN7JgAAABDAJo1JlyQ1NDSqoaGxxcdhNpsmjErzW84bFWUCAAAAASsm2q7Rw+6+5nbjRw5RZPduFiTC1SgTAAAACGjjRgxRj243tbj+ZkekRg29duGA7wVcmXj77bc1ZswY2e12hYVZe0pHQ0ODcnJyFBcXp8jISGVnZ6u6utrSDAAAAPAWEd5Vk+5Nb3H95HH3KCzMZmEiXBFwZSI6OloLFy7Uq6++avncBQUFKioqUklJiSorKyVJs2bNsjwHAAAAvA27u79uvSWmyXhS/K0aeEei9YEgyY9lYvfu3ZowYYLsdrscDodmzJghScrMzNTMmTOVlJRkeSaXyyWn06mkpCRFRUVpxYoVKi4u1vHjxy3PAgAAgL8LDQ3V1AkjvMZCJE0dP0IhISH+CQX/lInCwkJlZWVp4cKFqqqqUkVFhebNm+fTOQoKCjR48OA2b19TU6MTJ05o6NChnrHk5GTZ7XaVlpb6NBsAAADaLzm+twb2T/Q8T0+5U717xvovEKwvE3V1dVqwYIFcLpeys7MVERGhyMhIZWZmtun1EydOVFxcnF566aVWt8vNzdXBgwfbnKu2tlaSFBUV5TXucDjkdrvb/D4AAADoOJMz7pHNFqrwrl1035hh/o5zwwsxDMOwcsJt27Zp9uzZqqqqanWX1K5duzRx4kTV19d7jVdWVuo3v/mNKisr9dxzz/ksV01NjaKjo7V//36lpqZ6xqOiorRhwwZNmzbNZ3M1J3e5q0PfHwAAADCjwDm/5ZWGxdavX2/ccccd19xu586dhs1ma3bd2rVrje9///u+jmbEx8cbb775puf50aNHDUlGeXm5z+cCAF9wFrze7ONAF4y5gzGzYQRn7mDMHKyC9XN94cJF48sv6/0dA4ZhWH6YU1pamsrLy7V161Y1NjaqpqZG27dv96xvaGjQhQsXdOnSJUnShQsXdOHCBRkW7ECZP3++li9frvLycrndbjmdTmVmZioxMbHD5wYAAEDbhId35VKwAcLyw5wkaf369crPz9fJkycVGRmpuXPnKi8vT5K0bt06PfHEE01eU15e7vmlft26ddc8zCk/P1+bNm3S4cOH25yroaFBTqdT69at08WLF3XffffJMx5aAgAAHwxJREFU5XIpNrbjT+zhMCcAAAAEooA6zMkXOuowJwAINsF6iEIw5g7GzIYRnLmDMXOw4nON62XtLaZ9YO7cuSopKdHFixdVUlKirVu3+jsSAAAAcEMKujKxZs0af0cAAAAAID/eARsAAABAcKNMAAAAADCFMgEAAADAFMoEAAAAAFMoEwAAAABMoUwAAAAAMIUyAQAAAMAUygQAAAAAUygTAAAAAEyhTAAAAAAwhTIBAAAAwBTKBAAAAABTKBMAAAAATKFMAAAAADCFMgEAAADAFMoEAAAAAFMoEwAAAABMoUwAAAAAMIUyAQAAAMAUygQAAAAAUygTAAAAAEyhTAAAAAAwhTIBAAAAwBTKBAAAAABTKBMAAAAATKFMAAAAADCFMgEAAADAFMoEAAAAAFMoEwAAAABMCfN3AAAAAHS8szVu7T34xybj2z/8n2YfDx30NcXeHGVJNgQvygQAAMANwGHvoc/KKvTn02e8xnd+fKDJ456x0Zo4epil+RCcOMwJAADgBhAaGqqp40e0adup40fIFsqvibg2vkoAAABuEEnxvTWof99Wt7mrX7zu6NvHokQIdpQJAACAG8jkccNlszX/K2BoaIgmj7vH4kQIZgFXJt5++22NGTNGdrtdYWHWntLR0NCgnJwcxcXFKTIyUtnZ2aqurrY0AwAAQEe62WHXmPTBza4bmTZIcTc7LE6EYBZwZSI6OloLFy7Uq6++avncBQUFKioqUklJiSorKyVJs2bNsjwHAABAR8q4J1U9ut/kNdbtpnBNGJXmp0QIVn4rE7t379aECRNkt9vlcDg0Y8YMSVJmZqZmzpyppKQkyzO5XC45nU4lJSUpKipKK1asUHFxsY4fP255FgAAgI4SEd5VmWPSvcYmjUnXTRHhfkqEYOWXMlFYWKisrCwtXLhQVVVVqqio0Lx583w6R0FBgQYPbn4XXnNqamp04sQJDR061DOWnJwsu92u0tJSn2YDAADwt6F391fvnjGSLl8KNj3lTj8nQjAKMQzDsHLCuro6JSQk6I033tCDDz7Y4na7du3SxIkTVV9f7xk7evSonnjiCRmGIcMw9Oqrr2rYMN9cA7miokLx8fEqKytT375/v8pBQkKC8vLy9Nhjj/lknpbkLnd16PsDAAAAZhQ457e80rDY+++/b8TGxhqNjY2tbrdz507DZrN5jVVXVxvV1dWGYRjG4cOHjdGjR/ss17lz5wxJxv79+73G7Xa7UVRU5LN5AMCXnAWvN/s40AVj7mDMbBjBmTsYMwez/znw//k7AoKY5Yc5VVdXKzo6WiEhIe1+bUxMjGJiLu+OCw8Pl81m81kuh8Oh+Ph47du3zzNWVlYmt9vdrsOlAAAAggmHN+F6WH6Y06FDhzRkyBC9++67mjJlitxut0pKSpSZmSnp8uVZv/zyS3344YeaPHmyzp8/L+lyebhSQBoaGjRt2jR95zvf0Te+8Q2fZcvLy9Nbb72l4uJixcTE6Mknn1Rtba2Ki4t9NkdLOMwJAAAAgSigDnMyDMNYt26d0b9/f6N79+5Gr169jKVLl3rWrV271pDUZCkvLzcMwzAaGxuNxx9/3PjpT3/a6hx5eXnGgAED2pWrvr7eWLJkiRETE2P06NHDyMrKMj7//PN2f3wAYJVgPRwkGHMHY2bDCM7cwZgZuFH55WpOs2fP1meffabz58/r1KlTysvL86ybM2eO5wTrq5fExERJ0ne+8x3169dP3/zmN1udY+nSpTp8+HC7ctlsNq1cuVLV1dWqra3Vu+++q9jY2HZ/fAAAAMCNIOBuWteaXbt2yeVyaceOHcrIyNBDDz3k70gAAADADSvM3wHaIyMjQ5cuXfJ3DAAAAAAKsj0TAAAAAAIHZQIAAACAKZQJAAAAAKZQJgAAAACYQpkAAAAAYAplAgAAAIAplAkAAAAAplAmAAAAAJhCmQAAAABgCmUCAAAAgCmUCQAAAACmUCYAAAAAmEKZAAAAAGAKZQIAAACAKZQJAAAAAKZQJgAAAACYQpkAAAAAYAplAgAAAIAplAkAAAAAplAmAAAAAJhCmQAAAABgCmUCAAAAgCmUCQAAAACmUCYAAAAAmEKZAAAAAGAKZQIAAACAKZQJAAAAAKZQJgAAAACYEubvAAAA4MbV0NCoi5cuNRn/4m8Xmn3cJSxMXbrw6wsQKPhuBAAAfvNlfb1efuMd1X1xwWv8xdVvNXkcIulbs7PUp1eclREBtILDnAAAgN9EhHfVpDHD2rRt2qD+FAkgwFAmAACAXw0bfKd6xd3c6jZdu4Qp8950ixIBaCvKBAAA8CtbaKimThjR6jYZ96TKHtndokQA2irgyoTT6dTAgQNlt9vVu3dvPfXUUzp79qwlczc0NCgnJ0dxcXGKjIxUdna2qqurLZkbAIAbWb+E2zTgjoRm1znsPTQmfbDFiQC0RcCVCZvNpo0bN+rMmTMqLS1VZWWl5syZY8ncBQUFKioqUklJiSorKyVJs2bNsmRuAABudJMz7pEttOmvJpMzhnMFJyBA+a1M7N69WxMmTJDdbpfD4dCMGTMkSfn5+RoyZIi6dOmiuLg4LV68WLt27bIkk8vlktPpVFJSkqKiorRixQoVFxfr+PHjlswPAMCNLPbmKI0aNshrLOG2nrr7ziQ/JQJwLX4pE4WFhcrKytLChQtVVVWliooKzZs3r9ltd+zYoZSUlHbPUVBQoMGD275LtKamRidOnNDQoUM9Y8nJybLb7SotLW33/AAAoP3Gj0xT924RnucPTBipkJAQPyYC0BrLy0RdXZ0WLFggl8ul7OxsRUREKDIyUpmZmU22LSws1GuvvaZVq1Z5xjZu3KgRI0ZoxIgR2rlzZ4vz5Obm6uDBg23OVVtbK0mKioryGnc4HHK73W1+HwAAYN7Vl4odOqi/+tzKpWCBQBZiGIZh5YTbtm3T7NmzVVVV1epfGrZs2aIFCxaosLBQ48aNk3R570FGRoZ+//vf6/z585o4caL27dun0GaOr2yvmpoaRUdHa//+/UpNTfWMR0VFacOGDZo2bdp1z9Ga3OWuDn1/AAAAwIwC5/yWVxoWW79+vXHHHXe0us2aNWuM6Oho43e/+53XeHFxsbFo0SLP8/vvv984evSoz7LFx8cbb775puf50aNHDUlGeXm5z+YAAF9yFrze7ONAF4y5gzGzYQRv7osXL/k7AoA2sPwwp7S0NJWXl2vr1q1qbGxUTU2Ntm/f7lm/evVqPfvss9q+fbtGjRrl9dozZ84oOjra8zw6OlpnzpzxWbb58+dr+fLlKi8vl9vtltPpVGZmphITE302BwAAuLauXbv4OwKANrD8MCdJWr9+vfLz83Xy5ElFRkZq7ty5ysvLuxwoJERhYWEKDw/3es358+e1fft2bdu2zXMOxZQpU/TjH/9YSUlNr/KQn5+vTZs26fDhw23O1dDQIKfTqXXr1unixYu677775HK5FBsbex0fbdtwmBMAAAACUWuHOfmlTJhVU1Oj8ePH6+OPP1ZdXZ3Gjx/vs3MmACAY5S53eX7IX/040AVj7mDMLAVvbgDBIajuAONwOPT0008rIyNDkvTyyy9TJAAAAAA/CaoyIUmPP/64Hn/8cX/HAAAAAG54/FkfAAAAgCmUCQAAAACmUCYAAAAAmEKZAAAAAGAKZQIAAACAKZQJAAAAAKZQJgAAAACYQpkAAAAAYAplAgAAAIAplAkAAAAAplAmAAAAAJhCmQAAAABgCmUCAAAAgCmUCQAAAACmUCYAAAAAmEKZAAAAAGAKZQIAAACAKZQJAAAAAKZQJgAAAACYQpkAAAAAYAplAgAAAIAplAkAAAAAplAmAAAAAJhCmQAAAABgCmUCAAAAgCmUCQAAAACmUCYAAAAAmEKZAAAAAGAKZQIAAACAKWH+DgAAAHxj/+H/1ZHjJ5uMb9m2q8njbhERun/ccIWGhFiUDkBnRJkAAKCTiO/dU/+x7QM1NDZ6jf/h//6pyeMHJoykSAC4bhzmBABAJxETbdeoYYOuuV3czVG6Z8gACxIB6OwoEwAAdCLjR6ape7eIVreZMn6EbDZ+BQBw/fhJAgBAJxIR3lWTxqS3uL5/39t1Z3K8hYkAdGYBVyacTqcGDhwou92u3r1766mnntLZs2ctmbuhoUE5OTmKi4tTZGSksrOzVV1dbcncAAD4Svrgr6lX3M1NxkNDQjRl/D1+SASgswq4MmGz2bRx40adOXNGpaWlqqys1Jw5cyyZu6CgQEVFRSopKVFlZaUkadasWZbMDQCAr4SGhuqBCSObjA8fMkA9Y6P9kAhAZ+W3MrF7925NmDBBdrtdDodDM2bMkCTl5+dryJAh6tKli+Li4rR48WLt2rXLkkwul0tOp1NJSUmKiorSihUrVFxcrOPHj1syPwAAvpKc0FsD7kj0PL8pIlwTRw/1XyAAnZJfykRhYaGysrK0cOFCVVVVqaKiQvPmzWt22x07diglJaXdcxQUFGjw4MFt3r6mpkYnTpzQ0KF//0GbnJwsu92u0tLSds8PAIC/TR43XLbQy//VTxw1VN1vav3EbABorxDDMAwrJ6yrq1NCQoLeeOMNPfjgg61uW1hYqDlz5uiDDz5QWlqaJGnixIkqLS3V4sWL9dxzz/ksV0VFheLj41VWVqa+fft6xhMSEpSXl6fHHnvMZ3M1J3e5q0PfHwAAADCjwDm/xXWW37Tugw8+UEhIiKZPn97qdlu2bNGCBQv03nvveYqEJK1bt06/+c1vPOc0+EpkZKQk6a9//avXeE1Njex2u0/nak5r/0gA0JLc5S7Pz4+rHwe6YMwdjJkl6cLFS/pz1Rkl3X6rv6MA6IQsP8ypurpa0dHRCmnlrptr167VggULtHXrVo0bN85rXZ8+fTokl8PhUHx8vPbt2+cZKysrk9vtbtfhUgAABJKI8K4UCQAdxvLDnA4dOqQhQ4bo3Xff1ZQpU+R2u1VSUqLMzExJ0urVq/Vv//ZvKi4uVnp689fJXrdunSorK316mJMk5eXl6a233lJxcbFiYmL05JNPqra2VsXFxT6dpzkc5gQAAIBA1OqeWMMP1q1bZ/Tv39/o3r270atXL2Pp0qWedZKMsLAwo3v37l7L1dauXWt8//vfb3WOvLw8Y8CAAe3KVV9fbyxZssSIiYkxevToYWRlZRmff/55u94DAKzkLHi92ceBLhhzB2NmAOholp8zIUmzZ8/W7Nmzm11n+GhHydKlS7V06dJ2vcZms2nlypVauXKlTzIAAAAAnZlfysT1mDt3rkpKSnTx4kWVlJRo69at/o4EAAAA3JCCrkysWbPG3xEAAAAAyI93wAYAAAAQ3CgTAAAAAEyhTAAAAAAwhTIBAAAAwBTKBAAAAABTKBMAAAAATKFMAAAAADCFMgEAAADAFMoEAAAAAFMoEwAAAABMoUwAAAAAMIUyAQAAAMAUygQAAAAAUygTAAAAAEyhTAAAAAAwhTIBAAAAwBTKBAAAAABTKBMAAAAATKFMAAAAADCFMgEAAADAFMoEAAAAAFMoEwAAAABMoUwAAAAAMIUyAQAAAMAUygQAAAAAUygTAAAAAEyhTAAAAAAwhTIBAAAAwJQwfwcAACDQ1Nc36My5vzYZP/352WYf33RThOw9ulmSDQACCWUCAICvCA0N0du/3KlTVWe8xn+05j+afbzgHx+gTAC4IXGYEwAAXxEaGqqpE0a0adu7v5akvrff2sGJACAwUSYAAGhGcnxvDeyf2Oo2YTab7h833JpAABCAKBMAALRgcsY9stla/q9yzNfv1s1RkRYmAoDAEnBlwul0auDAgbLb7erdu7eeeuopnT179tov9IGGhgbl5OQoLi5OkZGRys7OVnV1tSVzAwACT0y0XaOH3d3susjuNyljeKrFiQAgsARcmbDZbNq4caPOnDmj0tJSVVZWas6cOZbMXVBQoKKiIpWUlKiyslKSNGvWLEvmBgAEpnEjhqhHt5uajGfe+3WFh3f1QyIACBx+KxO7d+/WhAkTZLfb5XA4NGPGDElSfn6+hgwZoi5duiguLk6LFy/Wrl27LMnkcrnkdDqVlJSkqKgorVixQsXFxTp+/Lgl8wMAAk9EeFdNujfda+y2nrFKu7u/nxIBQODwS5koLCxUVlaWFi5cqKqqKlVUVGjevHnNbrtjxw6lpKS0e46CggINHjy4zdvX1NToxIkTGjp0qGcsOTlZdrtdpaWl7Z4fANB5DLu7v269JcbzfOqEEQoNCfFjIgAIDJaXibq6Oi1YsEAul0vZ2dmKiIhQZGSkMjMzm2xbWFio1157TatWrZIkHT16VPfee6/GjBmj0aNH65NPPmlxntzcXB08eLDNuWprayVJUVFRXuMOh0Nut7vN7wMA6HyuvlQsl4IFgL8LMQzDsHLCbdu2afbs2aqqqlJIK3/V2bJlixYsWKDCwkKNGzdOknTmzOWbB8XExOjTTz/VggUL9NFHH/kkV01NjaKjo7V//36lpv79hLqoqCht2LBB06ZN88k8Lcld7urQ9wcAAADMKHDOb3Gd5XfArq6uVnR0dKtFYu3atVqyZIm2bt2qUaNGecZjYv6+izk8PFw2m81nuRwOh+Lj47Vv3z5PmSgrK5Pb7W7X4VJmtfaPBAAtyV3u8vz8uPpxoAvW3A0Nja1eKhYAbjSW/0RMS0tTeXm5tm7dqsbGRtXU1Gj79u2e9atXr9azzz6r7du3exWJqzU0NGjRokXKzc31abb58+dr+fLlKi8vl9vtltPpVGZmphITE306DwAgOFEkAMCb5Yc5SdL69euVn5+vkydPKjIyUnPnzlVeXt7lQCEhCgsLU3h4uNdrzp8/L0kyDENz5szRPffco29+85stzpGfn69Nmzbp8OHDbc7V0NAgp9OpdevW6eLFi7rvvvvkcrkUGxtr4qNsHw5zAgAAQCBqbe+xX8rE9fj2t7+tnj176v/8n//j7ygA4HfBerhQsOYGAHgLqv21u3btksvl0o4dO5SRkaGHHnrI35EAAACAG5blJ2Bfj4yMDF26dMnfMQAAAAAoyPZMAAAAAAgclAkAAAAAplAmAAAAAJhCmQAAAABgCmUCAAAAgCmUCQAAAACmUCYAAAAAmEKZAAAAAGAKZQIAAACAKZQJAAAAAKZQJgAAAACYQpkAAAAAYAplAgAAAIAplAkAAAAAplAmAAAAAJhCmQAAAABgCmUCAAAAgCmUCQAAAACmUCYAAAAAmEKZAAAAAGAKZQIAAACAKZQJAAAAAKZQJgAAAACYQpkAAAAAYAplAgAAAIAplAkAAAAAplAmAAAAAJhCmQAAAABgCmUCAAAAgClh/g4AAOjcDn1Wrv8p/WOT8TXv/KrJ4/CuXfQPU8cpLMxmWT4AgHmUCQBAh+qXeJv+679/p/N1f/Ma/1N5RZPHmfemUyQAIIhwmBMAoENFhHdV5pj0a24XHRWp0el3W5AIAOArlAkAQIcbend/3XpLTKvbTM4Yri5h7DAHgGAScGXC6XRq4MCBstvt6t27t5566imdPXvWkrkbGhqUk5OjuLg4RUZGKjs7W9XV1ZbMDQCdWWhoqB6YMKLF9Yl9emnQ1/pamAgA4AsBVyZsNps2btyoM2fOqLS0VJWVlZozZ44lcxcUFKioqEglJSWqrKyUJM2aNcuSuQGgs0uK761B/ZsWhhBJD0wYqZCQEOtDAQCui9/KxO7duzVhwgTZ7XY5HA7NmDFDkpSfn68hQ4aoS5cuiouL0+LFi7Vr1y5LMrlcLjmdTiUlJSkqKkorVqxQcXGxjh8/bsn8ANDZ3T9uuGw27/96ht79Nd3WK9ZPiQAA18MvZaKwsFBZWVlauHChqqqqVFFRoXnz5jW77Y4dO5SSktLuOQoKCjR48OA2b19TU6MTJ05o6NChnrHk5GTZ7XaVlpa2e34AQFMxDrtGD/v7SdZdu3bRpHuvfXI2ACAwWV4m6urqtGDBArlcLmVnZysiIkKRkZHKzMxssm1hYaFee+01rVq1SpJ0+vRpjRw5UhkZGRo+fLh27NjR4jy5ubk6ePBgm3PV1tZKkqKiorzGHQ6H3G53m98HANC6cSOGqEf3my4/vidV9h7d/JwIAGBWiGEYhpUTbtu2TbNnz1ZVVVWrx8du2bJFCxYsUGFhocaNGyfp8gnS0uXzKsrKyvQP//AP2rt3r09y1dTUKDo6Wvv371dqaqpnPCoqShs2bNC0adN8Mk9Lcpe7OvT9AQAAADMKnPNbXGf5Nfiqq6sVHR3dapFYu3atlixZoq1bt2rUqFGecZvt7zcyqqmpaddhTNficDgUHx+vffv2ecpEWVmZ3G63T+dpSWv/SADQktzlLs/Pj6sfB7rGxkZV/qVa8b1v8XcUAMB1sPwwp7S0NJWXl2vr1q1qbGxUTU2Ntm/f7lm/evVqPfvss9q+fbtXkbiivLxco0ePVmZmprKysnyabf78+Vq+fLnKy8vldrvldDqVmZmpxMREn84DADe60NBQigQAdAKWH+YkSevXr1d+fr5OnjypyMhIzZ07V3l5eZcDhYQoLCxM4eHhXq85f/681/OysjKNHz9ex44da3aO/Px8bdq0SYcPH25zroaGBjmdTq1bt04XL17UfffdJ5fLpdjYjr/KCIc5AQAAIBC1ttfbL2XCrIsXL3pKRnV1tTIyMnTo0CE/pwIA/wnWw5wAAJ2D5edMXI+9e/dq6dKlstls+vLLLz1XeQIAAABgvaAqE6NHj9aHH37o7xgAAAAA5Mc7YAMAAAAIbpQJAAAAAKZQJgAAAACYQpkAAAAAYAplAgAAAIAplAkAAAAAplAmAAAAAJhCmQAAAABgCmUCAAAAgCmUCQAAAACmUCYAAAAAmEKZAAAAAGAKZQIAAACAKZQJAAAAAKZQJgAAAACYQpkAAAAAYAplAgAAAIAplAkAAAAAplAmAAAAAJhCmQAAAABgCmUCAAAAgCmUCQAAAACmUCYAAAAAmEKZAAAAAGAKZQIAAACAKZQJAAAAAKZQJgAAAACYQpkAAAAAYAplAgAAAIApYf4OAABom8bGRh098ecm4/97rLLZx5Hdu6lX3M2WZAMA3JhCDMMw/B0CANA2m/7rv/V/Pytv07ZzZ9yv/km3d3AiAMCNjMOcACCI3J8xXGE22zW3uzM5niIBAOhwlAkACCI3O+wanX53q9uEhoZo8rh7LEoEALiRUSYAIMiMuydVkd1vanH9iCEDdUuMw8JEAIAbVcCVCafTqYEDB8put6t379566qmndPbsWUvmbmhoUE5OjuLi4hQZGans7GxVV1dbMjcAtFV4eFdl3vv1Ztd1iwjXhFFpFicCANyoAq5M2Gw2bdy4UWfOnFFpaakqKys1Z84cS+YuKChQUVGRSkpKVFl5+Yoos2bNsmRuAGiPtLv7q3fPmCbjE0cPVbebIvyQCABwI/Lb1Zx2796tZcuWae/evQoNDdV9992nLVu2NNmuuLhYjzzyiNxud4dnSkhI0LJly/Tkk09Kko4ePap+/frp2LFjSkhI6PD5AaA9yitO6fXNWz3Pb4mJ1uK52bKFBtzfiQAAnZRf/scpLCxUVlaWFi5cqKqqKlVUVGjevHnNbrtjxw6lpKS0e46CggINHjy4zdvX1NToxIkTGjp0qGcsOTlZdrtdpaWl7Z4fADpa39tv1d1fS/I8nzr+HooEAMBSlv+vU1dXpwULFsjlcik7O1sRERGKjIxUZmZmk20LCwv12muvadWqVV7jZ86cUXR0tDZu3NjiPLm5uTp48GCbc9XW1kqSoqKivMYdDocle0UAwIz7M76uMJtNX0u6nUvBAgAsZ/kdsD/44AOFhIRo+vTprW63ZcsWLViwQO+9957S0rxPJnzppZc0evRon+aKjIyUJP31r3/1Gq+pqZHdbvfpXM3JXe7q8DkAdF6flVXwcwQA0CEKnPNbXGd5maiurlZ0dLRCQkJa3Gbt2rVasmSJtm7dqlGjRnmtO3LkiM6cOeN1OJIvOBwOxcfHa9++fUpNTZUklZWVye12t+twKbNa+0cCgNYYhtHqz1QAADqK5Yc5paWlqby8XFu3blVjY6Nqamq0fft2z/rVq1fr2Wef1fbt25sUCUlatmyZnn/++Q7JNn/+fC1fvlzl5eVyu91yOp3KzMxUYmJih8wHAL5AkQAA+IvleyYGDRqkN954Q88++6xmzpypyMhIzZ0713POxOLFixUWFqZx48Z5ve78+fPas2ePYmJilJycfM158vPztWnTJh0+fLjN2XJzc3Xu3Dmlp6fr4sWLuu+++1o9L8OXODwBAAAAgai1I2j8dmlYM1avXq3CwkLddNNNOnLkiLp3767XXntNI0aM8Hc0AAAA4IYTVGXiai+88IL69eunxx57zN9RAAAAgBtS0JYJAAAAAP7F3Y0AAAAAmEKZAAAAAGAKZQIAAACAKZQJAAAAAKZQJgAAAACYQpkAAAAAYAplAgAAAIAplAkAAAAAplAmAAAAAJhCmQAAAABgCmUCAAAAgCmUCQAAAACm/P/t17EAAAAAwCB/6znsLotkAgAAWGQCAABYZAIAAFhkAgAAWGQCAABYZAIAAFhkAgAAWGQCAABYZAIAAFhkAgAAWGQCAABYZAIAAFgCAbl8zk7NmrgAAAAASUVORK5CYII=\n",
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- "execution_count": 19,
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- "output_type": "execute_result"
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- ],
- "source": [
- "circuit_drawer(circuit, output='mpl', plot_barriers=False)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": []
- }
- ],
- "metadata": {
- "anaconda-cloud": {},
- "kernelspec": {
- "display_name": "Python 3",
- "language": "python",
- "name": "python3"
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- "version": 3
- },
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- "library": "var_list.py",
- "varRefreshCmd": "print(var_dic_list())"
- },
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- "delete_cmd_prefix": "rm(",
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- "varRefreshCmd": "cat(var_dic_list()) "
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diff --git a/qiskit/advanced/terra/writing_a_transpiler_pass.ipynb b/qiskit/advanced/terra/writing_a_transpiler_pass.ipynb
deleted file mode 100644
index 51a24951b..000000000
--- a/qiskit/advanced/terra/writing_a_transpiler_pass.ipynb
+++ /dev/null
@@ -1,629 +0,0 @@
-{
- "cells": [
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- " Trusted Notebook\" align=\"middle\">"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "The latest version of this notebook is available on https://github.com/Qiskit/qiskit-tutorial."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "# Writing a Transpiler Pass"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Introduction"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "A central component of Qiskit Terra is the transpiler, which is designed for modularity and extensibility. The goal is to be able to easily write new circuit transformations (known as transpiler *passes*), and combine them with other existing passes. In this way, the transpiler opens up the door for research into aggressive optimization of quantum circuits.\n",
- "\n",
- "In this notebook, we show how to develop a simple transpiler pass. To do so, we first introduce the internal representation of quantum circuits in Qiskit, in the form of a Directed Acyclic Graph, or **DAG**. Then, we illustrate a simple swap mapper pass, which transforms an input circuit to be compatible with a limited-connectivity quantum device."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Introducing the DAG"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "In Qiskit, we represent circuits internally using a Directed Acyclic Graph (DAG). The advantage of this representation over a pure list of gates (i.e., *netlist*) is that the flow of information between operations are explicit, making it easier for passes to make transformation decisions without changing the semantics of the circuit.\n",
- "\n",
- "Let's start by building a simple circuit, and examining its DAG."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 7,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 7,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit\n",
- "from qiskit.dagcircuit import DAGCircuit\n",
- "q = QuantumRegister(3, 'q')\n",
- "c = ClassicalRegister(3, 'c')\n",
- "circ = QuantumCircuit(q, c)\n",
- "circ.h(q[0])\n",
- "circ.cx(q[0], q[1])\n",
- "circ.measure(q[0], c[0])\n",
- "circ.rz(0.5, q[1]).c_if(c, 2)\n",
- "circ.draw()"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "In the DAG, there are three kinds of graph nodes: qubit/clbit input nodes (green), operation nodes (blue), and output nodes (red). Each edge indicates data flow (or dependency) between two nodes. "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 8,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "image/png": 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IdU2cuC8C1vQXcyhY21/ECMwciuJaKgTWr1+PY8eOySOx7t27o3///mjbtq2cx8fHJ1Ve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LRW7l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\n",
- "text/plain": [
- ""
- ]
- },
- "execution_count": 8,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "from qiskit.converters import circuit_to_dag\n",
- "from qiskit.tools.visualization import dag_drawer\n",
- "dag = circuit_to_dag(circ)\n",
- "dag_drawer(dag)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Therefore, writing a transpiler pass means using Qiskit's DAGCircuit API to analyze or transform the circuit. Let's see some examples of this."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "**a. Get all op nodes in the DAG:**"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 9,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "[,\n",
- " ,\n",
- " ,\n",
- " ]"
- ]
- },
- "execution_count": 9,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "dag.op_nodes()"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Each node is an instance of the ``DAGNode`` class. Let's examine the information stored in the second op node."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 10,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "node name: rz\n",
- "node op: \n",
- "node qargs: [(QuantumRegister(3, 'q'), 1)]\n",
- "node cargs: []\n",
- "node condition: (ClassicalRegister(3, 'c'), 2)\n"
- ]
- }
- ],
- "source": [
- "node = dag.op_nodes()[3]\n",
- "print(\"node name: \", node.name)\n",
- "print(\"node op: \", node.op)\n",
- "print(\"node qargs: \", node.qargs)\n",
- "print(\"node cargs: \", node.cargs)\n",
- "print(\"node condition: \", node.condition)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "**b. Add an operation to the back:**"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 11,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "image/png": 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SP5vE8aQyhhIb116lVJQST1j5m7w+JVOI3TPwShdt9LGEQsJDMH/0fMJFHWDq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\nzTEv0rAPA4nDZkBGfi1FoHLlyopemV3TCuVuBJx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GdnyGXgZ/onKdcDxZpz6iImkr86CX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Wq6Z231lUyZ1nbt2rUDP85NhQoV0tFHolnt5b7C7CWLAJ3O4IUJFYMRp5Yfw/AiTxSQUCYfbnDK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\ndmoJAAAAAElFTkSuQmCC\n",
- "text/plain": [
- ""
- ]
- },
- "execution_count": 11,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "from qiskit.extensions.standard import HGate\n",
- "dag.apply_operation_back(HGate(), qargs=[q[0]])\n",
- "dag_drawer(dag)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "**c. Add an operation to the front:**"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 12,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "image/png": 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gHRJ1pKak4pfZ35qz3L7GUogpCsgtJAhkWQSEKRt46dl/RLUaCv7Z4V6YpSbt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1NWkD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\n",
- "text/plain": [
- ""
- ]
- },
- "execution_count": 12,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "from qiskit.extensions.standard import ToffoliGate\n",
- "dag.apply_operation_front(ToffoliGate(), qargs=[q[0], q[1], q[2]], cargs=[])\n",
- "dag_drawer(dag)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "**d. Substitute a node with a subcircuit:**"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 13,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "image/png": 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+zoqtnugm/zckUYYkkI7JaV7r7v/OnwlHnjzutqLXKwElEGgE3NdSgXZHXhhP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\nu928twqucxQrUPZe2c373bmMT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- "text/plain": [
- ""
- ]
- },
- "execution_count": 13,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "from qiskit.extensions.standard import CHGate, U2Gate, CnotGate\n",
- "mini_dag = DAGCircuit()\n",
- "p = QuantumRegister(2, \"p\")\n",
- "mini_dag.add_qreg(p)\n",
- "mini_dag.apply_operation_back(CHGate(), qargs=[p[1], p[0]])\n",
- "mini_dag.apply_operation_back(U2Gate(0.1, 0.2), qargs=[p[1]])\n",
- "\n",
- "# substitute the cx node with the above mini-dag\n",
- "cx_node = dag.op_nodes(op=CnotGate).pop()\n",
- "dag.substitute_node_with_dag(node=cx_node, input_dag=mini_dag, wires=[p[0], p[1]])\n",
- "dag_drawer(dag)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Finally, after all transformations are complete, we can convert back to a regular QuantumCircuit object.\n",
- "This is what the transpiler does! It takes a circuit, operates on it in DAG form, and outputs a transformed circuit."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 14,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/html": [
- ""
- ]
- },
- "execution_count": 14,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "from qiskit.converters import dag_to_circuit\n",
- "circuit = dag_to_circuit(dag)\n",
- "circuit.draw()"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Implementing a BasicMapper Pass"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Now that we are familiar with the DAG, let's use it to write a transpiler pass. Here we will implement a basic pass for mapping an arbitrary circuit to a device with limited qubit connectivity. We call this the BasicMapper. This pass is included in Qiskit Terra as well.\n",
- "\n",
- "The first thing to do when writing a transpiler pass is to decide whether the pass class derives from a ``TransformationPass`` or ``AnalysisPass``. Transformation passes modify the circuit, while analysis passes only collect information about a circuit (to be used by other passes). Then, the ``run(dag)`` method is implemented, which does the main task. Finally, the pass is registered inside the ``qiskit.transpiler.passes`` module.\n",
- "\n",
- "This pass functions as follows: it traverses the DAG layer-by-layer (each layer is a group of operations that does not act on independent qubits, so in theory all operations in a layer can be done independently). For each operation, if it does not already meet the coupling map constraints, the pass identifies a swap path and inserts swaps to bring the two qubits close to each other.\n",
- "\n",
- "Follow the comments in the code for more details."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 15,
- "metadata": {
- "collapsed": true
- },
- "outputs": [],
- "source": [
- "from copy import copy\n",
- "\n",
- "from qiskit.transpiler.basepasses import TransformationPass\n",
- "from qiskit.transpiler import Layout\n",
- "from qiskit.extensions.standard import SwapGate\n",
- "\n",
- "\n",
- "class BasicSwap(TransformationPass):\n",
- " \"\"\"\n",
- " Maps (with minimum effort) a DAGCircuit onto a `coupling_map` adding swap gates.\n",
- " \"\"\"\n",
- "\n",
- " def __init__(self,\n",
- " coupling_map,\n",
- " initial_layout=None):\n",
- " \"\"\"\n",
- " Maps a DAGCircuit onto a `coupling_map` using swap gates.\n",
- " Args:\n",
- " coupling_map (CouplingMap): Directed graph represented a coupling map.\n",
- " initial_layout (Layout): initial layout of qubits in mapping\n",
- " \"\"\"\n",
- " super().__init__()\n",
- " self.coupling_map = coupling_map\n",
- " self.initial_layout = initial_layout\n",
- "\n",
- " def run(self, dag):\n",
- " \"\"\"\n",
- " Runs the BasicSwap pass on `dag`.\n",
- " Args:\n",
- " dag (DAGCircuit): DAG to map.\n",
- "\n",
- " Returns:\n",
- " DAGCircuit: A mapped DAG.\n",
- "\n",
- " Raises:\n",
- " TranspilerError: if the coupling map or the layout are not\n",
- " compatible with the DAG\n",
- " \"\"\"\n",
- " new_dag = DAGCircuit()\n",
- "\n",
- " if self.initial_layout is None:\n",
- " if self.property_set[\"layout\"]:\n",
- " self.initial_layout = self.property_set[\"layout\"]\n",
- " else:\n",
- " self.initial_layout = Layout.generate_trivial_layout(*dag.qregs.values())\n",
- "\n",
- " if len(dag.qubits()) != len(self.initial_layout):\n",
- " raise TranspilerError('The layout does not match the amount of qubits in the DAG')\n",
- "\n",
- " if len(self.coupling_map.physical_qubits) != len(self.initial_layout):\n",
- " raise TranspilerError(\n",
- " \"Mappers require to have the layout to be the same size as the coupling map\")\n",
- "\n",
- " current_layout = self.initial_layout.copy()\n",
- "\n",
- " for layer in dag.serial_layers():\n",
- " subdag = layer['graph']\n",
- "\n",
- " for gate in subdag.twoQ_gates():\n",
- " physical_q0 = current_layout[gate.qargs[0]]\n",
- " physical_q1 = current_layout[gate.qargs[1]]\n",
- " if self.coupling_map.distance(physical_q0, physical_q1) != 1:\n",
- " # Insert a new layer with the SWAP(s).\n",
- " swap_layer = DAGCircuit()\n",
- "\n",
- " path = self.coupling_map.shortest_undirected_path(physical_q0, physical_q1)\n",
- " for swap in range(len(path) - 2):\n",
- " connected_wire_1 = path[swap]\n",
- " connected_wire_2 = path[swap + 1]\n",
- "\n",
- " qubit_1 = current_layout[connected_wire_1]\n",
- " qubit_2 = current_layout[connected_wire_2]\n",
- "\n",
- " # create qregs\n",
- " for qreg in current_layout.get_registers():\n",
- " if qreg not in swap_layer.qregs.values():\n",
- " swap_layer.add_qreg(qreg)\n",
- "\n",
- " # create the swap operation\n",
- " swap_layer.apply_operation_back(SwapGate(),\n",
- " qargs=[qubit_1, qubit_2],\n",
- " cargs=[])\n",
- "\n",
- " # layer insertion\n",
- " edge_map = current_layout.combine_into_edge_map(self.initial_layout)\n",
- " new_dag.compose_back(swap_layer, edge_map)\n",
- "\n",
- " # update current_layout\n",
- " for swap in range(len(path) - 2):\n",
- " current_layout.swap(path[swap], path[swap + 1])\n",
- "\n",
- " edge_map = current_layout.combine_into_edge_map(self.initial_layout)\n",
- " new_dag.extend_back(subdag, edge_map)\n",
- "\n",
- " return new_dag"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Let's test this pass on a small example circuit."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 16,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- ""
- ]
- },
- "execution_count": 16,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "q = QuantumRegister(7, 'q')\n",
- "in_circ = QuantumCircuit(q)\n",
- "in_circ.h(q[0])\n",
- "in_circ.cx(q[0], q[4])\n",
- "in_circ.cx(q[2], q[3])\n",
- "in_circ.cx(q[6], q[1])\n",
- "in_circ.cx(q[5], q[0])\n",
- "in_circ.rz(0.1, q[2])\n",
- "in_circ.cx(q[5], q[0])"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Now we construct a pass manager that contains our new pass. We pass the example circuit above to this pass manager, and obtain a new, transformed circuit."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 17,
- "metadata": {},
- "outputs": [],
- "source": [
- "from qiskit.transpiler import PassManager\n",
- "from qiskit.transpiler import CouplingMap\n",
- "from qiskit import BasicAer\n",
- "pm = PassManager()\n",
- "coupling = [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6]]\n",
- "coupling_map = CouplingMap(couplinglist=coupling)\n",
- "\n",
- "pm.append([BasicSwap(coupling_map)])\n",
- "\n",
- "out_circ = pm.run(in_circ)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 18,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "image/png": 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mZmLLli2IiIhAQkKCUevx8vIyyvW+5mT+/PnYunUrxowZg+7duwMARo0ahdzc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\nsP8fP9i9tzotKb4AAAAASUVORK5CYII=\n",
- "text/plain": [
- ""
- ]
- },
- "execution_count": 18,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "in_circ.draw(output='mpl')"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 21,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "image/png": 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auHHjxk0b2759+2BkZIQ+ffogMzNT9Z747bff6r22mrZ79+5h6NChMDAwwMaN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\nw/Xr12tdV21gYIDIyEgdVlW3yMjIWv8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- ]
- },
- "execution_count": 21,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "out_circ.draw(output='mpl')"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Note that this pass only inserts the swaps necessary to make every two-qubit interaction conform to the device coupling map. It does not, for example, care about the direction of interactions, or the native gate set supported by the device. This is a design philosophy of Qiskit's transpiler: every pass performs a small, well-defined action, and the aggressive circuit optimization is achieved by the pass manager through combining multiple passes."
- ]
- }
- ],
- "metadata": {
- "kernelspec": {
- "display_name": "Python 3",
- "language": "python",
- "name": "python3"
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diff --git a/qiskit/fundamentals/7_summary_of_quantum_operations.ipynb b/qiskit/fundamentals/7_summary_of_quantum_operations.ipynb
new file mode 100644
index 000000000..d7e8641ab
--- /dev/null
+++ b/qiskit/fundamentals/7_summary_of_quantum_operations.ipynb
@@ -0,0 +1,3094 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "![\"Note:](\"../../images/qiskit_header.png\")
Trusted Notebook\" align=\"middle\">"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Summary of Quantum Operations "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ " In this section we will go into the different operations that are available in Qiskit Terra. These are:\n",
+ "- Single-qubit quantum gates\n",
+ "- Multi-qubit quantum gates\n",
+ "- Measurements\n",
+ "- Reset\n",
+ "- Conditionals\n",
+ "- State initialization\n",
+ "\n",
+ "We will also show you how to use the three different simulators:\n",
+ "- unitary_simulator\n",
+ "- qasm_simulator\n",
+ "- statevector_simulator"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:54:28.396755Z",
+ "start_time": "2019-08-21T08:54:27.713006Z"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "# Useful additional packages \n",
+ "import matplotlib.pyplot as plt\n",
+ "%matplotlib inline\n",
+ "import numpy as np\n",
+ "from math import pi"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:54:32.622706Z",
+ "start_time": "2019-08-21T08:54:28.407651Z"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister, execute\n",
+ "from qiskit.tools.visualization import circuit_drawer\n",
+ "from qiskit.quantum_info import state_fidelity\n",
+ "from qiskit import BasicAer\n",
+ "\n",
+ "backend = BasicAer.get_backend('unitary_simulator')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Single Qubit Quantum states\n",
+ "\n",
+ "A single qubit quantum state can be written as\n",
+ "\n",
+ "$$\\left|\\psi\\right\\rangle = \\alpha\\left|0\\right\\rangle + \\beta \\left|1\\right\\rangle$$\n",
+ "\n",
+ "\n",
+ "where $\\alpha$ and $\\beta$ are complex numbers. In a measurement the probability of the bit being in $\\left|0\\right\\rangle$ is $|\\alpha|^2$ and $\\left|1\\right\\rangle$ is $|\\beta|^2$. As a vector this is\n",
+ "\n",
+ "$$\n",
+ "\\left|\\psi\\right\\rangle = \n",
+ "\\begin{pmatrix}\n",
+ "\\alpha \\\\\n",
+ "\\beta\n",
+ "\\end{pmatrix}.\n",
+ "$$\n",
+ "\n",
+ "Note due to conservation probability $|\\alpha|^2+ |\\beta|^2 = 1$ and since global phase is undetectable $\\left|\\psi\\right\\rangle := e^{i\\delta} \\left|\\psi\\right\\rangle$ we only requires two real numbers to describe a single qubit quantum state.\n",
+ "\n",
+ "A convenient representation is\n",
+ "\n",
+ "$$\\left|\\psi\\right\\rangle = \\cos(\\theta/2)\\left|0\\right\\rangle + \\sin(\\theta/2)e^{i\\phi}\\left|1\\right\\rangle$$\n",
+ "\n",
+ "where $0\\leq \\phi < 2\\pi$, and $0\\leq \\theta \\leq \\pi$. From this it is clear that there is a one-to-one correspondence between qubit states ($\\mathbb{C}^2$) and the points on the surface of a unit sphere ($\\mathbb{R}^3$). This is called the Bloch sphere representation of a qubit state.\n",
+ "\n",
+ "Quantum gates/operations are usually represented as matrices. A gate which acts on a qubit is represented by a $2\\times 2$ unitary matrix $U$. The action of the quantum gate is found by multiplying the matrix representing the gate with the vector which represents the quantum state.\n",
+ "\n",
+ "$$\\left|\\psi'\\right\\rangle = U\\left|\\psi\\right\\rangle$$\n",
+ "\n",
+ "A general unitary must be able to take the $\\left|0\\right\\rangle$ to the above state. That is \n",
+ "\n",
+ "$$\n",
+ "U = \\begin{pmatrix}\n",
+ "\\cos(\\theta/2) & a \\\\\n",
+ "e^{i\\phi}\\sin(\\theta/2) & b \n",
+ "\\end{pmatrix}\n",
+ "$$ \n",
+ "\n",
+ "where $a$ and $b$ are complex numbers constrained such that $U^\\dagger U = I$ for all $0\\leq\\theta\\leq\\pi$ and $0\\leq \\phi<2\\pi$. This gives 3 constraints and as such $a\\rightarrow -e^{i\\lambda}\\sin(\\theta/2)$ and $b\\rightarrow e^{i\\lambda+i\\phi}\\cos(\\theta/2)$ where $0\\leq \\lambda<2\\pi$ giving \n",
+ "\n",
+ "$$\n",
+ "U = \\begin{pmatrix}\n",
+ "\\cos(\\theta/2) & -e^{i\\lambda}\\sin(\\theta/2) \\\\\n",
+ "e^{i\\phi}\\sin(\\theta/2) & e^{i\\lambda+i\\phi}\\cos(\\theta/2) \n",
+ "\\end{pmatrix}.\n",
+ "$$\n",
+ "\n",
+ "This is the most general form of a single qubit unitary."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Single-Qubit Gates\n",
+ "\n",
+ "The single-qubit gates available are:\n",
+ "- u gates\n",
+ "- Identity gate\n",
+ "- Pauli gates\n",
+ "- Clifford gates\n",
+ "- $C3$ gates\n",
+ "- Standard rotation gates \n",
+ "\n",
+ "We have provided a backend: `unitary_simulator` to allow you to calculate the unitary matrices. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:54:32.638412Z",
+ "start_time": "2019-08-21T08:54:32.635777Z"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "q = QuantumRegister(1)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### u gates\n",
+ "\n",
+ "In Qiskit we give you access to the general unitary using the $u3$ gate\n",
+ "\n",
+ "$$\n",
+ "u3(\\theta, \\phi, \\lambda) = U(\\theta, \\phi, \\lambda) \n",
+ "$$\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:54:32.658121Z",
+ "start_time": "2019-08-21T08:54:32.650725Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ ""
+ ]
+ },
+ "execution_count": 4,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "qc = QuantumCircuit(q)\n",
+ "qc.u3(pi/2,pi/2,pi/2,q)\n",
+ "qc.draw()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:54:32.696192Z",
+ "start_time": "2019-08-21T08:54:32.672580Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([[ 0.707+0.j , 0. -0.707j],\n",
+ " [ 0. +0.707j, -0.707+0.j ]])"
+ ]
+ },
+ "execution_count": 5,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "job = execute(qc, backend)\n",
+ "job.result().get_unitary(qc, decimals=3)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The $u2(\\phi, \\lambda) =u3(\\pi/2, \\phi, \\lambda)$ has the matrix form\n",
+ "\n",
+ "$$\n",
+ "u2(\\phi, \\lambda) = \n",
+ "\\frac{1}{\\sqrt{2}} \\begin{pmatrix}\n",
+ "1 & -e^{i\\lambda} \\\\\n",
+ "e^{i\\phi} & e^{i(\\phi + \\lambda)}\n",
+ "\\end{pmatrix}.\n",
+ "$$\n",
+ "\n",
+ "This is a useful gate as it allows us to create superpositions"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:54:32.721409Z",
+ "start_time": "2019-08-21T08:54:32.715443Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ ""
+ ]
+ },
+ "execution_count": 6,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "qc = QuantumCircuit(q)\n",
+ "qc.u2(pi/2,pi/2,q)\n",
+ "qc.draw()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:54:32.757686Z",
+ "start_time": "2019-08-21T08:54:32.742747Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([[ 0.707+0.j , 0. -0.707j],\n",
+ " [ 0. +0.707j, -0.707+0.j ]])"
+ ]
+ },
+ "execution_count": 7,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "job = execute(qc, backend)\n",
+ "job.result().get_unitary(qc, decimals=3)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The $u1(\\lambda)= u3(0, 0, \\lambda)$ gate has the matrix form\n",
+ "\n",
+ "$$\n",
+ "u1(\\lambda) = \n",
+ "\\begin{pmatrix}\n",
+ "1 & 0 \\\\\n",
+ "0 & e^{i \\lambda}\n",
+ "\\end{pmatrix},\n",
+ "$$\n",
+ "\n",
+ "which is a useful as it allows us to apply a quantum phase."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:54:32.778776Z",
+ "start_time": "2019-08-21T08:54:32.772820Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ ""
+ ]
+ },
+ "execution_count": 8,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "qc = QuantumCircuit(q)\n",
+ "qc.u1(pi/2,q)\n",
+ "qc.draw()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 20,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:55:36.635190Z",
+ "start_time": "2019-08-21T08:55:36.623163Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([[1.+0.j, 0.+0.j],\n",
+ " [0.+0.j, 1.+0.j]])"
+ ]
+ },
+ "execution_count": 20,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "job = execute(qc, backend)\n",
+ "job.result().get_unitary(qc, decimals=3)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Identity gate\n",
+ "\n",
+ "The identity gate is $Id = u0(1)$."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 21,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:55:36.992414Z",
+ "start_time": "2019-08-21T08:55:36.986898Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ ""
+ ]
+ },
+ "execution_count": 21,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "qc = QuantumCircuit(q)\n",
+ "qc.iden(q)\n",
+ "qc.draw()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 22,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:55:37.181158Z",
+ "start_time": "2019-08-21T08:55:37.170249Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([[1.+0.j, 0.+0.j],\n",
+ " [0.+0.j, 1.+0.j]])"
+ ]
+ },
+ "execution_count": 22,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "job = execute(qc, backend)\n",
+ "job.result().get_unitary(qc, decimals=3)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Pauli gates\n",
+ "\n",
+ "#### $X$: bit-flip gate\n",
+ "\n",
+ "The bit-flip gate $X$ is defined as:\n",
+ "\n",
+ "$$\n",
+ "X = \n",
+ "\\begin{pmatrix}\n",
+ "0 & 1\\\\\n",
+ "1 & 0\n",
+ "\\end{pmatrix}= u3(\\pi,0,\\pi)\n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 23,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:55:37.492730Z",
+ "start_time": "2019-08-21T08:55:37.487214Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ ""
+ ]
+ },
+ "execution_count": 23,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "qc = QuantumCircuit(q)\n",
+ "qc.x(q)\n",
+ "qc.draw()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 24,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:55:37.771126Z",
+ "start_time": "2019-08-21T08:55:37.751176Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([[0.+0.j, 1.+0.j],\n",
+ " [1.+0.j, 0.+0.j]])"
+ ]
+ },
+ "execution_count": 24,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "job = execute(qc, backend)\n",
+ "job.result().get_unitary(qc, decimals=3)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### $Y$: bit- and phase-flip gate\n",
+ "\n",
+ "The $Y$ gate is defined as:\n",
+ "\n",
+ "$$\n",
+ "Y = \n",
+ "\\begin{pmatrix}\n",
+ "0 & -i\\\\\n",
+ "i & 0\n",
+ "\\end{pmatrix}=u3(\\pi,\\pi/2,\\pi/2)\n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 25,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:55:38.139841Z",
+ "start_time": "2019-08-21T08:55:38.134360Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ ""
+ ]
+ },
+ "execution_count": 25,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "qc = QuantumCircuit(q)\n",
+ "qc.y(q)\n",
+ "qc.draw()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 26,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:55:38.338922Z",
+ "start_time": "2019-08-21T08:55:38.324715Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([[0.+0.j, 0.-1.j],\n",
+ " [0.+1.j, 0.+0.j]])"
+ ]
+ },
+ "execution_count": 26,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "job = execute(qc, backend)\n",
+ "job.result().get_unitary(qc, decimals=3)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### $Z$: phase-flip gate\n",
+ "\n",
+ "The phase flip gate $Z$ is defined as:\n",
+ "\n",
+ "$$\n",
+ "Z = \n",
+ "\\begin{pmatrix}\n",
+ "1 & 0\\\\\n",
+ "0 & -1\n",
+ "\\end{pmatrix}=u1(\\pi)\n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 27,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:55:38.680879Z",
+ "start_time": "2019-08-21T08:55:38.675275Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ ""
+ ]
+ },
+ "execution_count": 27,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "qc = QuantumCircuit(q)\n",
+ "qc.z(q)\n",
+ "qc.draw()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 28,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:55:38.896243Z",
+ "start_time": "2019-08-21T08:55:38.884073Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([[ 1.+0.j, 0.+0.j],\n",
+ " [ 0.+0.j, -1.+0.j]])"
+ ]
+ },
+ "execution_count": 28,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "job = execute(qc, backend)\n",
+ "job.result().get_unitary(qc, decimals=3)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Clifford gates\n",
+ "\n",
+ "#### Hadamard gate\n",
+ "\n",
+ "$$\n",
+ "H = \n",
+ "\\frac{1}{\\sqrt{2}}\n",
+ "\\begin{pmatrix}\n",
+ "1 & 1\\\\\n",
+ "1 & -1\n",
+ "\\end{pmatrix}= u2(0,\\pi)\n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 29,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:55:39.291931Z",
+ "start_time": "2019-08-21T08:55:39.286455Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ ""
+ ]
+ },
+ "execution_count": 29,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "qc = QuantumCircuit(q)\n",
+ "qc.h(q)\n",
+ "qc.draw()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 30,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:55:39.490699Z",
+ "start_time": "2019-08-21T08:55:39.478536Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([[ 0.707+0.j, 0.707+0.j],\n",
+ " [ 0.707+0.j, -0.707+0.j]])"
+ ]
+ },
+ "execution_count": 30,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "job = execute(qc, backend)\n",
+ "job.result().get_unitary(qc, decimals=3)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### $S$ (or, $\\sqrt{Z}$ phase) gate\n",
+ "\n",
+ "$$\n",
+ "S = \n",
+ "\\begin{pmatrix}\n",
+ "1 & 0\\\\\n",
+ "0 & i\n",
+ "\\end{pmatrix}= u1(\\pi/2)\n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 31,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:55:40.054653Z",
+ "start_time": "2019-08-21T08:55:40.049332Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ ""
+ ]
+ },
+ "execution_count": 31,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "qc = QuantumCircuit(q)\n",
+ "qc.s(q)\n",
+ "qc.draw()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 32,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:55:40.340040Z",
+ "start_time": "2019-08-21T08:55:40.327313Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([[1.+0.j, 0.+0.j],\n",
+ " [0.+0.j, 0.+1.j]])"
+ ]
+ },
+ "execution_count": 32,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "job = execute(qc, backend)\n",
+ "job.result().get_unitary(qc, decimals=3)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### $S^{\\dagger}$ (or, conjugate of $\\sqrt{Z}$ phase) gate\n",
+ "\n",
+ "$$\n",
+ "S^{\\dagger} = \n",
+ "\\begin{pmatrix}\n",
+ "1 & 0\\\\\n",
+ "0 & -i\n",
+ "\\end{pmatrix}= u1(-\\pi/2)\n",
+ "$$\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 33,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:55:40.893533Z",
+ "start_time": "2019-08-21T08:55:40.887218Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ ""
+ ]
+ },
+ "execution_count": 33,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "qc = QuantumCircuit(q)\n",
+ "qc.sdg(q)\n",
+ "qc.draw()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 34,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:55:41.186813Z",
+ "start_time": "2019-08-21T08:55:41.173783Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([[1.+0.j, 0.+0.j],\n",
+ " [0.+0.j, 0.-1.j]])"
+ ]
+ },
+ "execution_count": 34,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "job = execute(qc, backend)\n",
+ "job.result().get_unitary(qc, decimals=3)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### $C3$ gates\n",
+ "#### $T$ (or, $\\sqrt{S}$ phase) gate\n",
+ "\n",
+ "$$\n",
+ "T = \n",
+ "\\begin{pmatrix}\n",
+ "1 & 0\\\\\n",
+ "0 & e^{i \\pi/4}\n",
+ "\\end{pmatrix}= u1(\\pi/4) \n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 35,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:55:41.712311Z",
+ "start_time": "2019-08-21T08:55:41.706924Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ ""
+ ]
+ },
+ "execution_count": 35,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "qc = QuantumCircuit(q)\n",
+ "qc.t(q)\n",
+ "qc.draw()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 36,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:55:42.082078Z",
+ "start_time": "2019-08-21T08:55:42.068425Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([[1. +0.j , 0. +0.j ],\n",
+ " [0. +0.j , 0.707+0.707j]])"
+ ]
+ },
+ "execution_count": 36,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "job = execute(qc, backend)\n",
+ "job.result().get_unitary(qc, decimals=3)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### $T^{\\dagger}$ (or, conjugate of $\\sqrt{S}$ phase) gate\n",
+ "\n",
+ "$$\n",
+ "T^{\\dagger} = \n",
+ "\\begin{pmatrix}\n",
+ "1 & 0\\\\\n",
+ "0 & e^{-i \\pi/4}\n",
+ "\\end{pmatrix}= u1(-pi/4)\n",
+ "$$\n",
+ "\n",
+ "They can be added as below."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 37,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:55:42.567878Z",
+ "start_time": "2019-08-21T08:55:42.562458Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ ""
+ ]
+ },
+ "execution_count": 37,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "qc = QuantumCircuit(q)\n",
+ "qc.tdg(q)\n",
+ "qc.draw()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 38,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:55:42.798583Z",
+ "start_time": "2019-08-21T08:55:42.785608Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([[1. +0.j , 0. +0.j ],\n",
+ " [0. +0.j , 0.707-0.707j]])"
+ ]
+ },
+ "execution_count": 38,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "job = execute(qc, backend)\n",
+ "job.result().get_unitary(qc, decimals=3)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Standard Rotations\n",
+ "\n",
+ "The standard rotation gates are those that define rotations around the Paulis $P=\\{X,Y,Z\\}$. They are defined as \n",
+ "\n",
+ "$$ R_P(\\theta) = \\exp(-i \\theta P/2) = \\cos(\\theta/2)I -i \\sin(\\theta/2)P$$\n",
+ "\n",
+ "#### Rotation around X-axis\n",
+ "\n",
+ "$$\n",
+ "R_x(\\theta) = \n",
+ "\\begin{pmatrix}\n",
+ "\\cos(\\theta/2) & -i\\sin(\\theta/2)\\\\\n",
+ "-i\\sin(\\theta/2) & \\cos(\\theta/2)\n",
+ "\\end{pmatrix} = u3(\\theta, -\\pi/2,\\pi/2)\n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 39,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:55:43.240683Z",
+ "start_time": "2019-08-21T08:55:43.234929Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ ""
+ ]
+ },
+ "execution_count": 39,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "qc = QuantumCircuit(q)\n",
+ "qc.rx(pi/2,q)\n",
+ "qc.draw()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 40,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:55:43.476371Z",
+ "start_time": "2019-08-21T08:55:43.463329Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([[0.707+0.j , 0. -0.707j],\n",
+ " [0. -0.707j, 0.707+0.j ]])"
+ ]
+ },
+ "execution_count": 40,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "job = execute(qc, backend)\n",
+ "job.result().get_unitary(qc, decimals=3)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### Rotation around Y-axis\n",
+ "\n",
+ "$$\n",
+ "R_y(\\theta) =\n",
+ "\\begin{pmatrix}\n",
+ "\\cos(\\theta/2) & - \\sin(\\theta/2)\\\\\n",
+ "\\sin(\\theta/2) & \\cos(\\theta/2).\n",
+ "\\end{pmatrix} =u3(\\theta,0,0)\n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 41,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:55:43.958486Z",
+ "start_time": "2019-08-21T08:55:43.952515Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ ""
+ ]
+ },
+ "execution_count": 41,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "qc = QuantumCircuit(q)\n",
+ "qc.ry(pi/2,q)\n",
+ "qc.draw()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 42,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:55:44.185984Z",
+ "start_time": "2019-08-21T08:55:44.173535Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([[ 0.707+0.j, -0.707+0.j],\n",
+ " [ 0.707+0.j, 0.707+0.j]])"
+ ]
+ },
+ "execution_count": 42,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "job = execute(qc, backend)\n",
+ "job.result().get_unitary(qc, decimals=3)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### Rotation around Z-axis\n",
+ "\n",
+ "$$\n",
+ "R_z(\\phi) = \n",
+ "\\begin{pmatrix}\n",
+ "e^{-i \\phi/2} & 0 \\\\\n",
+ "0 & e^{i \\phi/2}\n",
+ "\\end{pmatrix}\\equiv u1(\\phi)\n",
+ "$$\n",
+ "\n",
+ "Note here we have used an equivalent as is different to u1 by global phase $e^{-i \\phi/2}$."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 43,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:55:44.611839Z",
+ "start_time": "2019-08-21T08:55:44.606231Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ ""
+ ]
+ },
+ "execution_count": 43,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "qc = QuantumCircuit(q)\n",
+ "qc.rz(pi/2,q)\n",
+ "qc.draw()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 44,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:55:44.847493Z",
+ "start_time": "2019-08-21T08:55:44.835188Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([[1.+0.j, 0.+0.j],\n",
+ " [0.+0.j, 0.+1.j]])"
+ ]
+ },
+ "execution_count": 44,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "job = execute(qc, backend)\n",
+ "job.result().get_unitary(qc, decimals=3)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Note this is different due only to a global phase"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Multi-Qubit Gates\n",
+ "\n",
+ "### Mathematical Preliminaries\n",
+ "\n",
+ "The space of quantum computer grows exponential with the number of qubits. For $n$ qubits the complex vector space has dimensions $d=2^n$. To describe states of a multi-qubit system, the tensor product is used to \"glue together\" operators and basis vectors.\n",
+ "\n",
+ "Let's start by considering a 2-qubit system. Given two operators $A$ and $B$ that each act on one qubit, the joint operator $A \\otimes B$ acting on two qubits is\n",
+ "\n",
+ "$$\\begin{equation}\n",
+ "\tA\\otimes B = \n",
+ "\t\\begin{pmatrix} \n",
+ "\t\tA_{00} \\begin{pmatrix} \n",
+ "\t\t\tB_{00} & B_{01} \\\\\n",
+ "\t\t\tB_{10} & B_{11}\n",
+ "\t\t\\end{pmatrix} & A_{01} \t\\begin{pmatrix} \n",
+ "\t\t\t\tB_{00} & B_{01} \\\\\n",
+ "\t\t\t\tB_{10} & B_{11}\n",
+ "\t\t\t\\end{pmatrix} \\\\\n",
+ "\t\tA_{10} \t\\begin{pmatrix} \n",
+ "\t\t\t\t\tB_{00} & B_{01} \\\\\n",
+ "\t\t\t\t\tB_{10} & B_{11}\n",
+ "\t\t\t\t\\end{pmatrix} & A_{11} \t\\begin{pmatrix} \n",
+ "\t\t\t\t\t\t\tB_{00} & B_{01} \\\\\n",
+ "\t\t\t\t\t\t\tB_{10} & B_{11}\n",
+ "\t\t\t\t\t\t\\end{pmatrix}\n",
+ "\t\\end{pmatrix},\t\t\t\t\t\t\n",
+ "\\end{equation}$$\n",
+ "\n",
+ "where $A_{jk}$ and $B_{lm}$ are the matrix elements of $A$ and $B$, respectively.\n",
+ "\n",
+ "Analogously, the basis vectors for the 2-qubit system are formed using the tensor product of basis vectors for a single qubit:\n",
+ "$$\\begin{equation}\\begin{split}\n",
+ "\t\\left|{00}\\right\\rangle &= \\begin{pmatrix} \n",
+ "\t\t1 \\begin{pmatrix} \n",
+ "\t\t\t1 \\\\\n",
+ "\t\t\t0\n",
+ "\t\t\\end{pmatrix} \\\\\n",
+ "\t\t0 \\begin{pmatrix} \n",
+ "\t\t\t1 \\\\\n",
+ "\t\t\t0 \n",
+ "\t\t\\end{pmatrix}\n",
+ "\t\\end{pmatrix} = \\begin{pmatrix} 1 \\\\ 0 \\\\ 0 \\\\0 \\end{pmatrix}~~~\\left|{01}\\right\\rangle = \\begin{pmatrix} \n",
+ "\t1 \\begin{pmatrix} \n",
+ "\t0 \\\\\n",
+ "\t1\n",
+ "\t\\end{pmatrix} \\\\\n",
+ "\t0 \\begin{pmatrix} \n",
+ "\t0 \\\\\n",
+ "\t1 \n",
+ "\t\\end{pmatrix}\n",
+ "\t\\end{pmatrix} = \\begin{pmatrix}0 \\\\ 1 \\\\ 0 \\\\ 0 \\end{pmatrix}\\end{split}\n",
+ "\\end{equation}$$\n",
+ " \n",
+ "$$\\begin{equation}\\begin{split}\\left|{10}\\right\\rangle = \\begin{pmatrix} \n",
+ "\t0\\begin{pmatrix} \n",
+ "\t1 \\\\\n",
+ "\t0\n",
+ "\t\\end{pmatrix} \\\\\n",
+ "\t1\\begin{pmatrix} \n",
+ "\t1 \\\\\n",
+ "\t0 \n",
+ "\t\\end{pmatrix}\n",
+ "\t\\end{pmatrix} = \\begin{pmatrix} 0 \\\\ 0 \\\\ 1 \\\\ 0 \\end{pmatrix}~~~ \t\\left|{11}\\right\\rangle = \\begin{pmatrix} \n",
+ "\t0 \\begin{pmatrix} \n",
+ "\t0 \\\\\n",
+ "\t1\n",
+ "\t\\end{pmatrix} \\\\\n",
+ "\t1\\begin{pmatrix} \n",
+ "\t0 \\\\\n",
+ "\t1 \n",
+ "\t\\end{pmatrix}\n",
+ "\t\\end{pmatrix} = \\begin{pmatrix} 0 \\\\ 0 \\\\ 0 \\\\1 \\end{pmatrix}\\end{split}\n",
+ "\\end{equation}.$$\n",
+ "\n",
+ "Note we've introduced a shorthand for the tensor product of basis vectors, wherein $\\left|0\\right\\rangle \\otimes \\left|0\\right\\rangle$ is written as $\\left|00\\right\\rangle$. The state of an $n$-qubit system can described using the $n$-fold tensor product of single-qubit basis vectors. Notice that the basis vectors for a 2-qubit system are 4-dimensional; in general, the basis vectors of an $n$-qubit sytsem are $2^{n}$-dimensional, as noted earlier.\n",
+ "\n",
+ "### Basis vector ordering in Qiskit\n",
+ "\n",
+ "Within the physics community, the qubits of a multi-qubit systems are typically ordered with the first qubit on the left-most side of the tensor product and the last qubit on the right-most side. For instance, if the first qubit is in state $\\left|0\\right\\rangle$ and second is in state $\\left|1\\right\\rangle$, their joint state would be $\\left|01\\right\\rangle$. Qiskit uses a slightly different ordering of the qubits, in which the qubits are represented from the most significant bit (MSB) on the left to the least significant bit (LSB) on the right (big-endian). This is similar to bitstring representation on classical computers, and enables easy conversion from bitstrings to integers after measurements are performed. For the example just given, the joint state would be represented as $\\left|10\\right\\rangle$. Importantly, _this change in the representation of multi-qubit states affects the way multi-qubit gates are represented in Qiskit_, as discussed below.\n",
+ "\n",
+ "The representation used in Qiskit enumerates the basis vectors in increasing order of the integers they represent. For instance, the basis vectors for a 2-qubit system would be ordered as $\\left|00\\right\\rangle$, $\\left|01\\right\\rangle$, $\\left|10\\right\\rangle$, and $\\left|11\\right\\rangle$. Thinking of the basis vectors as bit strings, they encode the integers 0,1,2 and 3, respectively.\n",
+ "\n",
+ "\n",
+ "### Controlled operations on qubits\n",
+ "\n",
+ "A common multi-qubit gate involves the application of a gate to one qubit, conditioned on the state of another qubit. For instance, we might want to flip the state of the second qubit when the first qubit is in $\\left|0\\right\\rangle$. Such gates are known as _controlled gates_. The standard multi-qubit gates consist of two-qubit gates and three-qubit gates. The two-qubit gates are:\n",
+ "- controlled Pauli gates\n",
+ "- controlled Hadamard gate\n",
+ "- controlled rotation gates\n",
+ "- controlled phase gate\n",
+ "- controlled u3 gate\n",
+ "- swap gate\n",
+ "\n",
+ "The three-qubit gates are: \n",
+ "- Toffoli gate \n",
+ "- Fredkin gate"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Two-qubit gates\n",
+ "\n",
+ "Most of the two-gates are of the controlled type (the SWAP gate being the exception). In general, a controlled two-qubit gate $C_{U}$ acts to apply the single-qubit unitary $U$ to the second qubit when the state of the first qubit is in $\\left|1\\right\\rangle$. Suppose $U$ has a matrix representation\n",
+ "\n",
+ "$$U = \\begin{pmatrix} u_{00} & u_{01} \\\\ u_{10} & u_{11}\\end{pmatrix}.$$\n",
+ "\n",
+ "We can work out the action of $C_{U}$ as follows. Recall that the basis vectors for a two-qubit system are ordered as $\\left|00\\right\\rangle, \\left|01\\right\\rangle, \\left|10\\right\\rangle, \\left|11\\right\\rangle$. Suppose the **control qubit** is **qubit 0** (which, according to Qiskit's convention, is one the _right-hand_ side of the tensor product). If the control qubit is in $\\left|1\\right\\rangle$, $U$ should be applied to the **target** (qubit 1, on the _left-hand_ side of the tensor product). Therefore, under the action of $C_{U}$, the basis vectors are transformed according to\n",
+ "\n",
+ "$$\\begin{align*}\n",
+ "C_{U}: \\underset{\\text{qubit}~1}{\\left|0\\right\\rangle}\\otimes \\underset{\\text{qubit}~0}{\\left|0\\right\\rangle} &\\rightarrow \\underset{\\text{qubit}~1}{\\left|0\\right\\rangle}\\otimes \\underset{\\text{qubit}~0}{\\left|0\\right\\rangle}\\\\\n",
+ "C_{U}: \\underset{\\text{qubit}~1}{\\left|0\\right\\rangle}\\otimes \\underset{\\text{qubit}~0}{\\left|1\\right\\rangle} &\\rightarrow \\underset{\\text{qubit}~1}{U\\left|0\\right\\rangle}\\otimes \\underset{\\text{qubit}~0}{\\left|1\\right\\rangle}\\\\\n",
+ "C_{U}: \\underset{\\text{qubit}~1}{\\left|1\\right\\rangle}\\otimes \\underset{\\text{qubit}~0}{\\left|0\\right\\rangle} &\\rightarrow \\underset{\\text{qubit}~1}{\\left|1\\right\\rangle}\\otimes \\underset{\\text{qubit}~0}{\\left|0\\right\\rangle}\\\\\n",
+ "C_{U}: \\underset{\\text{qubit}~1}{\\left|1\\right\\rangle}\\otimes \\underset{\\text{qubit}~0}{\\left|1\\right\\rangle} &\\rightarrow \\underset{\\text{qubit}~1}{U\\left|1\\right\\rangle}\\otimes \\underset{\\text{qubit}~0}{\\left|1\\right\\rangle}\\\\\n",
+ "\\end{align*}.$$\n",
+ "\n",
+ "In matrix form, the action of $C_{U}$ is\n",
+ "\n",
+ "$$\\begin{equation}\n",
+ "\tC_U = \\begin{pmatrix}\n",
+ "\t1 & 0 & 0 & 0 \\\\\n",
+ "\t0 & u_{00} & 0 & u_{01} \\\\\n",
+ "\t0 & 0 & 1 & 0 \\\\\n",
+ "\t0 & u_{10} &0 & u_{11}\n",
+ "\t\t\\end{pmatrix}.\n",
+ "\\end{equation}$$\n",
+ "\n",
+ "To work out these matrix elements, let\n",
+ "\n",
+ "$$C_{(jk), (lm)} = \\left(\\underset{\\text{qubit}~1}{\\left\\langle j \\right|} \\otimes \\underset{\\text{qubit}~0}{\\left\\langle k \\right|}\\right) C_{U} \\left(\\underset{\\text{qubit}~1}{\\left| l \\right\\rangle} \\otimes \\underset{\\text{qubit}~0}{\\left| k \\right\\rangle}\\right),$$\n",
+ "\n",
+ "compute the action of $C_{U}$ (given above), and compute the inner products.\n",
+ "\n",
+ "As shown in the examples below, this operation is implemented in Qiskit as `cU(q[0],q[1])`.\n",
+ "\n",
+ "\n",
+ "If **qubit 1 is the control and qubit 0 is the target**, then the basis vectors are transformed according to\n",
+ "$$\\begin{align*}\n",
+ "C_{U}: \\underset{\\text{qubit}~1}{\\left|0\\right\\rangle}\\otimes \\underset{\\text{qubit}~0}{\\left|0\\right\\rangle} &\\rightarrow \\underset{\\text{qubit}~1}{\\left|0\\right\\rangle}\\otimes \\underset{\\text{qubit}~0}{\\left|0\\right\\rangle}\\\\\n",
+ "C_{U}: \\underset{\\text{qubit}~1}{\\left|0\\right\\rangle}\\otimes \\underset{\\text{qubit}~0}{\\left|1\\right\\rangle} &\\rightarrow \\underset{\\text{qubit}~1}{\\left|0\\right\\rangle}\\otimes \\underset{\\text{qubit}~0}{\\left|1\\right\\rangle}\\\\\n",
+ "C_{U}: \\underset{\\text{qubit}~1}{\\left|1\\right\\rangle}\\otimes \\underset{\\text{qubit}~0}{\\left|0\\right\\rangle} &\\rightarrow \\underset{\\text{qubit}~1}{\\left|1\\right\\rangle}\\otimes \\underset{\\text{qubit}~0}{U\\left|0\\right\\rangle}\\\\\n",
+ "C_{U}: \\underset{\\text{qubit}~1}{\\left|1\\right\\rangle}\\otimes \\underset{\\text{qubit}~0}{\\left|1\\right\\rangle} &\\rightarrow \\underset{\\text{qubit}~1}{\\left|1\\right\\rangle}\\otimes \\underset{\\text{qubit}~0}{U\\left|1\\right\\rangle}\\\\\n",
+ "\\end{align*},$$\n",
+ "\n",
+ "\n",
+ "which implies the matrix form of $C_{U}$ is\n",
+ "$$\\begin{equation}\n",
+ "\tC_U = \\begin{pmatrix}\n",
+ "\t1 & 0 & 0 & 0 \\\\\n",
+ "\t0 & 1 & 0 & 0 \\\\\n",
+ "\t0 & 0 & u_{00} & u_{01} \\\\\n",
+ "\t0 & 0 & u_{10} & u_{11}\n",
+ "\t\t\\end{pmatrix}.\n",
+ "\\end{equation}$$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 45,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:55:46.416973Z",
+ "start_time": "2019-08-21T08:55:46.414377Z"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "q = QuantumRegister(2)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Controlled Pauli Gates\n",
+ "\n",
+ "#### Controlled-X (or, controlled-NOT) gate\n",
+ "The controlled-not gate flips the `target` qubit when the control qubit is in the state $\\left|1\\right\\rangle$. If we take the MSB as the control qubit (e.g. `cx(q[1],q[0])`), then the matrix would look like\n",
+ "\n",
+ "$$\n",
+ "C_X = \n",
+ "\\begin{pmatrix}\n",
+ "1 & 0 & 0 & 0\\\\\n",
+ "0 & 1 & 0 & 0\\\\\n",
+ "0 & 0 & 0 & 1\\\\\n",
+ "0 & 0 & 1 & 0\n",
+ "\\end{pmatrix}. \n",
+ "$$\n",
+ "\n",
+ "However, when the LSB is the control qubit, (e.g. `cx(q[0],q[1])`), this gate is equivalent to the following matrix:\n",
+ "\n",
+ "$$\n",
+ "C_X = \n",
+ "\\begin{pmatrix}\n",
+ "1 & 0 & 0 & 0\\\\\n",
+ "0 & 0 & 0 & 1\\\\\n",
+ "0 & 0 & 1 & 0\\\\\n",
+ "0 & 1 & 0 & 0\n",
+ "\\end{pmatrix}. \n",
+ "$$\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 46,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:55:46.841847Z",
+ "start_time": "2019-08-21T08:55:46.835972Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ ""
+ ]
+ },
+ "execution_count": 46,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "qc = QuantumCircuit(q)\n",
+ "qc.cx(q[0],q[1])\n",
+ "qc.draw()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 47,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:55:47.097437Z",
+ "start_time": "2019-08-21T08:55:47.085390Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([[1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n",
+ " [0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j],\n",
+ " [0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],\n",
+ " [0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j]])"
+ ]
+ },
+ "execution_count": 47,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "job = execute(qc, backend)\n",
+ "job.result().get_unitary(qc, decimals=3)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### Controlled $Y$ gate\n",
+ "\n",
+ "Apply the $Y$ gate to the target qubit if the control qubit is the MSB\n",
+ "\n",
+ "$$\n",
+ "C_Y = \n",
+ "\\begin{pmatrix}\n",
+ "1 & 0 & 0 & 0\\\\\n",
+ "0 & 1 & 0 & 0\\\\\n",
+ "0 & 0 & 0 & -i\\\\\n",
+ "0 & 0 & i & 0\n",
+ "\\end{pmatrix},\n",
+ "$$\n",
+ "\n",
+ "or when the LSB is the control\n",
+ "\n",
+ "$$\n",
+ "C_Y = \n",
+ "\\begin{pmatrix}\n",
+ "1 & 0 & 0 & 0\\\\\n",
+ "0 & 0 & 0 & -i\\\\\n",
+ "0 & 0 & 1 & 0\\\\\n",
+ "0 & i & 0 & 0\n",
+ "\\end{pmatrix}.\n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 48,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:55:47.616404Z",
+ "start_time": "2019-08-21T08:55:47.610576Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ ""
+ ]
+ },
+ "execution_count": 48,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "qc = QuantumCircuit(q)\n",
+ "qc.cy(q[0],q[1])\n",
+ "qc.draw()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 49,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:55:47.947599Z",
+ "start_time": "2019-08-21T08:55:47.857473Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([[1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n",
+ " [0.+0.j, 0.+0.j, 0.+0.j, 0.-1.j],\n",
+ " [0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],\n",
+ " [0.+0.j, 0.+1.j, 0.+0.j, 0.+0.j]])"
+ ]
+ },
+ "execution_count": 49,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "job = execute(qc, backend)\n",
+ "job.result().get_unitary(qc, decimals=3)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### Controlled $Z$ (or, controlled Phase) gate\n",
+ "\n",
+ "Similarly, the controlled Z gate flips the phase of the target qubit if the control qubit is $\\left|1\\right\\rangle$. The matrix looks the same regardless of whether the MSB or LSB is the control qubit:\n",
+ "\n",
+ "$$\n",
+ "C_Z = \n",
+ "\\begin{pmatrix}\n",
+ "1 & 0 & 0 & 0\\\\\n",
+ "0 & 1 & 0 & 0\\\\\n",
+ "0 & 0 & 1 & 0\\\\\n",
+ "0 & 0 & 0 & -1\n",
+ "\\end{pmatrix}\n",
+ "$$\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 50,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:55:48.328874Z",
+ "start_time": "2019-08-21T08:55:48.322865Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ ""
+ ]
+ },
+ "execution_count": 50,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "qc = QuantumCircuit(q)\n",
+ "qc.cz(q[0],q[1])\n",
+ "qc.draw()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 51,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:55:48.583091Z",
+ "start_time": "2019-08-21T08:55:48.566470Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([[ 1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n",
+ " [ 0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j],\n",
+ " [ 0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],\n",
+ " [ 0.+0.j, 0.+0.j, 0.+0.j, -1.+0.j]])"
+ ]
+ },
+ "execution_count": 51,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "job = execute(qc, backend)\n",
+ "job.result().get_unitary(qc, decimals=3)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Controlled Hadamard gate\n",
+ "\n",
+ "Apply $H$ gate to the target qubit if the control qubit is $\\left|1\\right\\rangle$. Below is the case where the control is the LSB qubit.\n",
+ "\n",
+ "$$\n",
+ "C_H = \n",
+ "\\begin{pmatrix}\n",
+ "1 & 0 & 0 & 0\\\\\n",
+ "0 & \\frac{1}{\\sqrt{2}} & 0 & \\frac{1}{\\sqrt{2}}\\\\\n",
+ "0 & 0 & 1 & 0\\\\\n",
+ "0 & \\frac{1}{\\sqrt{2}} & 0& -\\frac{1}{\\sqrt{2}}\n",
+ "\\end{pmatrix}\n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 52,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:55:49.041157Z",
+ "start_time": "2019-08-21T08:55:49.034254Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ ""
+ ]
+ },
+ "execution_count": 52,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "qc = QuantumCircuit(q)\n",
+ "qc.ch(q[0],q[1])\n",
+ "qc.draw()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 53,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:55:49.531168Z",
+ "start_time": "2019-08-21T08:55:49.514875Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([[ 1. +0.j, 0. +0.j, 0. +0.j, 0. +0.j],\n",
+ " [ 0. +0.j, 0.707+0.j, 0. +0.j, 0.707+0.j],\n",
+ " [ 0. +0.j, 0. +0.j, 1. +0.j, 0. +0.j],\n",
+ " [ 0. +0.j, 0.707+0.j, 0. +0.j, -0.707+0.j]])"
+ ]
+ },
+ "execution_count": 53,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "job = execute(qc, backend)\n",
+ "job.result().get_unitary(qc, decimals=3)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Controlled rotation gates\n",
+ "\n",
+ "#### Controlled rotation around Z-axis\n",
+ "\n",
+ "Perform rotation around Z-axis on the target qubit if the control qubit (here LSB) is $\\left|1\\right\\rangle$.\n",
+ "\n",
+ "$$\n",
+ "C_{Rz}(\\lambda) = \n",
+ "\\begin{pmatrix}\n",
+ "1 & 0 & 0 & 0\\\\\n",
+ "0 & e^{-i\\lambda/2} & 0 & 0\\\\\n",
+ "0 & 0 & 1 & 0\\\\\n",
+ "0 & 0 & 0 & e^{i\\lambda/2}\n",
+ "\\end{pmatrix}\n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 54,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:55:50.174677Z",
+ "start_time": "2019-08-21T08:55:50.168096Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ ""
+ ]
+ },
+ "execution_count": 54,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "qc = QuantumCircuit(q)\n",
+ "qc.crz(pi/2,q[0],q[1])\n",
+ "qc.draw()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 55,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:55:50.390216Z",
+ "start_time": "2019-08-21T08:55:50.373691Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([[1. +0.j , 0. +0.j , 0. +0.j , 0. +0.j ],\n",
+ " [0. +0.j , 0.707-0.707j, 0. +0.j , 0. +0.j ],\n",
+ " [0. +0.j , 0. +0.j , 1. +0.j , 0. +0.j ],\n",
+ " [0. +0.j , 0. +0.j , 0. +0.j , 0.707+0.707j]])"
+ ]
+ },
+ "execution_count": 55,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "job = execute(qc, backend)\n",
+ "job.result().get_unitary(qc, decimals=3)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Controlled phase rotation\n",
+ "\n",
+ "Perform a phase rotation if both qubits are in the $\\left|11\\right\\rangle$ state. The matrix looks the same regardless of whether the MSB or LSB is the control qubit.\n",
+ "\n",
+ "$$\n",
+ "C_{u1}(\\lambda) = \n",
+ "\\begin{pmatrix}\n",
+ "1 & 0 & 0 & 0\\\\\n",
+ "0 & 1 & 0 & 0\\\\\n",
+ "0 & 0 & 1 & 0\\\\\n",
+ "0 & 0 & 0 & e^{i\\lambda}\n",
+ "\\end{pmatrix}\n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 56,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:55:51.107598Z",
+ "start_time": "2019-08-21T08:55:51.100979Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ ""
+ ]
+ },
+ "execution_count": 56,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "qc = QuantumCircuit(q)\n",
+ "qc.cu1(pi/2,q[0], q[1])\n",
+ "qc.draw()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 57,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:55:51.376499Z",
+ "start_time": "2019-08-21T08:55:51.358089Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([[1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n",
+ " [0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j],\n",
+ " [0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],\n",
+ " [0.+0.j, 0.+0.j, 0.+0.j, 0.+1.j]])"
+ ]
+ },
+ "execution_count": 57,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "job = execute(qc, backend)\n",
+ "job.result().get_unitary(qc, decimals=3)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Controlled $u3$ rotation\n",
+ "\n",
+ "Perform controlled-$u3$ rotation on the target qubit if the control qubit (here LSB) is $\\left|1\\right\\rangle$. \n",
+ "\n",
+ "$$\n",
+ "C_{u3}(\\theta, \\phi, \\lambda) \\equiv \n",
+ "\\begin{pmatrix}\n",
+ "1 & 0 & 0 & 0\\\\\n",
+ "0 & e^{-i(\\phi+\\lambda)/2}\\cos(\\theta/2) & 0 & -e^{-i(\\phi-\\lambda)/2}\\sin(\\theta/2)\\\\\n",
+ "0 & 0 & 1 & 0\\\\\n",
+ "0 & e^{i(\\phi-\\lambda)/2}\\sin(\\theta/2) & 0 & e^{i(\\phi+\\lambda)/2}\\cos(\\theta/2)\n",
+ "\\end{pmatrix}.\n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 58,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:55:52.429046Z",
+ "start_time": "2019-08-21T08:55:52.423018Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ ""
+ ]
+ },
+ "execution_count": 58,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "qc = QuantumCircuit(q)\n",
+ "qc.cu3(pi/2, pi/2, pi/2, q[0], q[1])\n",
+ "qc.draw()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 59,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:55:52.904237Z",
+ "start_time": "2019-08-21T08:55:52.885334Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([[ 1. +0.j , 0. +0.j , 0. +0.j , 0. +0.j ],\n",
+ " [ 0. +0.j , 0.707+0.j , 0. +0.j , 0. -0.707j],\n",
+ " [ 0. +0.j , 0. +0.j , 1. +0.j , 0. +0.j ],\n",
+ " [ 0. +0.j , 0. +0.707j, 0. +0.j , -0.707+0.j ]])"
+ ]
+ },
+ "execution_count": 59,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "job = execute(qc, backend)\n",
+ "job.result().get_unitary(qc, decimals=3)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### SWAP gate\n",
+ "\n",
+ "The SWAP gate exchanges the two qubits. It transforms the basis vectors as\n",
+ "\n",
+ "$$\\left|00\\right\\rangle \\rightarrow \\left|00\\right\\rangle~,~\\left|01\\right\\rangle \\rightarrow \\left|10\\right\\rangle~,~\\left|10\\right\\rangle \\rightarrow \\left|01\\right\\rangle~,~\\left|11\\right\\rangle \\rightarrow \\left|11\\right\\rangle,$$\n",
+ "\n",
+ "which gives a matrix representation of the form\n",
+ "\n",
+ "$$\n",
+ "\\mathrm{SWAP} = \n",
+ "\\begin{pmatrix}\n",
+ "1 & 0 & 0 & 0\\\\\n",
+ "0 & 0 & 1 & 0\\\\\n",
+ "0 & 1 & 0 & 0\\\\\n",
+ "0 & 0 & 0 & 1\n",
+ "\\end{pmatrix}.\n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 60,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:55:53.541227Z",
+ "start_time": "2019-08-21T08:55:53.535015Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ ""
+ ]
+ },
+ "execution_count": 60,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "qc = QuantumCircuit(q)\n",
+ "qc.swap(q[0], q[1])\n",
+ "qc.draw()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 61,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:55:54.100684Z",
+ "start_time": "2019-08-21T08:55:54.085594Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([[1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n",
+ " [0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],\n",
+ " [0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j],\n",
+ " [0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j]])"
+ ]
+ },
+ "execution_count": 61,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "job = execute(qc, backend)\n",
+ "job.result().get_unitary(qc, decimals=3)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Three-qubit gates\n",
+ "\n",
+ "\n",
+ "There are two commonly-used three-qubit gates. For three qubits, the basis vectors are ordered as\n",
+ "\n",
+ "$$\\left|000\\right\\rangle, \\left|001\\right\\rangle, \\left|010\\right\\rangle, \\left|011\\right\\rangle, \\left|100\\right\\rangle, \\left|101\\right\\rangle, \\left|110\\right\\rangle, \\left|111\\right\\rangle,$$\n",
+ "\n",
+ "which, as bitstrings, represent the integers $0,1,2,\\cdots, 7$. Again, Qiskit uses a representation in which the first qubit is on the right-most side of the tensor product and the third qubit is on the left-most side:\n",
+ "\n",
+ "$$\\left|abc\\right\\rangle : \\underset{\\text{qubit 2}}{\\left|a\\right\\rangle}\\otimes \\underset{\\text{qubit 1}}{\\left|b\\right\\rangle}\\otimes \\underset{\\text{qubit 0}}{\\left|c\\right\\rangle}.$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Toffoli gate ($ccx$ gate)\n",
+ "\n",
+ "The [Toffoli gate](https://en.wikipedia.org/wiki/Quantum_logic_gate#Toffoli_(CCNOT)_gate) flips the third qubit if the first two qubits (LSB) are both $\\left|1\\right\\rangle$:\n",
+ "\n",
+ "$$\\left|abc\\right\\rangle \\rightarrow \\left|bc\\oplus a\\right\\rangle \\otimes \\left|b\\right\\rangle \\otimes \\left|c\\right\\rangle.$$\n",
+ "\n",
+ "In matrix form, the Toffoli gate is\n",
+ "$$\n",
+ "C_{CX} = \n",
+ "\\begin{pmatrix}\n",
+ "1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
+ "0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
+ "0 & 0 & 1 & 0 & 0 & 0 & 0 & 0\\\\\n",
+ "0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\\\\n",
+ "0 & 0 & 0 & 0 & 1 & 0 & 0 & 0\\\\\n",
+ "0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\\\\n",
+ "0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\\\\\n",
+ "0 & 0 & 0 & 1 & 0 & 0 & 0 & 0\n",
+ "\\end{pmatrix}.\n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 62,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:55:55.265436Z",
+ "start_time": "2019-08-21T08:55:55.262507Z"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "q = QuantumRegister(3)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 63,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:55:55.629341Z",
+ "start_time": "2019-08-21T08:55:55.623307Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ ""
+ ]
+ },
+ "execution_count": 63,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "qc = QuantumCircuit(q)\n",
+ "qc.ccx(q[0], q[1], q[2])\n",
+ "qc.draw()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 64,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:55:56.074910Z",
+ "start_time": "2019-08-21T08:55:56.041905Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([[1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n",
+ " [0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n",
+ " [0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n",
+ " [0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j],\n",
+ " [0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n",
+ " [0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j],\n",
+ " [0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],\n",
+ " [0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j]])"
+ ]
+ },
+ "execution_count": 64,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "job = execute(qc, backend)\n",
+ "job.result().get_unitary(qc, decimals=3)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Controlled swap gate (Fredkin Gate)\n",
+ "\n",
+ "The [Fredkin gate](https://en.wikipedia.org/wiki/Quantum_logic_gate#Fredkin_(CSWAP)_gate), or the _controlled swap gate_, exchanges the second and third qubits if the first qubit (LSB) is $\\left|1\\right\\rangle$:\n",
+ "\n",
+ "$$ \\left|abc\\right\\rangle \\rightarrow \\begin{cases} \\left|bac\\right\\rangle~~\\text{if}~c=1 \\cr \\left|abc\\right\\rangle~~\\text{if}~c=0 \\end{cases}.$$\n",
+ "\n",
+ "In matrix form, the Fredkin gate is\n",
+ "\n",
+ "$$\n",
+ "C_{\\mathrm{SWAP}} = \n",
+ "\\begin{pmatrix}\n",
+ "1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
+ "0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
+ "0 & 0 & 1 & 0 & 0 & 0 & 0 & 0\\\\\n",
+ "0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\\\\n",
+ "0 & 0 & 0 & 0 & 1 & 0 & 0 & 0\\\\\n",
+ "0 & 0 & 0 & 1 & 0 & 0 & 0 & 0\\\\\n",
+ "0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\\\\\n",
+ "0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\n",
+ "\\end{pmatrix}.\n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 65,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:55:56.892569Z",
+ "start_time": "2019-08-21T08:55:56.886767Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ ""
+ ]
+ },
+ "execution_count": 65,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "qc = QuantumCircuit(q)\n",
+ "qc.cswap(q[0], q[1], q[2])\n",
+ "qc.draw()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 66,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:55:57.357927Z",
+ "start_time": "2019-08-21T08:55:57.317429Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([[1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n",
+ " [0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n",
+ " [0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n",
+ " [0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j],\n",
+ " [0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n",
+ " [0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n",
+ " [0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],\n",
+ " [0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j]])"
+ ]
+ },
+ "execution_count": 66,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "job = execute(qc, backend)\n",
+ "job.result().get_unitary(qc, decimals=3)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Non unitary operations\n",
+ "\n",
+ "Now we have gone through all the unitary operations in quantum circuits we also have access to non-unitary operations. These include measurements, reset of qubits, and classical conditional operations."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 67,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:55:58.221448Z",
+ "start_time": "2019-08-21T08:55:58.218540Z"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "q = QuantumRegister(1)\n",
+ "c = ClassicalRegister(1)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Measurements\n",
+ "\n",
+ "We don't have access to all the information when we make a measurement in a quantum computer. The quantum state is projected onto the standard basis. Below are two examples showing a circuit that is prepared in a basis state and the quantum computer prepared in a superposition state."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 68,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:55:59.196634Z",
+ "start_time": "2019-08-21T08:55:59.190848Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ ""
+ ]
+ },
+ "execution_count": 68,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "qc = QuantumCircuit(q, c)\n",
+ "qc.measure(q, c)\n",
+ "qc.draw()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 69,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:56:01.694539Z",
+ "start_time": "2019-08-21T08:56:01.678634Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "{'0': 1024}"
+ ]
+ },
+ "execution_count": 69,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "backend = BasicAer.get_backend('qasm_simulator')\n",
+ "job = execute(qc, backend, shots=1024)\n",
+ "job.result().get_counts(qc)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ " The simulator predicts that 100 percent of the time the classical register returns 0. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 70,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:56:02.140792Z",
+ "start_time": "2019-08-21T08:56:02.134144Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ ""
+ ]
+ },
+ "execution_count": 70,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "qc = QuantumCircuit(q, c)\n",
+ "qc.h(q)\n",
+ "qc.measure(q, c)\n",
+ "qc.draw()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 71,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:56:02.343572Z",
+ "start_time": "2019-08-21T08:56:02.322141Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "{'0': 525, '1': 499}"
+ ]
+ },
+ "execution_count": 71,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "job = execute(qc, backend, shots=1024)\n",
+ "job.result().get_counts(qc)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ " The simulator predicts that 50 percent of the time the classical register returns 0 or 1. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Reset\n",
+ "It is also possible to `reset` qubits to the $\\left|0\\right\\rangle$ state in the middle of computation. Note that `reset` is not a Gate operation, since it is irreversible."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 72,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:56:02.924205Z",
+ "start_time": "2019-08-21T08:56:02.917801Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ ""
+ ]
+ },
+ "execution_count": 72,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "qc = QuantumCircuit(q, c)\n",
+ "qc.reset(q[0])\n",
+ "qc.measure(q, c)\n",
+ "qc.draw()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 73,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:56:03.108038Z",
+ "start_time": "2019-08-21T08:56:03.094391Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "{'0': 1024}"
+ ]
+ },
+ "execution_count": 73,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "job = execute(qc, backend, shots=1024)\n",
+ "job.result().get_counts(qc)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 74,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:56:03.280559Z",
+ "start_time": "2019-08-21T08:56:03.273731Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ ""
+ ]
+ },
+ "execution_count": 74,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "qc = QuantumCircuit(q, c)\n",
+ "qc.h(q)\n",
+ "qc.reset(q[0])\n",
+ "qc.measure(q, c)\n",
+ "qc.draw()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 75,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:56:03.605317Z",
+ "start_time": "2019-08-21T08:56:03.468396Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "{'0': 1024}"
+ ]
+ },
+ "execution_count": 75,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "job = execute(qc, backend, shots=1024)\n",
+ "job.result().get_counts(qc)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Here we see that for both of these circuits the simulator always predicts that the output is 100 percent in the 0 state."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Conditional operations\n",
+ "It is also possible to do operations conditioned on the state of the classical register"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 76,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:56:04.040524Z",
+ "start_time": "2019-08-21T08:56:04.034030Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ ""
+ ]
+ },
+ "execution_count": 76,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "qc = QuantumCircuit(q, c)\n",
+ "qc.x(q[0]).c_if(c, 0)\n",
+ "qc.measure(q,c)\n",
+ "qc.draw()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Here the classical bit always takes the value 0 so the qubit state is always flipped. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 77,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:56:04.727452Z",
+ "start_time": "2019-08-21T08:56:04.710715Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "{'1': 1024}"
+ ]
+ },
+ "execution_count": 77,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "job = execute(qc, backend, shots=1024)\n",
+ "job.result().get_counts(qc)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 78,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:56:04.925588Z",
+ "start_time": "2019-08-21T08:56:04.918673Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ ""
+ ]
+ },
+ "execution_count": 78,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "qc = QuantumCircuit(q, c)\n",
+ "qc.h(q)\n",
+ "qc.measure(q,c)\n",
+ "qc.x(q[0]).c_if(c, 0)\n",
+ "qc.measure(q,c)\n",
+ "qc.draw()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 79,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:56:05.290449Z",
+ "start_time": "2019-08-21T08:56:05.125650Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "{'1': 1024}"
+ ]
+ },
+ "execution_count": 79,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "job = execute(qc, backend, shots=1024)\n",
+ "job.result().get_counts(qc)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Here the classical bit by the first measurement is random but the conditional operation results in the qubit being deterministically put into $\\left|1\\right\\rangle$."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Arbitrary initialization\n",
+ "What if we want to initialize a qubit register to an arbitrary state? An arbitrary state for $n$ qubits may be specified by a vector of $2^n$ amplitudes, where the sum of amplitude-norms-squared equals 1. For example, the following three-qubit state can be prepared:\n",
+ "\n",
+ "$$\\left|\\psi\\right\\rangle = \\frac{i}{4}\\left|000\\right\\rangle + \\frac{1}{\\sqrt{8}}\\left|001\\right\\rangle + \\frac{1+i}{4}\\left|010\\right\\rangle + \\frac{1+2i}{\\sqrt{8}}\\left|101\\right\\rangle + \\frac{1}{4}\\left|110\\right\\rangle$$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 80,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:56:08.133147Z",
+ "start_time": "2019-08-21T08:56:05.919296Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 80,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "# Initializing a three-qubit quantum state\n",
+ "import math\n",
+ "desired_vector = [\n",
+ " 1 / math.sqrt(16) * complex(0, 1),\n",
+ " 1 / math.sqrt(8) * complex(1, 0),\n",
+ " 1 / math.sqrt(16) * complex(1, 1),\n",
+ " 0,\n",
+ " 0,\n",
+ " 1 / math.sqrt(8) * complex(1, 2),\n",
+ " 1 / math.sqrt(16) * complex(1, 0),\n",
+ " 0]\n",
+ "\n",
+ "\n",
+ "q = QuantumRegister(3)\n",
+ "\n",
+ "qc = QuantumCircuit(q)\n",
+ "\n",
+ "qc.initialize(desired_vector, [q[0],q[1],q[2]])\n",
+ "qc.draw(output='latex')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 81,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:56:08.227207Z",
+ "start_time": "2019-08-21T08:56:08.151498Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([0.25 +0.j , 0. -0.35355339j,\n",
+ " 0.25 -0.25j , 0. +0.j ,\n",
+ " 0. +0.j , 0.70710678-0.35355339j,\n",
+ " 0. -0.25j , 0. +0.j ])"
+ ]
+ },
+ "execution_count": 81,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "backend = BasicAer.get_backend('statevector_simulator')\n",
+ "job = execute(qc, backend)\n",
+ "qc_state = job.result().get_statevector(qc)\n",
+ "qc_state "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "[Fidelity](https://en.wikipedia.org/wiki/Fidelity_of_quantum_states) is useful to check whether two states are same or not.\n",
+ "For quantum (pure) states $\\left|\\psi_1\\right\\rangle$ and $\\left|\\psi_2\\right\\rangle$, the fidelity is\n",
+ "\n",
+ "$$\n",
+ "F\\left(\\left|\\psi_1\\right\\rangle,\\left|\\psi_2\\right\\rangle\\right) = \\left|\\left\\langle\\psi_1\\middle|\\psi_2\\right\\rangle\\right|^2.\n",
+ "$$\n",
+ "\n",
+ "The fidelity is equal to $1$ if and only if two states are same."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 82,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:56:08.389811Z",
+ "start_time": "2019-08-21T08:56:08.378898Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "1.0"
+ ]
+ },
+ "execution_count": 82,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "state_fidelity(desired_vector,qc_state)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### Further details:\n",
+ "\n",
+ "How does the desired state get generated behind the scenes? There are multiple methods for doing this. Qiskit uses a [method proposed by Shende et al](https://arxiv.org/abs/quant-ph/0406176). Here, the idea is to assume the quantum register to have started from our desired state, and construct a circuit that takes it to the $\\left|00..0\\right\\rangle$ state. The initialization circuit is then the reverse of such circuit.\n",
+ "\n",
+ "To take an arbitrary quantum state to the zero state in the computational basis, we perform an iterative procedure that disentangles qubits from the register one-by-one. We know that any arbitrary single-qubit state $\\left|\\rho\\right\\rangle$ can be taken to the $\\left|0\\right\\rangle$ state using a $\\phi$-degree rotation about the Z axis followed by a $\\theta$-degree rotation about the Y axis:\n",
+ "\n",
+ "$$R_y(-\\theta)R_z(-\\phi)\\left|\\rho\\right\\rangle = re^{it}\\left|0\\right\\rangle$$\n",
+ "\n",
+ "Since now we are dealing with $n$ qubits instead of just 1, we must factorize the state vector to separate the Least Significant Bit (LSB):\n",
+ "\n",
+ "$$\\begin{align*}\n",
+ " \\left|\\psi\\right\\rangle =& \\alpha_{0_0}\\left|00..00\\right\\rangle + \\alpha_{0_1}\\left|00..01\\right\\rangle + \\alpha_{1_0}\\left|00..10\\right\\rangle + \\alpha_{1_1}\\left|00..11\\right\\rangle + ... \\\\&+ \\alpha_{(2^{n-1}-1)_0}\\left|11..10\\right\\rangle + \\alpha_{(2^{n-1}-1)_1}\\left|11..11\\right\\rangle \\\\\n",
+ "=& \\left|00..0\\right\\rangle (\\alpha_{0_0}\\left|0\\right\\rangle + \\alpha_{0_1}\\left|1\\right\\rangle) + \\left|00..1\\right\\rangle (\\alpha_{1_0}\\left|0\\right\\rangle + \\alpha_{1_1}\\left|1\\right\\rangle) + ... \\\\&+ \\left|11..1\\right\\rangle (\\alpha_{(2^{n-1}-1)_0}(\\left|0\\right\\rangle + \\alpha_{(2^{n-1}-1)_1}\\left|1\\right\\rangle) \\\\\n",
+ "=& \\left|00..0\\right\\rangle\\left|\\rho_0\\right\\rangle + \\left|00..1\\right\\rangle\\left|\\rho_1\\right\\rangle + ... + \\left|11..1\\right\\rangle\\left|\\rho_{2^{n-1}-1}\\right\\rangle\n",
+ "\\end{align*}$$\n",
+ "\n",
+ "Now each of the single-qubit states $\\left|\\rho_0\\right\\rangle, ..., \\left|\\rho_{2^{n-1}-1}\\right\\rangle$ can be taken to $\\left|0\\right\\rangle$ by finding appropriate $\\phi$ and $\\theta$ angles per the equation above. Doing this simultaneously on all states amounts to the following unitary, which disentangles the LSB:\n",
+ "\n",
+ "$$U = \\begin{pmatrix} \n",
+ "R_{y}(-\\theta_0)R_{z}(-\\phi_0) & & & &\\\\ \n",
+ "& R_{y}(-\\theta_1)R_{z}(-\\phi_1) & & &\\\\\n",
+ "& . & & &\\\\\n",
+ "& & . & &\\\\\n",
+ "& & & & R_y(-\\theta_{2^{n-1}-1})R_z(-\\phi_{2^{n-1}-1})\n",
+ "\\end{pmatrix} $$\n",
+ "\n",
+ "Hence,\n",
+ "\n",
+ "$$U\\left|\\psi\\right\\rangle = \\begin{pmatrix} r_0e^{it_0}\\\\ r_1e^{it_1}\\\\ . \\\\ . \\\\ r_{2^{n-1}-1}e^{it_{2^{n-1}-1}} \\end{pmatrix}\\otimes\\left|0\\right\\rangle$$\n",
+ "\n",
+ "\n",
+ "U can be implemented as a \"quantum multiplexor\" gate, since it is a block diagonal matrix. In the quantum multiplexor formalism, a block diagonal matrix of size $2^n \\times 2^n$, and consisting of $2^s$ blocks, is equivalent to a multiplexor with $s$ select qubits and $n-s$ data qubits. Depending on the state of the select qubits, the corresponding blocks are applied to the data qubits. A multiplexor of this kind can be implemented after recursive decomposition to primitive gates of cx, rz and ry."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 84,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:56:29.333291Z",
+ "start_time": "2019-08-21T08:56:29.326082Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "
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+ ],
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+ },
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+ "text/html": [
+ ""
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "import qiskit.tools.jupyter\n",
+ "%qiskit_version_table\n",
+ "%qiskit_copyright"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "anaconda-cloud": {},
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
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+ "pygments_lexer": "ipython3",
+ "version": "3.7.4"
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+ "lenType": 16,
+ "lenVar": 40
+ },
+ "kernels_config": {
+ "python": {
+ "delete_cmd_postfix": "",
+ "delete_cmd_prefix": "del ",
+ "library": "var_list.py",
+ "varRefreshCmd": "print(var_dic_list())"
+ },
+ "r": {
+ "delete_cmd_postfix": ") ",
+ "delete_cmd_prefix": "rm(",
+ "library": "var_list.r",
+ "varRefreshCmd": "cat(var_dic_list()) "
+ }
+ },
+ "types_to_exclude": [
+ "module",
+ "function",
+ "builtin_function_or_method",
+ "instance",
+ "_Feature"
+ ],
+ "window_display": false
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 1
+}
Trusted Notebook\" align=\"middle\">"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "The latest version of this notebook is available on https://github.com/Qiskit/qiskit-tutorial."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "# Writing a Transpiler Pass"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Introduction"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "A central component of Qiskit Terra is the transpiler, which is designed for modularity and extensibility. The goal is to be able to easily write new circuit transformations (known as transpiler *passes*), and combine them with other existing passes. In this way, the transpiler opens up the door for research into aggressive optimization of quantum circuits.\n",
- "\n",
- "In this notebook, we show how to develop a simple transpiler pass. To do so, we first introduce the internal representation of quantum circuits in Qiskit, in the form of a Directed Acyclic Graph, or **DAG**. Then, we illustrate a simple swap mapper pass, which transforms an input circuit to be compatible with a limited-connectivity quantum device."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Introducing the DAG"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "In Qiskit, we represent circuits internally using a Directed Acyclic Graph (DAG). The advantage of this representation over a pure list of gates (i.e., *netlist*) is that the flow of information between operations are explicit, making it easier for passes to make transformation decisions without changing the semantics of the circuit.\n",
- "\n",
- "Let's start by building a simple circuit, and examining its DAG."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 7,
- "metadata": {},
- "outputs": [
- {
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Trusted Notebook\" align=\"middle\">"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Summary of Quantum Operations "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ " In this section we will go into the different operations that are available in Qiskit Terra. These are:\n",
+ "- Single-qubit quantum gates\n",
+ "- Multi-qubit quantum gates\n",
+ "- Measurements\n",
+ "- Reset\n",
+ "- Conditionals\n",
+ "- State initialization\n",
+ "\n",
+ "We will also show you how to use the three different simulators:\n",
+ "- unitary_simulator\n",
+ "- qasm_simulator\n",
+ "- statevector_simulator"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:54:28.396755Z",
+ "start_time": "2019-08-21T08:54:27.713006Z"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "# Useful additional packages \n",
+ "import matplotlib.pyplot as plt\n",
+ "%matplotlib inline\n",
+ "import numpy as np\n",
+ "from math import pi"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:54:32.622706Z",
+ "start_time": "2019-08-21T08:54:28.407651Z"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister, execute\n",
+ "from qiskit.tools.visualization import circuit_drawer\n",
+ "from qiskit.quantum_info import state_fidelity\n",
+ "from qiskit import BasicAer\n",
+ "\n",
+ "backend = BasicAer.get_backend('unitary_simulator')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Single Qubit Quantum states\n",
+ "\n",
+ "A single qubit quantum state can be written as\n",
+ "\n",
+ "$$\\left|\\psi\\right\\rangle = \\alpha\\left|0\\right\\rangle + \\beta \\left|1\\right\\rangle$$\n",
+ "\n",
+ "\n",
+ "where $\\alpha$ and $\\beta$ are complex numbers. In a measurement the probability of the bit being in $\\left|0\\right\\rangle$ is $|\\alpha|^2$ and $\\left|1\\right\\rangle$ is $|\\beta|^2$. As a vector this is\n",
+ "\n",
+ "$$\n",
+ "\\left|\\psi\\right\\rangle = \n",
+ "\\begin{pmatrix}\n",
+ "\\alpha \\\\\n",
+ "\\beta\n",
+ "\\end{pmatrix}.\n",
+ "$$\n",
+ "\n",
+ "Note due to conservation probability $|\\alpha|^2+ |\\beta|^2 = 1$ and since global phase is undetectable $\\left|\\psi\\right\\rangle := e^{i\\delta} \\left|\\psi\\right\\rangle$ we only requires two real numbers to describe a single qubit quantum state.\n",
+ "\n",
+ "A convenient representation is\n",
+ "\n",
+ "$$\\left|\\psi\\right\\rangle = \\cos(\\theta/2)\\left|0\\right\\rangle + \\sin(\\theta/2)e^{i\\phi}\\left|1\\right\\rangle$$\n",
+ "\n",
+ "where $0\\leq \\phi < 2\\pi$, and $0\\leq \\theta \\leq \\pi$. From this it is clear that there is a one-to-one correspondence between qubit states ($\\mathbb{C}^2$) and the points on the surface of a unit sphere ($\\mathbb{R}^3$). This is called the Bloch sphere representation of a qubit state.\n",
+ "\n",
+ "Quantum gates/operations are usually represented as matrices. A gate which acts on a qubit is represented by a $2\\times 2$ unitary matrix $U$. The action of the quantum gate is found by multiplying the matrix representing the gate with the vector which represents the quantum state.\n",
+ "\n",
+ "$$\\left|\\psi'\\right\\rangle = U\\left|\\psi\\right\\rangle$$\n",
+ "\n",
+ "A general unitary must be able to take the $\\left|0\\right\\rangle$ to the above state. That is \n",
+ "\n",
+ "$$\n",
+ "U = \\begin{pmatrix}\n",
+ "\\cos(\\theta/2) & a \\\\\n",
+ "e^{i\\phi}\\sin(\\theta/2) & b \n",
+ "\\end{pmatrix}\n",
+ "$$ \n",
+ "\n",
+ "where $a$ and $b$ are complex numbers constrained such that $U^\\dagger U = I$ for all $0\\leq\\theta\\leq\\pi$ and $0\\leq \\phi<2\\pi$. This gives 3 constraints and as such $a\\rightarrow -e^{i\\lambda}\\sin(\\theta/2)$ and $b\\rightarrow e^{i\\lambda+i\\phi}\\cos(\\theta/2)$ where $0\\leq \\lambda<2\\pi$ giving \n",
+ "\n",
+ "$$\n",
+ "U = \\begin{pmatrix}\n",
+ "\\cos(\\theta/2) & -e^{i\\lambda}\\sin(\\theta/2) \\\\\n",
+ "e^{i\\phi}\\sin(\\theta/2) & e^{i\\lambda+i\\phi}\\cos(\\theta/2) \n",
+ "\\end{pmatrix}.\n",
+ "$$\n",
+ "\n",
+ "This is the most general form of a single qubit unitary."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Single-Qubit Gates\n",
+ "\n",
+ "The single-qubit gates available are:\n",
+ "- u gates\n",
+ "- Identity gate\n",
+ "- Pauli gates\n",
+ "- Clifford gates\n",
+ "- $C3$ gates\n",
+ "- Standard rotation gates \n",
+ "\n",
+ "We have provided a backend: `unitary_simulator` to allow you to calculate the unitary matrices. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:54:32.638412Z",
+ "start_time": "2019-08-21T08:54:32.635777Z"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "q = QuantumRegister(1)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### u gates\n",
+ "\n",
+ "In Qiskit we give you access to the general unitary using the $u3$ gate\n",
+ "\n",
+ "$$\n",
+ "u3(\\theta, \\phi, \\lambda) = U(\\theta, \\phi, \\lambda) \n",
+ "$$\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2019-08-21T08:54:32.658121Z",
+ "start_time": "2019-08-21T08:54:32.650725Z"
+ }
+ },
+ "outputs": [
+ {
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Version Information
| Qiskit Software | Version |
|---|---|
| Qiskit | None |
| Terra | 0.9.0 |
| Aer | 0.3.0 |
| Ignis | 0.2.0 |
| Aqua | 0.5.6 |
| IBM Q Provider | 0.3.2rc1 |
| System information | |
| Python | 3.7.4 (default, Aug 13 2019, 15:17:50) \n", + "[Clang 4.0.1 (tags/RELEASE_401/final)] |
| OS | Darwin |
| CPUs | 4 |
| Memory (Gb) | 16.0 |
| Wed Aug 21 04:56:29 2019 EDT | |
This code is a part of Qiskit
© Copyright IBM 2017, 2019.
This code is licensed under the Apache License, Version 2.0. You may
obtain a copy of this license in the LICENSE.txt file in the root directory
of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
Any modifications or derivative works of this code must retain this
copyright notice, and modified files need to carry a notice indicating
that they have been altered from the originals.