diff --git a/docs/guides/_toc.json b/docs/guides/_toc.json index 5247565ea67..453327e80b2 100644 --- a/docs/guides/_toc.json +++ b/docs/guides/_toc.json @@ -133,6 +133,10 @@ "title": "Construct circuits", "url": "/guides/construct-circuits" }, + { + "title": "Fractional gates", + "url": "/guides/fractional-gates" + }, { "title": "Classical feedforward and control flow", "url": "/guides/classical-feedforward-and-control-flow" diff --git a/docs/guides/fractional-gates.ipynb b/docs/guides/fractional-gates.ipynb new file mode 100644 index 00000000000..9e55d9b9002 --- /dev/null +++ b/docs/guides/fractional-gates.ipynb @@ -0,0 +1,377 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "116af785-a9b7-4eaf-8a86-b1eeb235da18", + "metadata": {}, + "source": [ + "# Fractional gates\n", + "\n", + "This page introduces two newly supported gate types on the IBM Quantum™ fleet of QPUs. These *fractional* gates are supported on [Heron QPUs](/guides/processor-types#heron) in the form of:\n", + "- $R_{ZZ}(\\theta)$ for $0 \\lt \\theta \\leq \\pi/2$\n", + "- $R_X(\\theta)$ for any $\\theta$\n", + "\n", + "This page discusses the use cases where implementing fractional gates can improve the efficiency of your workflows, as well as how to use these gates on IBM Quantum QPUs." + ] + }, + { + "cell_type": "markdown", + "id": "ee241e99-d095-4cb5-9506-da3d92c32e1c", + "metadata": {}, + "source": [ + "## How to use fractional gates\n", + "\n", + "Internally, these fractional gates work by directly executing an $R_{ZZ}(\\theta)$ and $R_X(\\theta)$ rotation for an arbitrary angle. Use of the $R_X(\\theta)$ gate can reduce the duration and error for single-qubit rotations of arbitrary angle by up to a factor of two. The direct execution of the $R_{ZZ}(\\theta)$ gate rotation avoids decomposition into multiple `CZGate`s, similarly reducing a circuit's duration and error. This is especially useful for circuits that contain many single- and two-qubit rotations, such as when simulating the dynamics of a quantum system or when using a variational ansatz with many parameters.\n", + "\n", + "\n", + "While these types of gates are in the [library of standard gates](./circuit-library) which a `QuantumCircuit` can possess, they can only be used on specific IBM Quantum QPUs, and which must be loaded with the flag `use_fractional_gates` set to `True` (shown below). This flag will ensure that fractional gates are included in the backend's `Target` for the transpiler.\n", + "\n", + "```python\n", + "service = QiskitRuntimeService()\n", + "backend = service.backend('ibm_torino', use_fractional_gates=True)\n", + "```\n", + "\n", + "This code example demonstrates how to use fractional gates in the context of a workflow that simulates the dynamics of an Ising chain using fractional gates. The circuit duration is then compared against a backend that does not use fractional gates.\n", + "\n", + "\n", + " The error value reported in the `Target` of a backend with fractional gates enabled is just a copy of the non-fractional gate's counterpart (which may not be the same). This is because the reporting of error rates on the fractional gates is not yet supported.\n", + "\n", + " However, since the gate time of fractional versus non-fractional gates are the same, it is a reasonable assumption that their error rates are comparable -- especially when the dominant source of error in a circuit is due to relaxation.\n", + "" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "9cb7f696-dec0-4393-9320-fe945326c893", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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", + "text/plain": [ + "
" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from qiskit import QuantumCircuit\n", + "from qiskit.circuit import Parameter\n", + "from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager\n", + "from qiskit.visualization.timeline import draw as draw_timeline, IQXSimple\n", + "\n", + "from qiskit_ibm_runtime import QiskitRuntimeService\n", + "\n", + "\n", + "num_qubits = 5\n", + "num_time_steps = 3\n", + "rx_angle = 0.1\n", + "rzz_angle = 0.1\n", + "\n", + "ising_circuit = QuantumCircuit(num_qubits)\n", + "for i in range(num_time_steps):\n", + " # rx layer\n", + " for q in range(num_qubits):\n", + " ising_circuit.rx(rx_angle, q)\n", + " for q in range(1, num_qubits - 1, 2):\n", + " ising_circuit.rzz(rzz_angle, q, q + 1)\n", + " # 2nd rzz layer\n", + " for q in range(0, num_qubits - 1, 2):\n", + " ising_circuit.rzz(rzz_angle, q, q + 1)\n", + " ising_circuit.barrier()\n", + "ising_circuit.draw(\"mpl\")" + ] + }, + { + "cell_type": "markdown", + "id": "983bbe11-fa20-4043-a146-66af18cae054", + "metadata": {}, + "source": [ + "Specify two backend objects: one with fractional gates enabled, and the other with them disabled, then transpile them both." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "09ef3ed0-7126-45a2-a876-35a4f540c949", + "metadata": {}, + "outputs": [], + "source": [ + "service = QiskitRuntimeService()\n", + "backend_fractional = service.backend(\"ibm_torino\", use_fractional_gates=True)\n", + "backend_conventional = service.backend(\n", + " \"ibm_torino\", use_fractional_gates=False\n", + ")\n", + "\n", + "pm_fractional = generate_preset_pass_manager(\n", + " optimization_level=3, backend=backend_fractional, scheduling_method=\"alap\"\n", + ")\n", + "pm_conventional = generate_preset_pass_manager(\n", + " optimization_level=3,\n", + " backend=backend_conventional,\n", + " scheduling_method=\"alap\",\n", + ")\n", + "\n", + "ising_circuit_fractional = pm_fractional.run(ising_circuit)\n", + "ising_circuit_conventional = pm_conventional.run(ising_circuit)" + ] + }, + { + "cell_type": "markdown", + "id": "cf108858-b8ee-44a8-b252-3e7748b691f8", + "metadata": {}, + "source": [ + "Display the timeline of the circuit using the two types of gates." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "0013f5fa-4072-4aa4-94fe-7e195435f828", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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", + "text/plain": [ + "
" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Draw timeline of circuit with conventional gates\n", + "draw_timeline(\n", + " ising_circuit_conventional,\n", + " idle_wires=False,\n", + " time_range=(0, 500),\n", + " style=IQXSimple(),\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "08dd1cdf-8b34-47c2-8324-f3538c9d1ab6", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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", + "text/plain": [ + "
" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Draw timeline of circuit with fractional gates\n", + "draw_timeline(\n", + " ising_circuit_fractional,\n", + " idle_wires=False,\n", + " time_range=(0, 500),\n", + " style=IQXSimple(),\n", + ")" + ] + }, + { + "cell_type": "markdown", + "id": "48bad5e6-3c7a-4bd0-b050-e440c3257be2", + "metadata": {}, + "source": [ + "## Where to use fractional gates\n", + "\n", + "Historically, the basis gates available on IBM Quantum QPUs have been **`CZ`**, **`X`**, **`RZ`**, **`SX`**, and **`ID`**, which can not efficiently represent circuits with single- and two-qubit rotations that are not multiples of $\\pi / 2$. For example, an $R_X(\\theta)$ gate, when transpiled, must decompose into a series of $RZ$ and $\\sqrt{X}$ gates, which creates a circuit with two gates of finite duration instead of one.\n", + "\n", + "Similarly, when two-qubit rotations such as an $R_{ZZ}(\\theta)$ gate are transpiled, the decomposition requires two **`CZ`** gates and several single-qubit gates, which increases the circuit depth. These decompositions are shown in the following code." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "11b003ee-aa8e-4794-a84a-b6870d15fa11", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "iVBORw0KGgoAAAANSUhEUgAAAKIAAABuCAYAAACk2MjUAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjkuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8hTgPZAAAACXBIWXMAAA9hAAAPYQGoP6dpAAAHM0lEQVR4nO3dfUwUdx7H8c9uF9zlwVZAb1FXhYIV5EEj0nB6NmKupzES26RpLdWzMZdrAsXmCHvJ/VFrc40SyVXB9EJSW5trY7hYWyz0SUobKLEtdrEihw/dZasrO5YVGwUpsuzcH+Y2Z07v2GVlvjv3ef23s8PO9493fjP7MMGgqqoKIo0ZtR6ACAyRpGCIJAJDJBEYIonAEEkEhkgiMEQSgSGSCAyRRGCIJAJDJBEYIonAEEkEhkgiMEQSgSGSCAyRRGCIJAJDJBEYIonAEEkEhkgiMEQSgSGSCAyRRGCIJAJDJBEYIonAEEkEhkgiMEQSgSGSCAyRRGCIJAJDJBEYIolg0noAPVNVFf6RUa3HCInJMg0Gg2HqjzvlR/w/4h8ZxTsPPqP1GCEpdb6NmDjzlB+Xp2YSgSGSCAyRRGCIJAJDJBEYIonAEEkEfo4okLVoMdYe2XnbtrHhEVxzeeE83IbeAx9CHQ9oNt+9wBAFcx1ph6fVARgMsMx8ABlPPILCnVtxf+YcHK+q13q8iGKIgl3p7oPr3fbg47MHP8Fj7fuw8Ok1cOw+hNEr1zSdL5J4jRhF/COjGHCch8FoxPT5v9B6nIhiiFEmccGtAEd/GtJ6lIjiqVkwkyUW05ISg9eID215FMm56RhwnMc1l1fr8SJKdyuiz+eD3W5HRkYGzGYzbDYbtm/fjuHhYWzbtg0GgwH79+/XeswJWWp/Cpt63sSm029g4+d/Qdaza+Fu/gqtW6u1Hi3idLUinjx5EuvWrYOiKIiPj0d2djb6+/tRW1sLp9OJwcFBAMCSJUu0HnVCzv7tU7g/OA5jjAkzFs1DTtlGxKcmY3z0ZnAfY6wJGz7dg7732nFq35Hg9pV7y2Ce+QBaSl/RaPrQ6GZF9Pl82LBhAxRFQWVlJbxeLxwOBxRFQXV1NZqbm9HZ2QmDwYC8vDytx52Qay4F3vZuXGrtwunXGvHZb3cjZcmDKKr+fXCfwE0/vqyoQ27F45iRPR8AMG/tcsz9dQE6/vCahtOHRjchVlRUwOPxoLy8HDU1NUhMTAw+Z7fbkZ+fD7/fjwULFmD69OmazhqugRNn4TzchrSNKzCz4KHg9iunXOj561H8qvZ5xKUmoWjPc/j6T69j5PJVTecNhS5C7O3tRUNDA1JSUrBr16477rNs2TIAQH5+/hRPF1nfvXoYAf84llY9efv2ve8iMD6OkmN7oHScRl9jh2YzhkMXIR46dAiBQAClpaVISEi44z4WiwXQQYjX3Qr6Gjswe1UeZj2cFdyu+scx0HkW5uT78X3D55rOGA5dhNja2goAWL169V338Xg8gA5CBIBT+26tfv++Ks56OAsZT65G74EPUfjys7jPHKvpjKEyqKqqaj3EZNlsNng8HnR1dd3xHbHf70dqaip8Ph+cTifS09PDOk5BQQEURZnw/jGqETsChWEdKxSmODNKPqvBP+qbcOatT7DuvZfh+86Jzh0HQ36tncZvMGYI7wcVVqsVJ06cCOtvdfHxzfDwMABgZGTkjs83NDTA5/MhMTERaWlpYR9HURRcunRpwvvHGu4DpuCbuOUvbcHQhR9x5uDHAIAvt+9HSUsNLnz0NS5/1RvSa/V7+3FTHb9Hk96dLkK0Wq24evUqHA4HioqKbnvO6/WiqqoKAJCXlzepe3atVmtI+8eoRuAe/1prTvFSpJWsQOOayuC26z9cxrevvIMVr5bhaHFlSPdWz06dPakVMVy6ODVXVFSgrq4ONpsNLS0tWLhwIQCgs7MTmzdvhsvlwtjYGMrKyqb0W5WxGz/zvuYJ0sWbFbvdjuTkZFy8eBGLFy9Gbm4uMjMzUVhYiPT0dBQXFwM6eaOiV7oIce7cuWhvb8f69ethNpvhdruRlJSE+vp6NDc349y5cwBDFE0X14gAkJWVhaampv/YPjQ0BLfbDaPRiJycHE1mo/9NFyvif9PT0wNVVZGZmYm4uDitx6G70H2I3d3dAE/L4unm1Hw3egxxRvZ8/LLmOcQkWDDsGUDb83VRf/8KV8QotHJvOY5X1eP9VS+g7+hxLH9xi9YjTZruV8R/fQ+tF0k5afDf+BmDPW4AgPPvX2D5ji0wxpgQGPNrPV7YdB+i3iTMm4UZi+ah5Nie4DaTZRrirEkYuvijprNNBkOMQgNd53Fs05+Dj586fUDTeSJB99eIejP0w2XEz0kJPo5JsMAUZ8YNZVDTuSaLIUaZwR43AmPjSF11676bRVt/g77Gjqi+PgRPzdGprWwfVu4tQ+zu3+G6W0Fbea3WI00aQ4xCP525gKa1f9R6jIjiqZlEYIgkAkMkERgiicAQSQRd3LMiFf8p5MQxRBKBp2YSgSGSCAyRRGCIJAJDJBEYIonAEEkEhkgiMEQSgSGSCAyRRGCIJAJDJBEYIonAEEkEhkgiMEQSgSGSCAyRRGCIJAJDJBEYIonAEEkEhkgiMEQS4Z8DqBaqnaf+0gAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qc = QuantumCircuit(1)\n", + "param = Parameter(\"θ\")\n", + "qc.rx(param, 0)\n", + "qc.draw(\"mpl\")" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "5da9bba4-9a3b-4569-9997-c5b9ccf87b6a", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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", + "text/plain": [ + "
" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Decomposition of an RX(θ) gate using the IBM Quantum QPU basis\n", + "service = QiskitRuntimeService()\n", + "backend = service.backend(\"ibm_torino\")\n", + "optimization_level = 3\n", + "pm = generate_preset_pass_manager(optimization_level, backend=backend)\n", + "transpiled_circuit = pm.run(qc)\n", + "transpiled_circuit.draw(\"mpl\", idle_wires=False)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "6b256201-0237-4f63-91ff-fde1bb884804", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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", + "text/plain": [ + "
" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from qiskit import QuantumCircuit\n", + "from qiskit.circuit import Parameter\n", + "from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager\n", + "\n", + "from qiskit_ibm_runtime import QiskitRuntimeService\n", + "\n", + "qc = QuantumCircuit(2)\n", + "param = Parameter(\"θ\")\n", + "qc.rzz(param, 0, 1)\n", + "qc.draw(\"mpl\")" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "f07217b9-a6f0-4adf-b341-6da447535c33", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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", + "text/plain": [ + "
" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Decomposition of an RZZ(θ) gate using the IBM Quantum QPU basis\n", + "service = QiskitRuntimeService()\n", + "backend = service.backend(\"ibm_torino\")\n", + "optimization_level = 3\n", + "pm = generate_preset_pass_manager(optimization_level, backend=backend)\n", + "transpiled_circuit = pm.run(qc)\n", + "transpiled_circuit.draw(\"mpl\", idle_wires=False)" + ] + }, + { + "cell_type": "markdown", + "id": "5bc4f276-80e4-49af-bd5c-d9dceedc9aa3", + "metadata": {}, + "source": [ + "For workflows that require many single-qubit $R_X(\\theta)$ or two-qubit rotations (such as in a variational ansatz or when simulating the time evolution of quantum systems), this constraint causes the circuit depth to grow rapidly. However, fractional gates remove this requirement, because the single- and two-qubit rotations are executed directly, and create a more efficient (and thus error-suppressed) quantum circuit." + ] + }, + { + "cell_type": "markdown", + "id": "c601cc20-be04-45b6-9917-e8fe2925d36b", + "metadata": {}, + "source": [ + "## When *not* to use fractional gates\n", + "\n", + "It is important to note that fractional gates are an *experimental* feature and the behavior of the `use_fractional_gates` flag may change in the future. Look to the [release notes](/api/qiskit-ibm-runtime/release-notes) for new versions of Qiskit Runtime for more information. See also the API reference documentation for [QiskitRuntimeService.backend](/api/qiskit-ibm-runtime/qiskit_ibm_runtime.QiskitRuntimeService#backend), which describes `use_fractional_gates`.\n", + "\n", + "Additionally, the Qiskit transpiler has limited capability to use $R_{ZZ}(\\theta)$ in its optimization passes. This requires you to take more care in crafting and optimizing circuits that contain these instructions.\n", + "\n", + "Lastly, using fractional gates is not supported for:\n", + "- [Dynamic circuits](/guides/classical-feedforward-and-control-flow)\n", + "- [Pauli twirling](/guides/error-mitigation-and-suppression-techniques#pauli-twirling) - however, [measurement twirling with TREX](/guides/error-mitigation-and-suppression-techniques#twirled-readout-error-extinction-trex) *is* supported.\n", + "- [Probabilistic error cancellation](/guides/error-mitigation-and-suppression-techniques#probabilistic-error-cancellation-pec)\n", + "- [Zero-noise extrapolation (using probabilistic error amplification)](/guides/error-mitigation-and-suppression-techniques#probabilistic-error-amplification-pea)\n", + "\n", + "Read the guide on [primitive options](/guides/runtime-options-overview) to learn more about customizing the error mitigation and suppression techniques for a given quantum workload." + ] + }, + { + "cell_type": "markdown", + "id": "bf0a38a6-60d1-4848-bbde-df19bb496510", + "metadata": {}, + "source": [ + "## Next steps\n", + "\n", + "\n", + " - To learn more about transpilation, see the [introduction to transpilation](/guides/transpile) page.\n", + " - Read about [writing a custom transpiler pass](/guides/custom-transpiler-pass).\n", + " - Understand how to [configure error mitigation](/guides/configure-error-mitigation) for Qiskit Runtime.\n", + "" + ] + } + ], + "metadata": { + "description": "Use fractional gates to execute single- and two-qubit rotations", + "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" + }, + "title": "Fractional gates" + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/docs/guides/map-problem-to-circuits.mdx b/docs/guides/map-problem-to-circuits.mdx index 0c50694b192..fa5627f22a1 100644 --- a/docs/guides/map-problem-to-circuits.mdx +++ b/docs/guides/map-problem-to-circuits.mdx @@ -30,6 +30,7 @@ The output of this step in a Qiskit pattern is normally a collection of circuits * [Construct circuits](./construct-circuits) * [Measure qubits](./measure-qubits) * [Visualize circuits](./visualize-circuits) +* [Fractional gates](./fractional-gates) * [Classical feedforward and control flow](./classical-feedforward-and-control-flow) * [Synthesize unitary operators](./synthesize-unitary-operators) * [Bit-ordering in the Qiskit SDK](./bit-ordering) diff --git a/qiskit_bot.yaml b/qiskit_bot.yaml index 8501d25f8d0..a52b8d0f850 100644 --- a/qiskit_bot.yaml +++ b/qiskit_bot.yaml @@ -73,6 +73,8 @@ notifications: - "`@lerongil`" - "@jyu00" - "@beckykd" + "docs/guides/fractional-gates": + - "@kaelynj" "docs/guides/measure-qubits": - "@beckykd" "docs/guides/get-qpu-information": diff --git a/scripts/config/notebook-testing.toml b/scripts/config/notebook-testing.toml index 28417ba63de..93f1ed49775 100644 --- a/scripts/config/notebook-testing.toml +++ b/scripts/config/notebook-testing.toml @@ -45,6 +45,7 @@ notebooks_exclude = [ "docs/guides/functions.ipynb", "docs/guides/qunasys-quri-chemistry.ipynb", "docs/guides/ibm-circuit-function.ipynb", + "docs/guides/fractional-gates.ipynb", ] # The following notebooks submit jobs that can be mocked with a simulator