QAOA+for+maxcut+.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## QAOA for MAXCUT\n",
    "\n",
    "Here we follow an altered tutorial for maxcut below:\n",
    "https://qiskit.org/textbook/ch-applications/qaoa.html\n",
    "Then we will try to test how the parameters passed in to qaoa affect the energy of a graph\n",
    "--energy defined as the cost function evaluated in qaoa for p=1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "#modified from https://github.com/Chriz91/qaoa-max-cut\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import nlopt\n",
    "import networkx as nx\n",
    "import qiskit\n",
    "from qiskit import BasicAer\n",
    "from qiskit.optimization.ising import max_cut\n",
    "from qiskit.aqua import QuantumInstance\n",
    "from qiskit.aqua.components.optimizers.nlopts.esch import ESCH\n",
    "from qiskit.aqua.algorithms import QAOA\n",
    "from qiskit.quantum_info import Pauli\n",
    "from qiskit.aqua.operators.weighted_pauli_operator import WeightedPauliOperator\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'qiskit-terra': '0.12.0',\n",
       " 'qiskit-aer': '0.4.1',\n",
       " 'qiskit-ignis': '0.2.0',\n",
       " 'qiskit-ibmq-provider': '0.5.0',\n",
       " 'qiskit-aqua': '0.6.4',\n",
       " 'qiskit': '0.16.1'}"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qiskit.__qiskit_version__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/victorli/anaconda3/lib/python3.7/site-packages/networkx/drawing/nx_pylab.py:579: MatplotlibDeprecationWarning: \n",
      "The iterable function was deprecated in Matplotlib 3.1 and will be removed in 3.3. Use np.iterable instead.\n",
      "  if not cb.iterable(width):\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 6  # Number of nodes in graph\n",
    "G = nx.Graph()\n",
    "G.add_nodes_from(np.arange(0, n, 1))\n",
    "elist = [(0, 1, 1.0), (0, 2, 1.0), (0, 3, 1.0), (0, 4, 1.0), (1, 2, 1.0), (1, 5, 1.0), (4, 5, 1.0), (2, 3, 1.0)]\n",
    "G.add_weighted_edges_from(elist)\n",
    "\n",
    "colors = ['r' for node in G.nodes()]\n",
    "pos = nx.spring_layout(G)\n",
    "default_axes = plt.axes(frameon=True)\n",
    "nx.draw_networkx(G, node_color=colors, node_size=600, alpha=.8, ax=default_axes, pos=pos)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "weight matrix\n",
      "[[0. 1. 1. 1. 1. 0.]\n",
      " [1. 0. 1. 0. 0. 1.]\n",
      " [1. 1. 0. 1. 0. 0.]\n",
      " [1. 0. 1. 0. 0. 0.]\n",
      " [1. 0. 0. 0. 0. 1.]\n",
      " [0. 1. 0. 0. 1. 0.]]\n"
     ]
    }
   ],
   "source": [
    "w = np.zeros([n, n])\n",
    "for i in range(n):\n",
    "    for j in range(n):\n",
    "        temp = G.get_edge_data(i, j, default=0)\n",
    "        if temp != 0:\n",
    "            w[i, j] = temp['weight']\n",
    "\n",
    "print(\"weight matrix\")\n",
    "print(w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Best solution = [0, 1, 0, 1, 1, 0] cost = 7.0\n"
     ]
    }
   ],
   "source": [
    "best_cost_brute = 0\n",
    "for b in range(2**n):\n",
    "    x = [int(t) for t in reversed(list(bin(b)[2:].zfill(n)))]\n",
    "    cost = 0\n",
    "    for i in range(n):\n",
    "        for j in range(n):\n",
    "            cost = cost + w[i, j]*x[i]*(1-x[j])\n",
    "    if best_cost_brute < cost:\n",
    "        best_cost_brute = cost\n",
    "        xbest_brute = x\n",
    "    #print('case = ' + str(x) + ' cost = ' + str(cost))\n",
    "\n",
    "print('\\nBest solution = ' + str(xbest_brute) + ' cost = ' + str(best_cost_brute))\n",
    "\n",
    "#NOTE THAT [1,0,1,0,0,1] IS AN EQUIVALENTLY GOOD PARTITION, so we hope to evolve into the subspace\n",
    "#spanned by 101001 and 010110"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Converts adjacency matrix into a list of Pauli z operators (idk what the x part does)\n",
    "#xp is here to make sure there is no complex component in pauli generated and that it is strictly z\n",
    "num_nodes = w.shape[0]\n",
    "pauli_list = []\n",
    "for i in range(num_nodes):\n",
    "    for j in range(i):\n",
    "        if w[i, j] != 0:\n",
    "            xp = np.zeros(num_nodes, dtype=np.bool)\n",
    "            zp = np.zeros(num_nodes, dtype=np.bool)\n",
    "            zp[i] = True\n",
    "            zp[j] = True\n",
    "            pauli_list.append([0.5 * w[i, j], Pauli(zp, xp)])\n",
    "qubitOp = WeightedPauliOperator(paulis=pauli_list)\n",
    "#print(qubitOp.paulis)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'num_optimizer_evals': 100, 'min_val': -0.966796875, 'opt_params': array([1.91748357, 0.41713172, 1.66758152, 0.01450238, 0.16736141,\n",
      "       0.01172316, 2.11574651, 0.16446149, 1.14544705, 3.57374789,\n",
      "       0.31270954, 2.87762134, 0.36740155, 1.72085939, 3.64222932,\n",
      "       0.20051554, 0.35610368, 0.1646642 ]), 'eval_time': 7.944586992263794, 'eval_count': 100, 'energy': -0.966796875, 'eigvals': array([-0.96679688]), 'min_vector': {'010101': 14, '101011': 10, '011011': 1, '010010': 4, '000101': 1, '011100': 49, '101101': 6, '111101': 8, '011101': 6, '011001': 2, '101110': 3, '001011': 2, '010011': 17, '101001': 2, '001100': 13, '111011': 13, '111111': 1, '111100': 10, '000011': 13, '011010': 57, '000010': 3, '110100': 1, '001111': 10, '100110': 1, '111001': 1, '100001': 12, '100011': 56, '101100': 21, '101010': 24, '010110': 5, '010100': 17, '101000': 1, '100000': 3, '110010': 1, '100100': 2, '100010': 13, '011000': 3, '110101': 4, '110000': 5, '100111': 3, '000100': 8, '111010': 2, '110011': 15, '010111': 1, '001010': 7, '011110': 9, '100101': 52}, 'eigvecs': array([{'010101': 14, '101011': 10, '011011': 1, '010010': 4, '000101': 1, '011100': 49, '101101': 6, '111101': 8, '011101': 6, '011001': 2, '101110': 3, '001011': 2, '010011': 17, '101001': 2, '001100': 13, '111011': 13, '111111': 1, '111100': 10, '000011': 13, '011010': 57, '000010': 3, '110100': 1, '001111': 10, '100110': 1, '111001': 1, '100001': 12, '100011': 56, '101100': 21, '101010': 24, '010110': 5, '010100': 17, '101000': 1, '100000': 3, '110010': 1, '100100': 2, '100010': 13, '011000': 3, '110101': 4, '110000': 5, '100111': 3, '000100': 8, '111010': 2, '110011': 15, '010111': 1, '001010': 7, '011110': 9, '100101': 52}],\n",
      "      dtype=object)}\n",
      "energy: -0.966796875\n",
      "time: 7.944586992263794\n",
      "solution: [0 1 0 1 1 0]\n",
      "optimal parameters [1.91748357 0.41713172 1.66758152 0.01450238 0.16736141 0.01172316\n",
      " 2.11574651 0.16446149 1.14544705 3.57374789 0.31270954 2.87762134\n",
      " 0.36740155 1.72085939 3.64222932 0.20051554 0.35610368 0.1646642 ]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/victorli/anaconda3/lib/python3.7/site-packages/qiskit/optimization/ising/max_cut.py:117: DeprecationWarning: sample_most_likely function has been moved to qiskit.optimization.ising.common, the method here will be removed after Aqua 0.7+\n",
      "  DeprecationWarning)\n"
     ]
    }
   ],
   "source": [
    "#Note from above, our goal is to maximum 1/2 - 1/2*sum(z_i*z_j) but we are equivalently minimizing 1/2*sum(z_i*z_j)\n",
    "#Therefore the true energy is 1/2 - (calculated min energy)\n",
    "\n",
    "n_shots = 512\n",
    "p_steps = 1\n",
    "\n",
    "backend = BasicAer.get_backend('qasm_simulator')\n",
    "quantum_instance = QuantumInstance(backend, shots=n_shots)\n",
    "\n",
    "qaoa = QAOA(qubitOp, ESCH(max_evals=100), p=p_steps+8)\n",
    "result = qaoa.run(quantum_instance)\n",
    "#State-vectors in result are written LSB (0th vertex is last qubit)\n",
    "print(result)\n",
    "\n",
    "solution = max_cut.sample_most_likely(result['eigvecs'][0]) #returns vector with highest counts\n",
    "print('energy:', result['energy'])\n",
    "print('time:', result['eval_time'])\n",
    "#print('solution:', max_cut.get_graph_solution(x)) #inverts string - idk why this is needed\n",
    "print('solution:', solution)\n",
    "print('optimal parameters', result['opt_params'])\n",
    "#9 params are the beta and gamma"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/victorli/anaconda3/lib/python3.7/site-packages/networkx/drawing/nx_pylab.py:579: MatplotlibDeprecationWarning: \n",
      "The iterable function was deprecated in Matplotlib 3.1 and will be removed in 3.3. Use np.iterable instead.\n",
      "  if not cb.iterable(width):\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#min vec 011010, solutio 010110, graph 100101\n",
    "colors = ['r' if solution[i] == 0 else 'b' for i in range(n)]\n",
    "nx.draw_networkx(G, node_color=colors, node_size=600, alpha=.7, pos=pos)\n",
    "plt.show()\n",
    "df = pd.DataFrame.from_dict(result['min_vector'], orient='index') / n_shots\n",
    "df = df.sort_index()\n",
    "barplot = df.plot.bar(legend=False, figsize=(10, 5), fontsize=8)\n",
    "plt.show() #as you can see, the reversed solution 011010 is the most common"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#how do parameters, maximizing states, minimum energy (maximum for the true cost function as explained a couple cells above) \n",
    "n_shots = 512\n",
    "p_steps = 1\n",
    "\n",
    "backend_same_graph = BasicAer.get_backend('qasm_simulator')\n",
    "quantum_instance_same_graph = QuantumInstance(backend_same_graph, shots=n_shots)\n",
    "\n",
    "opt_params_same_graph = []\n",
    "opt_energies_same_graph = []\n",
    "opt_states_same_graph = []\n",
    "for i in range(100):\n",
    "    qaoa_same_graph = QAOA(qubitOp, ESCH(max_evals=80), p=p_steps)\n",
    "    result_same_graph = qaoa_same_graph.run(quantum_instance_same_graph)\n",
    "    opt_params_same_graph.append(result_same_graph['opt_params'])\n",
    "    opt_energies_same_graph.append(result_same_graph['energy'])\n",
    "    opt_states_same_graph.append(max_cut.sample_most_likely(result_same_graph['eigvecs'][0]))\n",
    "\n",
    "param_data_same_graph = np.array(opt_params_same_graph).T\n",
    "plt.scatter(param_data_same_graph[0], param_data_same_graph[1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Beta</th>\n",
       "      <th>Gamma</th>\n",
       "      <th>State</th>\n",
       "      <th>Energy</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2.785082</td>\n",
       "      <td>0.733787</td>\n",
       "      <td>[0, 1, 0, 1, 1, 0]</td>\n",
       "      <td>1.816406</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.144202</td>\n",
       "      <td>0.840414</td>\n",
       "      <td>[1, 0, 1, 0, 0, 1]</td>\n",
       "      <td>1.527344</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.252504</td>\n",
       "      <td>0.215405</td>\n",
       "      <td>[1, 0, 1, 0, 0, 1]</td>\n",
       "      <td>1.191406</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2.843253</td>\n",
       "      <td>0.763386</td>\n",
       "      <td>[1, 0, 1, 0, 0, 1]</td>\n",
       "      <td>1.796875</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2.880661</td>\n",
       "      <td>0.571900</td>\n",
       "      <td>[0, 1, 0, 1, 1, 0]</td>\n",
       "      <td>1.626953</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Beta     Gamma               State    Energy\n",
       "0  2.785082  0.733787  [0, 1, 0, 1, 1, 0]  1.816406\n",
       "1  1.144202  0.840414  [1, 0, 1, 0, 0, 1]  1.527344\n",
       "2  1.252504  0.215405  [1, 0, 1, 0, 0, 1]  1.191406\n",
       "3  2.843253  0.763386  [1, 0, 1, 0, 0, 1]  1.796875\n",
       "4  2.880661  0.571900  [0, 1, 0, 1, 1, 0]  1.626953"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result_table_same_graph = pd.DataFrame(data = {\"Beta\":param_data_same_graph[0], \"Gamma\":param_data_same_graph[1],\n",
    "                            \"State\":opt_states_same_graph, \"Energy\": .5-np.array(opt_energies_same_graph)})\n",
    "result_table_same_graph.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/victorli/anaconda3/lib/python3.7/site-packages/qiskit/optimization/ising/max_cut.py:117: DeprecationWarning: sample_most_likely function has been moved to qiskit.optimization.ising.common, the method here will be removed after Aqua 0.7+\n",
      "  DeprecationWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "energy: -0.3125\n",
      "time: 0.08076000213623047\n",
      "solution: [1 0 1 0 0 1]\n",
      "optimal parameters [2. 5.]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_shots = 512\n",
    "p_steps = 1\n",
    "\n",
    "backend = BasicAer.get_backend('qasm_simulator')\n",
    "quantum_instance = QuantumInstance(backend, shots=n_shots)\n",
    "\n",
    "qaoa = QAOA(qubitOp, ESCH(max_evals=1), p=p_steps, initial_point = [2, 5])\n",
    "result = qaoa.run(quantum_instance)\n",
    "#State-vectors in result are written LSB (0th vertex is last qubit)\n",
    "#print(result)\n",
    "\n",
    "solution = max_cut.sample_most_likely(result['eigvecs'][0]) #returns vector with highest counts\n",
    "print('energy:', result['energy'])\n",
    "print('time:', result['eval_time'])\n",
    "#print('solution:', max_cut.get_graph_solution(x)) #inverts string - idk why this is needed\n",
    "print('solution:', solution)\n",
    "print('optimal parameters', result['opt_params'])\n",
    "df = pd.DataFrame.from_dict(result['min_vector'], orient='index') / n_shots\n",
    "df = df.sort_index()\n",
    "barplot = df.plot.bar(legend=False, figsize=(15, 5), fontsize=8)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}