cirq-maxcut_minimize.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import networkx as nx\n",
    "from networkx import Graph\n",
    "from cirq import LineQubit\n",
    "\n",
    "g = Graph()\n",
    "nodes = [LineQubit(i) for i in range(4)]\n",
    "edges = [(nodes[i], nodes[(i + 1) % 4]) for i in range(4)]\n",
    "g.add_nodes_from(nodes)\n",
    "g.add_edges_from(edges)\n",
    "nx.draw(g, with_labels=True, alpha=0.8, node_size=500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "outputs": [],
   "source": [
    "from cirq import Rx\n",
    "from sympy import Symbol\n",
    "\n",
    "\n",
    "def mixer(g: Graph, beta: Symbol):\n",
    "    return [Rx(rads=2 * beta)(q) for q in list(g.nodes())]"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "outputs": [],
   "source": [
    "from openfermion import Rzz\n",
    "\n",
    "\n",
    "def problem(g: Graph, gamma: Symbol):\n",
    "    return [Rzz(rads=2 * gamma)(i, j) for i, j in g.edges()]"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "outputs": [],
   "source": [
    "from cirq import Circuit, H, measure, Moment\n",
    "\n",
    "\n",
    "def create_qaoa_circ(g: Graph, theta: list[Symbol]):\n",
    "    nodes = list(g.nodes())\n",
    "    mid = len(theta) // 2\n",
    "    betas = theta[:mid]\n",
    "    gammas = theta[mid:]\n",
    "\n",
    "    circuit = Circuit(H.on_each(*nodes))\n",
    "\n",
    "    for i in range(mid):\n",
    "        circuit.append(problem(g, gammas[i]))\n",
    "        circuit.append(mixer(g, betas[i]))\n",
    "\n",
    "    circuit.append(measure(*nodes, key=\"cut\"))\n",
    "\n",
    "    return circuit"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "outputs": [],
   "source": [
    "from functools import reduce\n",
    "\n",
    "def maxcut_obj(x: str, g: Graph):\n",
    "    return reduce(lambda obj, e: obj - (1 if x[e[0].x] != x[e[1].x] else 0), g.edges(), 0)"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "outputs": [],
   "source": [
    "from collections import Counter\n",
    "\n",
    "def compute_expectation(cuts: Counter, g: Graph):\n",
    "    sum, count = reduce(lambda t, c: (t[0] + (maxcut_obj(c, g) * cuts[c]), t[1] + cuts[c]), cuts, (0, 0))\n",
    "    return sum / count"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "outputs": [],
   "source": [
    "from cirq import Simulator\n",
    "\n",
    "\n",
    "def get_expectation(g: Graph, nparams: int, shots=512):\n",
    "    sim = Simulator()\n",
    "    mid = nparams // 2\n",
    "    betas = [Symbol(f\"beta{i}\") for i in range(mid)]\n",
    "    gammas = [Symbol(f\"gamma{i}\") for i in range(mid)]\n",
    "    theta = betas + gammas\n",
    "    qc = create_qaoa_circ(g, theta)\n",
    "\n",
    "    def execute_circ(params: list[float]):\n",
    "        binding = {theta[i]:params[i] for i in range(len(params))}\n",
    "        result = sim.run(qc, binding, shots)\n",
    "        return compute_expectation(result.histogram(key=\"cut\", fold_func=lambda x: ''.join(list(map(lambda i: str(i), x)))), g)\n",
    "\n",
    "    return execute_circ"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "outputs": [
    {
     "data": {
      "text/plain": "     fun: -3.9453125\n   maxcv: 0.0\n message: 'Optimization terminated successfully.'\n    nfev: 47\n  status: 1\n success: True\n       x: array([1.06243384, 1.02222543, 1.02881248, 1.06975707])"
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.optimize import minimize\n",
    "\n",
    "init_params = [1.0, 1.0, 1.0, 1.0]\n",
    "expectation = get_expectation(g, len(init_params))\n",
    "res = minimize(expectation, init_params, method='COBYLA')\n",
    "res"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from cirq import plot_state_histogram\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "betas = [Symbol(\"beta0\"), Symbol(\"beta1\")]\n",
    "gammas = [Symbol(\"gamma0\"), Symbol(\"gamma1\")]\n",
    "theta = betas + gammas\n",
    "qc = create_qaoa_circ(g, theta)\n",
    "binding = {theta[i]: res.x[i] for i in range(4)}\n",
    "result = Simulator().run(qc, binding, 512)\n",
    "plot_state_histogram(result, plt.subplot())\n",
    "\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false
   }
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}