qiskit-grover-3-bits.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "# Grover's Algorithm, N = 8 (3 bits)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "outputs": [],
   "source": [
    "from qiskit import Aer, QuantumCircuit, transpile\n",
    "from qiskit.visualization import plot_histogram"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "outputs": [],
   "source": [
    "def reflect_zero(nqubits: int):\n",
    "    qc = QuantumCircuit(nqubits)\n",
    "    # Apply transformation |00..0> -> |11..1> (X-gates)\n",
    "    for qubit in range(nqubits):\n",
    "        qc.x(qubit)\n",
    "    # Do multi-controlled-Z gate\n",
    "    qc.h(nqubits-1)\n",
    "    qc.mct(list(range(nqubits-1)), nqubits-1)  # multi-controlled-toffoli\n",
    "    qc.h(nqubits-1)\n",
    "    # Apply transformation |11..1> -> |00..0>\n",
    "    for qubit in range(nqubits):\n",
    "        qc.x(qubit)\n",
    "    # We will return the diffuser as a gate\n",
    "    U_0 = qc.to_gate()\n",
    "    U_0.name = \"U$_0$\"\n",
    "    return U_0"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "outputs": [],
   "source": [
    "# 101 and 110\n",
    "def sample_oracle_3_bits():\n",
    "    qc = QuantumCircuit(3)\n",
    "    qc.cz(0, 2)\n",
    "    qc.cz(1, 2)\n",
    "    oracle_ex3 = qc.to_gate()\n",
    "    oracle_ex3.name = \"U$_\\chi$\"\n",
    "    return oracle_ex3"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "outputs": [],
   "source": [
    "n = 3\n",
    "qc = QuantumCircuit(n)\n",
    "# A\n",
    "for qubit in range(n):\n",
    "    qc.h(qubit)\n",
    "# S_\\chi\n",
    "qc.append(sample_oracle_3_bits(), [0,1,2])\n",
    "# A^-1\n",
    "for qubit in range(n):\n",
    "    qc.h(qubit)\n",
    "# S_0\n",
    "qc.append(reflect_zero(n), [0,1,2])\n",
    "# A\n",
    "for qubit in range(n):\n",
    "    qc.h(qubit)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "outputs": [],
   "source": [
    "qc.measure_all()"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 658.679x264.88 with 1 Axes>",
      "image/png": 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\n"
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc.draw('mpl')"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "outputs": [],
   "source": [
    "qasm_sim = Aer.get_backend('qasm_simulator')\n",
    "transpiled_grover_circuit = transpile(qc, qasm_sim)\n",
    "results = qasm_sim.run(transpiled_grover_circuit).result()"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 504x360 with 1 Axes>",
      "image/png": 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\n"
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "counts = results.get_counts()\n",
    "plot_histogram(counts)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "outputs": [],
   "source": [],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  }
 ],
 "metadata": {
  "kernelspec": {
   "name": "python3",
   "language": "python",
   "display_name": "Python 3"
  },
  "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
}