grover.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "75a9c456",
   "metadata": {},
   "source": [
    "#### toy grover search\n",
    "&nbsp; &nbsp; &nbsp; following Nielsen-Chuang ( chapter 6.1 ) and Hidary ( chapter 8.6 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "b8e69324",
   "metadata": {},
   "outputs": [],
   "source": [
    "import cirq\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "278c40cc",
   "metadata": {},
   "outputs": [],
   "source": [
    "def int2bit( n, k ): # the binary expansion of n, as a list of k bits\n",
    "    assert 0 <= n < 2 ** k\n",
    "    b = [ 0 if b == '0' else 1 for b in bin( n )[ 2 : ] ]\n",
    "    return ( k - len( b ) ) * [ 0 ] + b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "227cb709",
   "metadata": {},
   "outputs": [],
   "source": [
    "def bit2int( b ):\n",
    "    n = sum( [ bn * 2 ** n for n, bn in enumerate( reversed( b ) ) ] )\n",
    "    return n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "524d2018",
   "metadata": {},
   "outputs": [],
   "source": [
    "def reflection_gate( q ):\n",
    "    R = [ cirq.Z.controlled( len( q ) - 1 ).on( * q ) ]\n",
    "    return R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "b00a507e",
   "metadata": {},
   "outputs": [],
   "source": [
    "def oracle_gates( q, m ): # the oracle sends |m> to -|m>, fixing the other |n>'s\n",
    "    b = int2bit( m, len( q ) ) # bits of m\n",
    "    Xs = [ cirq.X( qn ) for qn, bn in zip( q, b ) if bn == 0 ]\n",
    "    R = reflection_gate( q )\n",
    "    return Xs + R + Xs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "5bdf65cd",
   "metadata": {},
   "outputs": [],
   "source": [
    "def diffusion_gates( q ):\n",
    "    Hs = [ cirq.H.on_each( q ) ]\n",
    "    Xs = [ cirq.X.on_each( q ) ]\n",
    "    R = reflection_gate( q )\n",
    "    return Hs + Xs + R + Xs + Hs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "e008471b",
   "metadata": {},
   "outputs": [],
   "source": [
    "def grover_gates( q, oracle, diffuser, size ):\n",
    "    Hs = [ cirq.H.on_each( q ) ]\n",
    "    rotations = size * ( oracle + diffuser ) # two reflections make a rotation\n",
    "    measurements = [ cirq.measure( qn, key = str( n ) ) for n, qn in enumerate( q ) ]\n",
    "    return Hs + rotations + measurements"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "36c667d5",
   "metadata": {},
   "outputs": [],
   "source": [
    "def simulate( q, circuit, times ):\n",
    "    result = cirq.Simulator( ).run( program = circuit, repetitions = times )\n",
    "    result = [ result.measurements[ str( n ) ] for n in range( len( q ) ) ]\n",
    "    return np.array( result ).squeeze( )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "71bfa6fd",
   "metadata": {},
   "outputs": [],
   "source": [
    "def interpret( result ):\n",
    "    measurement = [ bit2int( b ) for b in result.T ]\n",
    "    probability = np.zeros( 2 ** len( result ), dtype = 'float' )\n",
    "    for n in measurement : probability[ n ] += 1 / len( measurement )\n",
    "    return measurement, probability"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "3e7b04fe",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot( dimension, probability ):\n",
    "    fig, axis = plt.subplots( figsize = ( 14, 5 ), facecolor = 'white' )\n",
    "    axis.set_xlabel( 'measurement', size = '12' )\n",
    "    axis.set_ylabel( 'probability', size = '12' )\n",
    "    axis.plot( dimension, probability, color = 'black', marker = '.', linestyle = 'None' )\n",
    "    plt.show( )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "2a17682f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def display( circuit, result, size, m ):\n",
    "    [ k, times ] = result.shape\n",
    "    sqrt = int( 3.14 / 4 * 2 ** ( k / 2 ) ) # circuit complexity O( sqrt( 2 ** k ) )\n",
    "    print( 'grover circuit simulation\\n' )\n",
    "    print( f'qubits        { k }' )\n",
    "    print( f'optimal size  { sqrt } rotations' )\n",
    "    print( f'actual  size  { size } rotations' )\n",
    "    print( f'looking for   { m } among the numbers { 0 }, { 1 }, ..., { 2 ** k - 1 }\\n' )\n",
    "    measurement, probability = interpret( result )\n",
    "    if times < 300 : print( f'measurements\\n{ measurement }' )\n",
    "    if k < 20 : plot( range( 2 ** k ), probability )\n",
    "    if size <  4 : print( f'\\ncircuit diagram\\n{ circuit }' ) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "80b85ce5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "grover circuit simulation\n",
      "\n",
      "qubits        8\n",
      "optimal size  12 rotations\n",
      "actual  size  7 rotations\n",
      "looking for   6 among the numbers 0, 1, ..., 255\n",
      "\n",
      "measurements\n",
      "[6, 6, 188, 6, 6, 6, 6, 128, 61, 6, 6, 6, 6, 6, 6, 6, 6, 28, 6, 146, 6, 6, 188, 6, 6, 172, 6, 39, 6, 77, 6, 6, 6, 6, 59, 6, 6, 6, 6, 6, 6, 6, 37, 6, 163, 226, 23, 6, 129, 6, 6, 77, 6, 47, 6, 6, 6, 126, 248, 65, 6, 6, 6, 14, 6, 6, 6, 6, 6, 6, 6, 6, 6, 232, 6, 6, 115, 184, 109, 6, 6, 6, 6, 6, 6, 6, 6, 6, 74, 152, 68, 6, 6, 6, 57, 6, 178, 6, 6, 68]\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1008x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m = 6 # is the number that we hope to measure at the end of the circuit\n",
    "k = 8 # is the number of qubits in the circuit\n",
    "size = 7 # is the number of rotations in the circuit\n",
    "times = 100 # is the number of circuit simulations\n",
    "\n",
    "q = cirq.LineQubit.range( k )\n",
    "oracle = oracle_gates( q, m )\n",
    "diffuser = diffusion_gates( q )\n",
    "grover = cirq.Circuit( grover_gates( q, oracle, diffuser, size ) )\n",
    "result = simulate( q, grover, times )\n",
    "display( grover, result, size, m )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "670f61e9",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "grover circuit simulation\n",
      "\n",
      "qubits        16\n",
      "optimal size  200 rotations\n",
      "actual  size  100 rotations\n",
      "looking for   55555 among the numbers 0, 1, ..., 65535\n",
      "\n",
      "measurements\n",
      "[568, 31711, 55555, 55555, 29434, 22692, 55555, 55555, 55555, 20187, 52613, 63739, 55555, 27386, 55555, 55555, 37273, 41873, 14125, 17547, 55555, 55938, 87, 55555, 62051, 59936, 24752, 11524, 55555, 55555, 55555, 55555, 55555, 55555, 25099, 5004, 28673, 5169, 55555, 60833, 55555, 55555, 55555, 23892, 55555, 2617, 55555, 55555, 55555, 55555, 55555, 25984, 49354, 55555, 40432, 55555, 55555, 65373, 41209, 55555, 55555, 65162, 55555, 12554, 3640, 1932, 55555, 8526, 21353, 55555, 55555, 55555, 42719, 55555, 55555, 63061, 5631, 55555, 55555, 59254, 55555, 55555, 55555, 55555, 8651, 34852, 55555, 22543, 55555, 43582, 8863, 55555, 40655, 55555, 55555, 61826, 58469, 55555, 64999, 55555]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m = 55555\n",
    "k = 16\n",
    "size = 100\n",
    "times = 100\n",
    "\n",
    "q = cirq.LineQubit.range( k )\n",
    "oracle = oracle_gates( q, m )\n",
    "diffuser = diffusion_gates( q )\n",
    "grover = cirq.Circuit( grover_gates( q, oracle, diffuser, size ) )\n",
    "result = simulate( q, grover, times )\n",
    "display( grover, result, size, m )"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.8.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}