{
    "nbformat": 2, 
    "metadata": {
        "name": "grovers"
    }, 
    "worksheets": [
        {
            "cells": [
                {
                    "source": "<h1>Grover's Algorithm</h1>", 
                    "cell_type": "markdown"
                }, 
                {
                    "cell_type": "code", 
                    "language": "python", 
                    "outputs": [], 
                    "collapsed": true, 
                    "prompt_number": 1, 
                    "input": "%load_ext sympyprinting"
                }, 
                {
                    "cell_type": "code", 
                    "language": "python", 
                    "outputs": [], 
                    "collapsed": true, 
                    "prompt_number": 2, 
                    "input": "from sympy import sqrt, symbols, Rational\nfrom sympy import expand, Eq, Symbol, simplify, exp, sin\nfrom sympy.physics.quantum import *\nfrom sympy.physics.quantum.qubit import *\nfrom sympy.physics.quantum.gate import *\nfrom sympy.physics.quantum.grover import *\nfrom sympy.physics.quantum.qft import QFT, IQFT, Fourier\nfrom sympy.physics.quantum.circuitplot import circuit_plot"
                }, 
                {
                    "cell_type": "code", 
                    "language": "python", 
                    "outputs": [], 
                    "collapsed": true, 
                    "prompt_number": 3, 
                    "input": "nqubits = 3\n"
                }, 
                {
                    "source": "Grover's algorithm is a quantum algorithm which searches an unordered database (inverts a function).<br/>\nProvides polynomial speedup over classical brute-force search ($O(\\sqrt{N}) vs. O(N))$ ", 
                    "cell_type": "markdown"
                }, 
                {
                    "source": "Define a black box function that returns True if it is passed the state we are searching for.", 
                    "cell_type": "markdown"
                }, 
                {
                    "cell_type": "code", 
                    "language": "python", 
                    "outputs": [], 
                    "collapsed": true, 
                    "prompt_number": 4, 
                    "input": "def black_box(qubits):\n    return True if qubits == IntQubit(1, qubits.nqubits) else False\n"
                }, 
                {
                    "source": "Build a uniform superposition state to start the search.", 
                    "cell_type": "markdown"
                }, 
                {
                    "cell_type": "code", 
                    "language": "python", 
                    "outputs": [
                        {
                            "output_type": "pyout", 
                            "latex": "$$\\frac{1}{4} \\sqrt{2} {\\left|0\\right\\rangle } + \\frac{1}{4} \\sqrt{2} {\\left|1\\right\\rangle } + \\frac{1}{4} \\sqrt{2} {\\left|2\\right\\rangle } + \\frac{1}{4} \\sqrt{2} {\\left|3\\right\\rangle } + \\frac{1}{4} \\sqrt{2} {\\left|4\\right\\rangle } + \\frac{1}{4} \\sqrt{2} {\\left|5\\right\\rangle } + \\frac{1}{4} \\sqrt{2} {\\left|6\\right\\rangle } + \\frac{1}{4} \\sqrt{2} {\\left|7\\right\\rangle }$$", 
                            "prompt_number": 5, 
                            "png": "iVBORw0KGgoAAAANSUhEUgAAAtoAAAAkCAYAAAC36Z1zAAAABHNCSVQICAgIfAhkiAAADKdJREFU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\nTkSuQmCC\n", 
                            "text": "\u23bd\u23bd\u23bd         \u23bd\u23bd\u23bd         \u23bd\u23bd\u23bd         \u23bd\u23bd\u23bd         \u23bd\u23bd\u23bd         \u23bd\u23bd\u23bd         \u23bd\u23bd\u23bd \n\u2572\u2571 2 \u22c5\u27580\u27e9   \u2572\u2571 2 \u22c5\u27581\u27e9   \u2572\u2571 2 \u22c5\u27582\u27e9   \u2572\u2571 2 \u22c5\u27583\u27e9   \u2572\u2571 2 \u22c5\u27584\u27e9   \u2572\u2571 2 \u22c5\u27585\u27e9   \u2572\u2571 2 \u22c5\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\n    4           4           4           4           4           4           4 \n\n        \u23bd\u23bd\u23bd    \n\u27586\u27e9   \u2572\u2571 2 \u22c5\u27587\u27e9\n\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n          4"
                        }
                    ], 
                    "collapsed": false, 
                    "prompt_number": 5, 
                    "input": "psi = superposition_basis(nqubits); psi\n"
                }, 
                {
                    "cell_type": "code", 
                    "language": "python", 
                    "outputs": [], 
                    "collapsed": true, 
                    "prompt_number": 6, 
                    "input": "v = OracleGate(nqubits, black_box)\n"
                }, 
                {
                    "source": "Perform two iterations of Grover's algorithm.  Each iteration, the amplitude of the target state increases.", 
                    "cell_type": "markdown"
                }, 
                {
                    "cell_type": "code", 
                    "language": "python", 
                    "outputs": [
                        {
                            "output_type": "pyout", 
                            "latex": "$$\\frac{1}{8} \\sqrt{2} {\\left|0\\right\\rangle } + \\frac{5}{8} \\sqrt{2} {\\left|1\\right\\rangle } + \\frac{1}{8} \\sqrt{2} {\\left|2\\right\\rangle } + \\frac{1}{8} \\sqrt{2} {\\left|3\\right\\rangle } + \\frac{1}{8} \\sqrt{2} {\\left|4\\right\\rangle } + \\frac{1}{8} \\sqrt{2} {\\left|5\\right\\rangle } + \\frac{1}{8} \\sqrt{2} {\\left|6\\right\\rangle } + \\frac{1}{8} \\sqrt{2} {\\left|7\\right\\rangle }$$", 
                            "prompt_number": 7, 
                            "png": "iVBORw0KGgoAAAANSUhEUgAAAtoAAAAkCAYAAAC36Z1zAAAABHNCSVQICAgIfAhkiAAADOJJREFU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\nSUVORK5CYII=\n", 
                            "text": "\u23bd\u23bd\u23bd           \u23bd\u23bd\u23bd         \u23bd\u23bd\u23bd         \u23bd\u23bd\u23bd         \u23bd\u23bd\u23bd         \u23bd\u23bd\u23bd         \u23bd\u23bd\n\u2572\u2571 2 \u22c5\u27580\u27e9   5\u22c5\u2572\u2571 2 \u22c5\u27581\u27e9   \u2572\u2571 2 \u22c5\u27582\u27e9   \u2572\u2571 2 \u22c5\u27583\u27e9   \u2572\u2571 2 \u22c5\u27584\u27e9   \u2572\u2571 2 \u22c5\u27585\u27e9   \u2572\u2571 2\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\n    8            8            8           8           8           8           \n\n\u23bd         \u23bd\u23bd\u23bd    \n \u22c5\u27586\u27e9   \u2572\u2571 2 \u22c5\u27587\u27e9\n\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n8           8"
                        }
                    ], 
                    "collapsed": false, 
                    "prompt_number": 7, 
                    "input": "iter1 = qapply(grover_iteration(psi, v)); iter1\n"
                }, 
                {
                    "cell_type": "code", 
                    "language": "python", 
                    "outputs": [
                        {
                            "output_type": "pyout", 
                            "latex": "$$- \\frac{1}{16} \\sqrt{2} {\\left|0\\right\\rangle } + \\frac{11}{16} \\sqrt{2} {\\left|1\\right\\rangle } - \\frac{1}{16} \\sqrt{2} {\\left|2\\right\\rangle } - \\frac{1}{16} \\sqrt{2} {\\left|3\\right\\rangle } - \\frac{1}{16} \\sqrt{2} {\\left|4\\right\\rangle } - \\frac{1}{16} \\sqrt{2} {\\left|5\\right\\rangle } - \\frac{1}{16} \\sqrt{2} {\\left|6\\right\\rangle } - \\frac{1}{16} \\sqrt{2} {\\left|7\\right\\rangle }$$", 
                            "prompt_number": 8, 
                            "png": "iVBORw0KGgoAAAANSUhEUgAAAwUAAAAkCAYAAADYfZZ3AAAABHNCSVQICAgIfAhkiAAADSZJREFU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\nzSfShSQN5wAAAABJRU5ErkJggg==\n", 
                            "text": "\u23bd\u23bd\u23bd            \u23bd\u23bd\u23bd         \u23bd\u23bd\u23bd         \u23bd\u23bd\u23bd         \u23bd\u23bd\u23bd         \u23bd\u23bd\u23bd        \n  \u2572\u2571 2 \u22c5\u27580\u27e9   11\u22c5\u2572\u2571 2 \u22c5\u27581\u27e9   \u2572\u2571 2 \u22c5\u27582\u27e9   \u2572\u2571 2 \u22c5\u27583\u27e9   \u2572\u2571 2 \u22c5\u27584\u27e9   \u2572\u2571 2 \u22c5\u27585\u27e9   \u2572\n- \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - \u2500\n      16           16            16          16          16          16       \n\n \u23bd\u23bd\u23bd         \u23bd\u23bd\u23bd    \n\u2571 2 \u22c5\u27586\u27e9   \u2572\u2571 2 \u22c5\u27587\u27e9\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n   16          16"
                        }
                    ], 
                    "collapsed": false, 
                    "prompt_number": 8, 
                    "input": "iter2 = qapply(grover_iteration(iter1, v)); iter2\n"
                }, 
                {
                    "source": "A single shot measurement is performed to retrieve the target state.", 
                    "cell_type": "markdown"
                }, 
                {
                    "cell_type": "code", 
                    "language": "python", 
                    "outputs": [
                        {
                            "output_type": "pyout", 
                            "latex": "$${\\left|001\\right\\rangle }$$", 
                            "prompt_number": 9, 
                            "png": "iVBORw0KGgoAAAANSUhEUgAAACkAAAATCAYAAAANgSQ9AAAABHNCSVQICAgIfAhkiAAAAahJREFU\nSInt1rtrFUEcxfEPQeMr6DXiC3yksFHRRiQoiHVCKiuxyh9gYyMWVhaCooKttZXYiEZQ0yhib7AR\ng5GA+CgUITe+IFrMBMa9e/fO3NZ8YZjZ8zu7e3Z3dnZZoYgL3QqrkvEZPMV7tHAdbXzBWtzC28r+\nub5lNuIJTmOuUmtjGz43XckkRuJ4GlcrtVdYX9kn1zeIE3iOP9hXc/4tONcUMA05Gg+0P6mtw3dc\nTrRcXwv3hTt+ryEkXMJATsi7mK+pP8JMsp3rS7nYI+RxjFfFutRH8KZGn8Uh4bGU+Ep4EYP2DLkd\nCzV6O/Y7Cn2lzGNvKlRDbhLmVVsny1qrwNcPDzDRFPI3lmKrsjr2SwW+fpjAVFPIRd3XuA2x/1Dg\n64cRvEuFujk5g801+lDsPxb6SjgmvDz/0C3k7hr9qPDm/ij0lTCGhzkhX+IA9iTaVhzGtT58uQzj\nqx5zeVKYD4N4hptJ7bzwTV+TaLm+lBvCYt6xFuKssKx1kP5gLOJXbKeET9ttfMMunMTPxJ/rI/xU\n7MTBuP0Yr3EHV6I2hE9dLm6F/4e/u+tyeF0qLvsAAAAASUVORK5CYII=\n", 
                            "text": "\u2758001\u27e9"
                        }
                    ], 
                    "collapsed": false, 
                    "prompt_number": 9, 
                    "input": "measure_all_oneshot(iter2)\n"
                }
            ]
        }
    ]
}