{
    "nbformat": 2, 
    "metadata": {
        "name": "teleportation"
    }, 
    "worksheets": [
        {
            "cells": [
                {
                    "source": "<h1>Teleportation</h1>", 
                    "cell_type": "markdown"
                }, 
                {
                    "cell_type": "code", 
                    "language": "python", 
                    "outputs": [], 
                    "collapsed": false, 
                    "prompt_number": 5, 
                    "input": "%load_ext sympyprinting"
                }, 
                {
                    "cell_type": "code", 
                    "language": "python", 
                    "outputs": [], 
                    "collapsed": true, 
                    "prompt_number": 6, 
                    "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": [
                        {
                            "output_type": "pyout", 
                            "latex": "$$a {\\left|000\\right\\rangle } + b {\\left|001\\right\\rangle }$$", 
                            "prompt_number": 7, 
                            "png": "iVBORw0KGgoAAAANSUhEUgAAAHgAAAAVCAYAAACNDipWAAAABHNCSVQICAgIfAhkiAAAA4VJREFU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\nRK5CYII=\n", 
                            "text": "a\u22c5\u2758000\u27e9 + b\u22c5\u2758001\u27e9"
                        }
                    ], 
                    "collapsed": false, 
                    "prompt_number": 7, 
                    "input": "a,b = symbols('a b', real=True)\nstate = Qubit('000')*a + Qubit('001')*b; state"
                }, 
                {
                    "cell_type": "code", 
                    "language": "python", 
                    "outputs": [
                        {
                            "output_type": "pyout", 
                            "latex": "$$CNOT_{1,2} H_{1}$$", 
                            "prompt_number": 8, 
                            "png": "iVBORw0KGgoAAAANSUhEUgAAAGQAAAAcCAYAAACXkxr4AAAABHNCSVQICAgIfAhkiAAABNhJREFU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\nYII=\n", 
                            "text": "CNOT   \u22c5H \n    1,2  1"
                        }
                    ], 
                    "collapsed": false, 
                    "prompt_number": 8, 
                    "input": "entangle1_2 = CNOT(1,2)*HadamardGate(1); entangle1_2\n"
                }, 
                {
                    "cell_type": "code", 
                    "language": "python", 
                    "outputs": [
                        {
                            "output_type": "pyout", 
                            "latex": "$$\\frac{1}{2} \\sqrt{2} a {\\left|000\\right\\rangle } + \\frac{1}{2} \\sqrt{2} a {\\left|110\\right\\rangle } + \\frac{1}{2} \\sqrt{2} b {\\left|001\\right\\rangle } + \\frac{1}{2} \\sqrt{2} b {\\left|111\\right\\rangle }$$", 
                            "prompt_number": 9, 
                            "png": "iVBORw0KGgoAAAANSUhEUgAAAdoAAAAkCAYAAAAuC/tyAAAABHNCSVQICAgIfAhkiAAACKNJREFU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\nrkJggg==\n", 
                            "text": "\u23bd\u23bd\u23bd             \u23bd\u23bd\u23bd             \u23bd\u23bd\u23bd             \u23bd\u23bd\u23bd        \n\u2572\u2571 2 \u22c5a\u22c5\u2758000\u27e9   \u2572\u2571 2 \u22c5a\u22c5\u2758110\u27e9   \u2572\u2571 2 \u22c5b\u22c5\u2758001\u27e9   \u2572\u2571 2 \u22c5b\u22c5\u2758111\u27e9\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\n      2               2               2               2"
                        }
                    ], 
                    "collapsed": false, 
                    "prompt_number": 9, 
                    "input": "state = qapply(entangle1_2*state); state\n"
                }, 
                {
                    "cell_type": "code", 
                    "language": "python", 
                    "outputs": [
                        {
                            "output_type": "pyout", 
                            "latex": "$$H_{0} CNOT_{0,1}$$", 
                            "prompt_number": 10, 
                            "png": "iVBORw0KGgoAAAANSUhEUgAAAGQAAAAcCAYAAACXkxr4AAAABHNCSVQICAgIfAhkiAAABRFJREFU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\nYII=\n", 
                            "text": "H \u22c5CNOT   \n 0     0,1"
                        }
                    ], 
                    "collapsed": false, 
                    "prompt_number": 10, 
                    "input": "entangle0_1 = HadamardGate(0)*CNOT(0,1); entangle0_1\n"
                }, 
                {
                    "cell_type": "code", 
                    "language": "python", 
                    "outputs": [
                        {
                            "output_type": "pyout", 
                            "prompt_number": 11, 
                            "text": "&lt;sympy.physics.quantum.circuitplot.CircuitPlot object at 0x3b9fb90&gt;"
                        }, 
                        {
                            "output_type": "display_data", 
                            "png": "iVBORw0KGgoAAAANSUhEUgAAAQ8AAADFCAYAAABKK3dYAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n"
                        }
                    ], 
                    "collapsed": false, 
                    "prompt_number": 11, 
                    "input": "circuit_plot(entangle0_1*entangle1_2, nqubits=3)\n"
                }, 
                {
                    "cell_type": "code", 
                    "language": "python", 
                    "outputs": [
                        {
                            "output_type": "pyout", 
                            "latex": "$$\\frac{1}{2} a {\\left|000\\right\\rangle } + \\frac{1}{2} a {\\left|001\\right\\rangle } + \\frac{1}{2} a {\\left|110\\right\\rangle } + \\frac{1}{2} a {\\left|111\\right\\rangle } + \\frac{1}{2} b {\\left|010\\right\\rangle } - \\frac{1}{2} b {\\left|011\\right\\rangle } + \\frac{1}{2} b {\\left|100\\right\\rangle } - \\frac{1}{2} b {\\left|101\\right\\rangle }$$", 
                            "prompt_number": 12, 
                            "png": "iVBORw0KGgoAAAANSUhEUgAAAr4AAAAiCAYAAAC5vNpkAAAABHNCSVQICAgIfAhkiAAACOJJREFU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\nAABJRU5ErkJggg==\n", 
                            "text": "a\u22c5\u2758000\u27e9   a\u22c5\u2758001\u27e9   a\u22c5\u2758110\u27e9   a\u22c5\u2758111\u27e9   b\u22c5\u2758010\u27e9   b\u22c5\u2758011\u27e9   b\u22c5\u2758100\u27e9   b\u22c5\u2758101\u27e9\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\n   2         2         2         2         2         2         2         2"
                        }
                    ], 
                    "collapsed": false, 
                    "prompt_number": 12, 
                    "input": "state = qapply(entangle0_1*state); state\n"
                }, 
                {
                    "cell_type": "code", 
                    "language": "python", 
                    "outputs": [], 
                    "collapsed": true, 
                    "prompt_number": 13, 
                    "input": "result = measure_partial(state, (0,1))\n"
                }, 
                {
                    "cell_type": "code", 
                    "language": "python", 
                    "outputs": [
                        {
                            "output_type": "pyout", 
                            "latex": "$$\\frac{a {\\left|110\\right\\rangle }}{\\sqrt{a^{2} + b^{2}} \\sqrt{\\frac{1}{4} \\lvert{\\frac{a}{\\sqrt{a^{2} + b^{2}}}}\\rvert^{2} + \\frac{1}{4} \\lvert{\\frac{b}{\\sqrt{a^{2} + b^{2}}}}\\rvert^{2}}} + \\frac{b {\\left|010\\right\\rangle }}{\\sqrt{a^{2} + b^{2}} \\sqrt{\\frac{1}{4} \\lvert{\\frac{a}{\\sqrt{a^{2} + b^{2}}}}\\rvert^{2} + \\frac{1}{4} \\lvert{\\frac{b}{\\sqrt{a^{2} + b^{2}}}}\\rvert^{2}}}$$", 
                            "prompt_number": 14, 
                            "text": "a\u22c5\u2758110\u27e9                                              \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\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                      \u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd                     \n                     \u2571               2                 2                      \n                    \u2571  \u2502     a      \u2502    \u2502     b      \u2502                       \n                   \u2571   \u2502\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2502    \u2502\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2502                       \n                  \u2571    \u2502   \u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u2502    \u2502   \u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u2502                       \n   \u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd     \u2571     \u2502  \u2571  2    2 \u2502    \u2502  \u2571  2    2 \u2502        \u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd     \u2571\n  \u2571  2    2     \u2571      \u2502\u2572\u2571  a  + b  \u2502    \u2502\u2572\u2571  a  + b  \u2502       \u2571  2    2     \u2571 \n\u2572\u2571  a  + b  \u22c5  \u2571       \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    \u2572\u2571  a  + b  \u22c5  \u2571  \n             \u2572\u2571               4                 4                        \u2572\u2571   \n\n       b\u22c5\u2758010\u27e9                         \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\n    \u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\n   \u2571               2                 2 \n  \u2571  \u2502     a      \u2502    \u2502     b      \u2502  \n \u2571   \u2502\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2502    \u2502\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2502  \n\u2571    \u2502   \u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u2502    \u2502   \u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u2502  \n     \u2502  \u2571  2    2 \u2502    \u2502  \u2571  2    2 \u2502  \n     \u2502\u2572\u2571  a  + b  \u2502    \u2502\u2572\u2571  a  + b  \u2502  \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 \n            4                 4"
                        }
                    ], 
                    "collapsed": false, 
                    "prompt_number": 14, 
                    "input": "state = (result[2][0]*2).expand(); state"
                }, 
                {
                    "cell_type": "code", 
                    "language": "python", 
                    "outputs": [
                        {
                            "output_type": "pyout", 
                            "latex": "$$\\frac{a {\\left|010\\right\\rangle }}{\\sqrt{a^{2} + b^{2}} \\sqrt{\\frac{1}{4} \\lvert{\\frac{a}{\\sqrt{a^{2} + b^{2}}}}\\rvert^{2} + \\frac{1}{4} \\lvert{\\frac{b}{\\sqrt{a^{2} + b^{2}}}}\\rvert^{2}}} + \\frac{b {\\left|110\\right\\rangle }}{\\sqrt{a^{2} + b^{2}} \\sqrt{\\frac{1}{4} \\lvert{\\frac{a}{\\sqrt{a^{2} + b^{2}}}}\\rvert^{2} + \\frac{1}{4} \\lvert{\\frac{b}{\\sqrt{a^{2} + b^{2}}}}\\rvert^{2}}}$$", 
                            "prompt_number": 15, 
                            "text": "a\u22c5\u2758010\u27e9                                              \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\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                      \u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd                     \n                     \u2571               2                 2                      \n                    \u2571  \u2502     a      \u2502    \u2502     b      \u2502                       \n                   \u2571   \u2502\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2502    \u2502\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2502                       \n                  \u2571    \u2502   \u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u2502    \u2502   \u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u2502                       \n   \u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd     \u2571     \u2502  \u2571  2    2 \u2502    \u2502  \u2571  2    2 \u2502        \u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd     \u2571\n  \u2571  2    2     \u2571      \u2502\u2572\u2571  a  + b  \u2502    \u2502\u2572\u2571  a  + b  \u2502       \u2571  2    2     \u2571 \n\u2572\u2571  a  + b  \u22c5  \u2571       \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    \u2572\u2571  a  + b  \u22c5  \u2571  \n             \u2572\u2571               4                 4                        \u2572\u2571   \n\n       b\u22c5\u2758110\u27e9                         \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\n    \u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\n   \u2571               2                 2 \n  \u2571  \u2502     a      \u2502    \u2502     b      \u2502  \n \u2571   \u2502\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2502    \u2502\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2502  \n\u2571    \u2502   \u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u2502    \u2502   \u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u23bd\u2502  \n     \u2502  \u2571  2    2 \u2502    \u2502  \u2571  2    2 \u2502  \n     \u2502\u2572\u2571  a  + b  \u2502    \u2502\u2572\u2571  a  + b  \u2502  \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 \n            4                 4"
                        }
                    ], 
                    "collapsed": false, 
                    "prompt_number": 15, 
                    "input": "state = qapply(XGate(2)*state); state\n"
                }
            ]
        }
    ]
}