{
 "metadata": {
  "name": "",
  "signature": "sha256:d28ccc4483f72b8e3526855566be7c5b03ba2f6676557b81237bd4a4fb16b7d0"
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 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Examples for `sympy.physics.quantum` section"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "from matplotlib import pyplot as plt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sympy.physics.quantum import Commutator, Dagger, Operator, Ket, qapply\n",
      "A = Operator('A')\n",
      "B = Operator('B')\n",
      "C = Operator('C')\n",
      "D = Operator('D')\n",
      "a = Ket('a')\n",
      "comm = Commutator(A, B)\n",
      "comm"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 2,
       "text": [
        "[A,B]"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "qapply(Dagger(comm*a)).doit()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "-<a|*(Dagger(A)*Dagger(B) - Dagger(B)*Dagger(A))"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Commutator(C+B, A*D).expand(commutator=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "-[A,B]*D - [A,C]*D + A*[B,D] + A*[C,D]"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sympy.physics.quantum.qubit import Qubit\n",
      "q = Qubit('0101')\n",
      "q"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "|0101>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "q.flip(1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "|0111>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Dagger(q)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "<0101|"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ip = Dagger(q)*q\n",
      "ip"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "<0101|0101>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ip.doit()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "1"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sympy.physics.quantum.qubit import Qubit, measure_all\n",
      "from sympy.physics.quantum.gate import H, X, Y, Z\n",
      "from sympy.physics.quantum.qapply import qapply\n",
      "c = H(0)*H(1)*Qubit('00')\n",
      "c"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "H(0)*H(1)*|00>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "q = qapply(c)\n",
      "measure_all(q)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "[(|00>, 1/4), (|01>, 1/4), (|10>, 1/4), (|11>, 1/4)]"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sympy.physics.quantum.qft import QFT\n",
      "from sympy.physics.quantum.circuitplot import circuit_plot"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fourier = QFT(0,3).decompose()\n",
      "fourier"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "SWAP(0,2)*H(0)*C((0),S(1))*H(1)*C((0),T(2))*C((1),S(2))*H(2)"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "circuit_plot(fourier, nqubits=3);\n",
      "%mkdir -p './images'\n",
      "plt.savefig('./images/fig1-circuitplot-qft.pdf', format='pdf')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Qt27dlJ+fH8VUiDQKEwDuks/nk9vt1qRJk0Lmmpub5ff7lZ2drbS0NAfSIVIoTMSdU6dO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\nAAAY+B/Xn+RPbDV0uQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x2b5b5f34e080>"
       ]
      }
     ],
     "prompt_number": 14
    }
   ],
   "metadata": {}
  }
 ]
}