{
 "metadata": {
  "name": "identitysearch_example"
 }, 
 "nbformat": 2, 
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code", 
     "collapsed": true, 
     "input": [
      "\"\"\"Demonstration of quantum gate identity search.\"\"\"", 
      "", 
      "from sympy.physics.quantum.gate import (X, Y, Z, H, S, T, CNOT,", 
      "        IdentityGate, CGate, gate_simp)", 
      "from sympy.physics.quantum.identitysearch import *", 
      "from sympy.physics.quantum.dagger import Dagger"
     ], 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 1
    }, 
    {
     "cell_type": "code", 
     "collapsed": true, 
     "input": [
      "# Declare a few quantum gates", 
      "x = X(0)", 
      "y = Y(0)", 
      "z = Z(0)", 
      "h = H(0)", 
      "cnot = CNOT(1,0)", 
      "cgate_z = CGate((0,), Z(1))"
     ], 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 2
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": [
      "# Start with the trivial cases", 
      "gate_list = [x]", 
      "", 
      "bfs_identity_search(gate_list, 1, max_depth=2)"
     ], 
     "language": "python", 
     "outputs": [
      {
       "output_type": "pyout", 
       "prompt_number": 6, 
       "text": [
        "set([GateIdentity(X(0), X(0))])"
       ]
      }
     ], 
     "prompt_number": 6
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": [
      "gate_list = [y]", 
      "", 
      "bfs_identity_search(gate_list, 1, max_depth=2)"
     ], 
     "language": "python", 
     "outputs": [
      {
       "output_type": "pyout", 
       "prompt_number": 7, 
       "text": [
        "set([GateIdentity(Y(0), Y(0))])"
       ]
      }
     ], 
     "prompt_number": 7
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": [
      "# bfs_identity_search looks for circuits that reduce to a", 
      "# scalar value unless told otherwise.", 
      "# The following list should produce 4 identities as a result.", 
      "gate_list = [x, y, z]", 
      "", 
      "bfs_identity_search(gate_list, 2)"
     ], 
     "language": "python", 
     "outputs": [
      {
       "output_type": "pyout", 
       "prompt_number": 9, 
       "text": [
        "set([GateIdentity(X(0), X(0)),", 
        "     GateIdentity(Z(0), Z(0)),", 
        "     GateIdentity(X(0), Y(0), Z(0)),", 
        "     GateIdentity(Y(0), Y(0))])"
       ]
      }
     ], 
     "prompt_number": 9
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": [
      "gate_list = [x, y, z, h]", 
      "", 
      "bfs_identity_search(gate_list, 2)"
     ], 
     "language": "python", 
     "outputs": [
      {
       "output_type": "pyout", 
       "prompt_number": 10, 
       "text": [
        "set([GateIdentity(Y(0), H(0), Y(0), H(0)),", 
        "     GateIdentity(X(0), Y(0), X(0), Y(0)),", 
        "     GateIdentity(X(0), Y(0), Z(0)),", 
        "     GateIdentity(X(0), H(0), Z(0), H(0)),", 
        "     GateIdentity(Z(0), Z(0)),", 
        "     GateIdentity(X(0), X(0)),", 
        "     GateIdentity(Y(0), Y(0)),", 
        "     GateIdentity(X(0), Z(0), X(0), Z(0)),", 
        "     GateIdentity(Y(0), Z(0), Y(0), Z(0)),", 
        "     GateIdentity(H(0), H(0))])"
       ]
      }
     ], 
     "prompt_number": 10
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": [
      "# One has the option to limit the max size of the circuit.", 
      "# The default size is the size of the gate list.", 
      "bfs_identity_search(gate_list, 2, max_depth=3)"
     ], 
     "language": "python", 
     "outputs": [
      {
       "output_type": "pyout", 
       "prompt_number": 12, 
       "text": [
        "set([GateIdentity(X(0), X(0)),", 
        "     GateIdentity(X(0), Y(0), Z(0)),", 
        "     GateIdentity(Z(0), Z(0)),", 
        "     GateIdentity(H(0), H(0)),", 
        "     GateIdentity(Y(0), Y(0))])"
       ]
      }
     ], 
     "prompt_number": 12
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": [
      "# One also has the option to find circuits that only reduce", 
      "# to the Identity matrix rather than only scalar matrices.", 
      "bfs_identity_search(gate_list, 2, identity_only=True)"
     ], 
     "language": "python", 
     "outputs": [
      {
       "output_type": "pyout", 
       "prompt_number": 13, 
       "text": [
        "set([GateIdentity(X(0), X(0)),", 
        "     GateIdentity(Z(0), Z(0)),", 
        "     GateIdentity(H(0), H(0)),", 
        "     GateIdentity(Y(0), Y(0))])"
       ]
      }
     ], 
     "prompt_number": 13
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": [
      "gate_list = [cnot, cgate_z, h]", 
      "", 
      "bfs_identity_search(gate_list, 2, max_depth=4)"
     ], 
     "language": "python", 
     "outputs": [
      {
       "output_type": "pyout", 
       "prompt_number": 14, 
       "text": [
        "set([GateIdentity(CNOT(1,0), H(0), C((0),Z(1)), H(0)),", 
        "     GateIdentity(H(0), H(0)),", 
        "     GateIdentity(C((0),Z(1)), C((0),Z(1))),", 
        "     GateIdentity(CNOT(1,0), CNOT(1,0))])"
       ]
      }
     ], 
     "prompt_number": 14
    }
   ]
  }
 ]
}