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  "name": "",
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 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<a name=top></a>\n",
      "<center>\n",
      "<h2>This notebook is for testing code in sglib.py</h2>\n",
      "</center>\n",
      "<p>\n",
      "I <i>may</i> end up also using it for documenting sglib functions.\n",
      "<p>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<h2>Contents</h2>\n",
      "<ul>\n",
      "<li> <a href=\"#setup\">Setup Cell</a>\n",
      "<li> <a href=\"#kets\">kets and vectors</a>\n",
      "<li> <a href=\"#string_tensor\">string_tensor()</a>\n",
      "<li> <a href=\"#format_state\">sg_format_state()</a>\n",
      "<li> <a href=\"#myltx\">myltx() tests</a>\n",
      "</ul>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<hr size=3>\n",
      "<a name=setup></a>\n",
      "<h2><a href=\"#top\">^</a> Setup Cell</h2>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#%autosave 0\n",
      "%matplotlib inline\n",
      "import sglib\n",
      "reload(sglib)\n",
      "from sglib import *\n",
      "from sympy import Symbol\n",
      "alpha = Symbol('alpha'); beta = Symbol('beta')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<hr size=3>\n",
      "<a name=kets></a>\n",
      "<h2><a href=\"#top\">^</a> Kets and Vectors</h2>\n",
      "<p>\n",
      "You can create a state using either the <code>col()</code> or the\n",
      "<code>ket()</code> function. In both cases, the object that gets\n",
      "created is a column vector."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "col(1,0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ket('+z')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "When you use the <code>col()</code> the parameters you give it are simply\n",
      "the individual components of the column vector, separated by commas. The\n",
      "vector can have any dimension. Here's one of dimension 4:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "col(1,0,0,0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The <code>ket()</code> only takes a single parameter, and it needs to by\n",
      "enclosed in quotes. It will recognize the basic electron states, and a\n",
      "zero or one for the classical bit state."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ket('-y')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ket('0'), ket('1')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "psi = 1/sqrt(2)*ket('+z') + 1/sqrt(2)*ket('-z')\n",
      "fm = latex\n",
      "fm = sg_latex\n",
      "fm = sg_format_state(['+z','-z'], ',').format\n",
      "Print(r'$\\psi = %s$' % fm(psi))\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<hr size=3>\n",
      "<a name=string_tensor></a>\n",
      "<h2><a href=\"#top\">^</a> string_tensor()</h2>\n",
      "<p>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "string_tensor(2, ['0','1'], separator=',', D=False)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<hr size=3>\n",
      "<a name=format_state></a>\n",
      "<h2><a href=\"#top\">^</a> sg_format_state()</h2>\n",
      "<p>\n",
      "These all work (March 2015)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fs1 = sg_format_state(basis=['0', '1'], separator='').format\n",
      "fs2 = sg_format_state(basis=['+z', '-z'], separator='').format\n",
      "fs3 = sg_format_state(\n",
      "    basis=[r'\\mathrm{Heads}', '\\mathrm{Tails}'], separator='').format\n",
      "Print('-----------------------------------------------------------')\n",
      "psi = 1/sqrt(2)*col(1,0)+1/sqrt(2)*col(0,1)\n",
      "Print('$\\psi=%s$'%fs1(psi))\n",
      "Print('$\\psi=%s$'%fs2(psi))\n",
      "Print('$\\psi=%s$'%fs3(psi))\n",
      "Print('-----------------------------------------------------------')\n",
      "psi = 1/sqrt(2)*col(1,0)-1/sqrt(2)*col(0,1)\n",
      "Print('$\\psi=%s$'%fs1(psi))\n",
      "Print('$\\psi=%s$'%fs2(psi))\n",
      "Print('$\\psi=%s$'%fs3(psi))\n",
      "Print('-----------------------------------------------------------')\n",
      "psi = -1/sqrt(2)*col(1,0)+1/sqrt(2)*col(0,1)\n",
      "Print('$\\psi=%s$'%fs1(psi))\n",
      "Print('$\\psi=%s$'%fs2(psi))\n",
      "Print('$\\psi=%s$'%fs3(psi))\n",
      "Print('-----------------------------------------------------------')\n",
      "psi = -1/sqrt(2)*col(1,0)-1/sqrt(2)*col(0,1)\n",
      "Print('$\\psi=%s$'%fs1(psi))\n",
      "Print('$\\psi=%s$'%fs2(psi))\n",
      "Print('$\\psi=%s$'%fs3(psi))\n",
      "Print('-----------------------------------------------------------')\n",
      "psi = alpha*col(1,0) + beta*col(0,1)\n",
      "Print('$\\psi=%s$'%fs1(psi))\n",
      "psi = alpha*col(1,0) - beta*col(0,1)\n",
      "Print('$\\psi=%s$'%fs1(psi))\n",
      "psi = -alpha*col(1,0) + beta*col(0,1)\n",
      "Print('$\\psi=%s$'%fs1(psi))\n",
      "psi = -alpha*col(1,0) - beta*col(0,1)\n",
      "Print('$\\psi=%s$'%fs1(psi))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#\n",
      "# The Bell States\n",
      "#\n",
      "bell_1 = 1/sqrt(2)*TP(pZ,pZ) + 1/sqrt(2)*TP(mZ,mZ) # phi+\n",
      "bell_2 = 1/sqrt(2)*TP(pZ,pZ) - 1/sqrt(2)*TP(mZ,mZ) # phi-\n",
      "bell_3 = 1/sqrt(2)*TP(pZ,mZ) + 1/sqrt(2)*TP(mZ,pZ) # psi+ (Triplet)\n",
      "bell_4 = 1/sqrt(2)*TP(pZ,mZ) - 1/sqrt(2)*TP(mZ,pZ) # psi- (Singlet)\n",
      "#\n",
      "# pick a format\n",
      "#\n",
      "fs = sg_format_state(basis=['+z', '-z'], separator=',').format\n",
      "fs = sg_format_state(basis=['0', '1'], separator='').format\n",
      "Print('Bell$_1 = %s$' %(fs(bell_1)))\n",
      "Print('Bell$_2 = %s$' %(fs(bell_2)))\n",
      "Print('Bell$_3 = %s$' %(fs(bell_3)))\n",
      "Print('Bell$_4 = %s$' %(fs(bell_4)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<hr size=3>\n",
      "<a name=myltx></a>\n",
      "<h2><a href=\"#top\">^</a> myltx() Tests</h2>\n",
      "<p>\n",
      "The following all work right as of 05 March 2015:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "foo = 1/sqrt(2)\n",
      "Print(r'$%s \\rightarrow %s$' %(latex(foo), myltx(foo)))\n",
      "foo = 1/sqrt(2)*col(1,1)\n",
      "Print(r'$%s \\rightarrow %s$' %(latex(foo), myltx(foo)))\n",
      "foo = 1/sqrt(2)*mat(1,1,1,-1)\n",
      "Print(r'$%s \\rightarrow %s$' %(latex(foo), myltx(foo)))\n",
      "\n",
      "foo = 1/sqrt(2)*col(alpha, beta)\n",
      "Print(r'$%s \\rightarrow %s$' %(latex(foo), myltx(foo)))\n",
      "foo = 1/sqrt(2)*mat(1,1,1,-1)\n",
      "Print(r'$%s \\rightarrow %s$' %(latex(foo), myltx(foo)))\n",
      "foo = 1/sqrt(2)*col(alpha, beta)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "If there's a common denominator that not a root, then it's OK\n",
      "but it doesn't get reduced."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "state = oo = 1/sqrt(2)*col(1,1)\n",
      "M = OP(state,state)\n",
      "Print(r'$%s \\rightarrow %s$' %(latex(M), myltx(M)))\n",
      "state = oo = 1/sqrt(2)*col(alpha, beta)\n",
      "M = OP(state,state)\n",
      "Print(r'$%s \\rightarrow %s$' %(latex(M), myltx(M)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "And, numerators ..."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "foo = 2/sqrt(3)*mat(1,0,0,1)\n",
      "Print(r'$%s \\rightarrow %s$' %(latex(foo), myltx(foo)))\n",
      "\n",
      "foo = sqrt(3)*mat(1,0,0,1)\n",
      "Print(r'$%s \\rightarrow %s$' %(latex(foo), myltx(foo)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "However, myltx() can't currently deal with the coefficient of\n",
      "a symbolic value"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "foo = 5/sqrt(2)\n",
      "Print(r'$%s \\rightarrow %s$' %(latex(foo), myltx(foo)))\n",
      "foo = alpha/sqrt(2)\n",
      "Print(r'$%s \\rightarrow %s$' %(latex(foo), myltx(foo)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}