{
 "cells": [
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     "output_type": "stream",
     "text": [
      "Julia Version 1.7.1\n",
      "Commit ac5cc99908 (2021-12-22 19:35 UTC)\n",
      "Platform Info:\n",
      "  OS: Linux (x86_64-pc-linux-gnu)\n",
      "  CPU: AMD Ryzen 5 PRO 3400GE w/ Radeon Vega Graphics\n",
      "  WORD_SIZE: 64\n",
      "  LIBM: libopenlibm\n",
      "  LLVM: libLLVM-12.0.1 (ORCJIT, znver1)\n",
      "Environment:\n",
      "  JULIA_EDITOR = nvim\n",
      "  JULIA_SHELL = /bin/bash\n"
     ]
    }
   ],
   "source": [
    "versioninfo()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# DiracNotation.jl sample\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By using this package, matrix representation is changed into Dirac notation.\n",
    "\n",
    "## Basic usage\n",
    "\n",
    "In order to change display style, all you have to do is import this package."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-15T17:19:59.532000+09:00",
     "start_time": "2018-09-15T08:19:59.423Z"
    }
   },
   "outputs": [],
   "source": [
    "using DiracNotation, LinearAlgebra, Random; Random.seed!(0);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-15T17:20:02.009000+09:00",
     "start_time": "2018-09-15T08:20:01.782Z"
    }
   },
   "outputs": [],
   "source": [
    "ket = normalize(rand(Complex{Float64}, 4)); bra = ket';"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-15T17:20:04.171000+09:00",
     "start_time": "2018-09-15T08:20:02.697Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "$|\\psi\\rangle = (0.296201+0.0500454im)|00\\rangle+(0.62945+0.0627674im)|01\\rangle+(0.483044+0.0849307im)|10\\rangle+(0.0798625+0.512534im)|11\\rangle\n",
       "$"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dirac(ket)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-15T17:20:12.002000+09:00",
     "start_time": "2018-09-15T08:20:11.999Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "$\\langle\\psi| = (0.296201-0.0500454im)\\langle00|+(0.62945-0.0627674im)\\langle01|+(0.483044-0.0849307im)\\langle10|+(0.0798625-0.512534im)\\langle11|\n",
       "$"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dirac(bra)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-15T17:20:35.471000+09:00",
     "start_time": "2018-09-15T08:20:35.469Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "$|\\psi\\rangle = (0.296201+0.0500454im)|00\\rangle+(0.62945+0.0627674im)|01\\rangle+(0.483044+0.0849307im)|10\\rangle+(0.0798625+0.512534im)|11\\rangle\n",
       "$"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dirac(ket)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-15T17:20:36.769000+09:00",
     "start_time": "2018-09-15T08:20:36.542Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "$\\hat{\\rho} = 0.28951|0\\rangle\\langle0|+0.538639|0\\rangle\\langle1|+0.02855|1\\rangle\\langle0|+0.89699|1\\rangle\\langle1|\n",
       "$"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "op = rand(2,2);\n",
    "dirac(op)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Qudit system and Operator"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "7 dimensional state\n",
    "\n",
    "$| \\psi \\rangle \\in \\mathbb{C}^7$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-15T17:14:41.216000+09:00",
     "start_time": "2018-09-15T08:14:36.004Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "$|\\psi\\rangle = 0.178768|0\\rangle+0.234424|1\\rangle+0.29376|2\\rangle+0.625728|3\\rangle+0.515035|4\\rangle+0.107587|5\\rangle+0.398021|6\\rangle\n",
       "$"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dim = 7\n",
    "ket = normalize(rand(dim))\n",
    "dirac(ket, [dim])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "qubit-qutrit\n",
    "\n",
    "$| \\psi \\rangle \\in \\mathbb{C}^2 \\otimes \\mathbb{C}^3$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-15T17:14:41.255000+09:00",
     "start_time": "2018-09-15T08:14:36.007Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "$|\\psi\\rangle = -0.248521|00\\rangle-0.0145385|01\\rangle-0.701118|02\\rangle-0.334889|10\\rangle+0.0444954|11\\rangle-0.57648|12\\rangle\n",
       "$"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dims = [2,3]\n",
    "ket = normalize(randn(prod(dims)))\n",
    "dirac(ket, dims)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Operator\n",
    "\n",
    "$A: V \\rightarrow W$ where $V = \\mathbb{C}^2$ and $W = \\mathbb{C}^3$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-15T17:14:41.263000+09:00",
     "start_time": "2018-09-15T08:14:36.009Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "$\\hat{\\rho} = 0.573612|0\\rangle\\langle0|+0.862693|0\\rangle\\langle1|+0.443074|1\\rangle\\langle0|+0.518326|1\\rangle\\langle1|+0.62073|2\\rangle\\langle0|+0.766871|2\\rangle\\langle1|\n",
       "$"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A = rand(3,2)\n",
    "dirac(A, [3], [2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Precision"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-15T17:14:41.287000+09:00",
     "start_time": "2018-09-15T08:14:36.013Z"
    }
   },
   "outputs": [],
   "source": [
    "DiracNotation.set_properties(precision=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-15T17:14:41.289000+09:00",
     "start_time": "2018-09-15T08:14:36.015Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "$\\hat{\\rho} = 0.13|0\\rangle\\langle0|+0.35|0\\rangle\\langle1|+0.12|0\\rangle\\langle2|+0.087|1\\rangle\\langle0|+0.19|1\\rangle\\langle1|+0.9|1\\rangle\\langle2|\n",
       "$"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "op = rand(2,3);\n",
    "leftdims = [2];\n",
    "rightdims = [3];\n",
    "dirac(op, leftdims, rightdims)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Disable mathjax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-15T17:14:41.320000+09:00",
     "start_time": "2018-09-15T08:14:36.018Z"
    }
   },
   "outputs": [],
   "source": [
    "DiracNotation.set_properties(islatex=false)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-15T17:14:41.545000+09:00",
     "start_time": "2018-09-15T08:14:36.021Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ρ = 0.42|0⟩⟨0|+0.88|0⟩⟨1|+0.84|0⟩⟨2|+0.71|1⟩⟨0|+0.93|1⟩⟨1|+0.98|1⟩⟨2|\n"
     ]
    }
   ],
   "source": [
    "op = rand(2,3);\n",
    "leftdims = [2];\n",
    "rightdims = [3];\n",
    "dirac(op, leftdims, rightdims)"
   ]
  }
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