Quantum Computer Simulator in Julia.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A simple notebook showing how to build a quantum randum number generator. We're going to use Float32 for all calculations to save memory.\n",
    "\n",
    "We define some well known constants. The 2x2 identity matrix and the 2x2 zero matrix:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[32m\u001b[1mTest Passed\u001b[22m\u001b[39m"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Test, LinearAlgebra\n",
    "\n",
    "eye = Matrix{Float32}(I, 2, 2)\n",
    "ZEROS = zeros(Float32, 2, 2)\n",
    "\n",
    "@test eye*eye ≈ eye && eye * ZEROS == ZEROS"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll define the starting state for qubits as |0>."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Array{Float32,1}:\n",
       " 0.0\n",
       " 1.0"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "UP = [1f0, 0]\n",
    "DOWN = [0f0, 1f0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can define some basic gates:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[32m\u001b[1mTest Passed\u001b[22m\u001b[39m"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = [0f0 1; 1 0]\n",
    "H = Float32(1/sqrt(2)) * [1f0 1; 1 -1]\n",
    "halfX = Float32(0.5) * [1f0+im 1-im; 1-im 1+im]\n",
    "\n",
    "@test halfX*halfX ≈ X && H*H ≈ X*X && X*X ≈ eye"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "qubits (generic function with 1 method)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qubits(n) = foldr(kron, fill(UP, n))"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "%%latex\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\frac{x}{y}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "circuit (generic function with 1 method)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit(n) = foldr(kron, fill(H, n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "256-element Array{Float32,1}:\n",
       " 0.062499993\n",
       " 0.062499993\n",
       " 0.062499993\n",
       " 0.062499993\n",
       " 0.062499993\n",
       " 0.062499993\n",
       " 0.062499993\n",
       " 0.062499993\n",
       " 0.062499993\n",
       " 0.062499993\n",
       " 0.062499993\n",
       " 0.062499993\n",
       " 0.062499993\n",
       " ⋮          \n",
       " 0.062499993\n",
       " 0.062499993\n",
       " 0.062499993\n",
       " 0.062499993\n",
       " 0.062499993\n",
       " 0.062499993\n",
       " 0.062499993\n",
       " 0.062499993\n",
       " 0.062499993\n",
       " 0.062499993\n",
       " 0.062499993\n",
       " 0.062499993"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "register = circuit(8)*qubits(8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2×2 Array{Float32,2}:\n",
       " 1.0  0.0\n",
       " 0.0  0.0"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M0 = FALSE * transpose(FALSE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "false"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rand() > 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "measure (generic function with 1 method)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "measure(i, n) = transpose(register)*foldr(kron, map(k -> k==i ? M0 : eye, [1:8]...))*register"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "measureAll (generic function with 1 method)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "measureAll(n) = map(v -> measure(v, n), collect(1:8))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8-element Array{Float32,1}:\n",
       " 0.49999988\n",
       " 0.49999988\n",
       " 0.49999988\n",
       " 0.49999994\n",
       " 0.49999994\n",
       " 0.49999994\n",
       " 0.49999994\n",
       " 0.49999994"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "measureAll(8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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