{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PyOR Quantum\n",
    "### Author: Vineeth Thalakottoor\n",
    "### Introduction to Quantum Library"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the source path\n",
    "SourcePath = '/media/HD2/Vineeth/PostDoc_Simulations/Github/PyOR_V1/PyOR_Combined/Source_Doc'\n",
    "\n",
    "# Add source path\n",
    "import sys\n",
    "sys.path.append(SourcePath)\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "# Import PyOR package\n",
    "from PyOR_QuantumLibrary import QuantumLibrary\n",
    "QLib = QuantumLibrary()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Make two states ket1 and ket2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Quantum object initialized: shape=(2, 1), type='ket', dtype=complex128\n",
      "Quantum object initialized: shape=(2, 1), type='ket', dtype=complex128\n"
     ]
    }
   ],
   "source": [
    "# Make two states ket1 and ket2\n",
    "ket1 = QLib.Basis_Ket(2,0, PrintDefault=True)\n",
    "ket2 = QLib.Basis_Ket(2,1, PrintDefault=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1.0\\\\0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[1.0],\n",
       "[  0]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Matrix form of ket1\n",
    "ket1.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0\\\\1.0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[  0],\n",
       "[1.0]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Matrix form of ket2\n",
    "ket2.matrix"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Create a state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1.0\\\\2.0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[1.0],\n",
       "[2.0]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a state\n",
    "psi1 = 1 * ket1 + 2 * ket2\n",
    "\n",
    "# Matrix form\n",
    "psi1.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}10.0\\\\20.0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[10.0],\n",
       "[20.0]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a state\n",
    "psi2 = 10 * ket1 + 20 * ket2\n",
    "psi2.matrix"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Outer Product"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1.0 & 2.0\\\\2.0 & 4.0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[1.0, 2.0],\n",
       "[2.0, 4.0]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Outer Product\n",
    "rho1 = QLib.OuterProduct(psi1,psi1)\n",
    "\n",
    "# Matrix form\n",
    "rho1.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}100.0 & 200.0\\\\200.0 & 400.0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[100.0, 200.0],\n",
       "[200.0, 400.0]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Outer Product\n",
    "rho2 = QLib.OuterProduct(psi2,psi2)\n",
    "\n",
    "# Matrix form\n",
    "rho2.matrix"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Conversion from density matrix to vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Density matrix to vector\n",
    "QLib.RowColOrder = \"C\" # Vectorize by row\n",
    "#QLib.RowColOrder = \"F\" # Vectorize by col\n",
    "vec1 = QLib.DMToVec(rho1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1.0\\\\2.0\\\\2.0\\\\4.0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[1.0],\n",
       "[2.0],\n",
       "[2.0],\n",
       "[4.0]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Matrix form\n",
    "vec1.matrix"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Conversion from vector to density matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Vector to DM\n",
    "DM1 = QLib.VecToDM(vec1,shape=(2,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1.0 & 2.0\\\\2.0 & 4.0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[1.0, 2.0],\n",
       "[2.0, 4.0]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Matrix form\n",
    "DM1.matrix"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Create a bra state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Quantum object initialized: shape=(1, 2), type='bra', dtype=complex128\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1.0 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([[1.0, 0]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Bra state\n",
    "bra1 = QLib.Basis_Bra(2,0, PrintDefault=True)\n",
    "\n",
    "# Print matrix\n",
    "bra1.matrix"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Import spin operators"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Quantum object initialized: shape=(2, 2), type='operator', dtype=complex128\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & 0.5\\\\0.5 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[  0, 0.5],\n",
       "[0.5,   0]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Sx\n",
    "Sx = QLib.SSpinOp(1/2,\"x\", PrintDefault=True)\n",
    "\n",
    "# show matrix form (Sympy)\n",
    "Sx.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Sy\n",
    "Sy = QLib.SSpinOp(1/2,\"y\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Sz\n",
    "Sz = QLib.SSpinOp(1/2,\"z\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Creating Hamiltonian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0.5 & 0.5 - 0.5 i\\\\0.5 + 0.5 i & -0.5\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[        0.5, 0.5 - 0.5*I],\n",
       "[0.5 + 0.5*I,        -0.5]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H1 = Sx + Sy + Sz\n",
    "H1.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0.5 & 0.5 - 0.5 i\\\\0.5 + 0.5 i & -0.5\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[        0.5, 0.5 - 0.5*I],\n",
       "[0.5 + 0.5*I,        -0.5]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H2 = np.cos(np.pi) * Sz\n",
    "H1.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "False\n"
     ]
    }
   ],
   "source": [
    "H1.Positive()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H1.Hermitian()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Create Identity matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1.0 & 0\\\\0 & 1.0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[1.0,   0],\n",
       "[  0, 1.0]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Id = QLib.Identity(2)\n",
    "Id.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    }
   ],
   "source": [
    "Id.Positive()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Tensor Product"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & 0.5 & 0 & 0\\\\0.5 & 0 & 0 & 0\\\\0 & 0 & 0 & 0.5\\\\0 & 0 & 0.5 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[  0, 0.5,   0,   0],\n",
       "[0.5,   0,   0,   0],\n",
       "[  0,   0,   0, 0.5],\n",
       "[  0,   0, 0.5,   0]])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Sx1 = QLib.TensorProduct(Id,Sx)\n",
    "Sx1.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & 0 & 0.5 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0.5 & 0 & 0 & 0 & 0\\\\0.5 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0.5 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0.5 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0.5\\\\0 & 0 & 0 & 0 & 0.5 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0.5 & 0 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[  0,   0, 0.5,   0,   0,   0,   0,   0],\n",
       "[  0,   0,   0, 0.5,   0,   0,   0,   0],\n",
       "[0.5,   0,   0,   0,   0,   0,   0,   0],\n",
       "[  0, 0.5,   0,   0,   0,   0,   0,   0],\n",
       "[  0,   0,   0,   0,   0,   0, 0.5,   0],\n",
       "[  0,   0,   0,   0,   0,   0,   0, 0.5],\n",
       "[  0,   0,   0,   0, 0.5,   0,   0,   0],\n",
       "[  0,   0,   0,   0,   0, 0.5,   0,   0]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Sx2 = QLib.TensorProductMultiple(Id,Sx,Id)\n",
    "Sx2.matrix"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Direct Sum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0.5 & 0.5 - 0.5 i & 0 & 0\\\\0.5 + 0.5 i & -0.5 & 0 & 0\\\\0 & 0 & -0.5 & 0\\\\0 & 0 & 0 & 0.5\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[        0.5, 0.5 - 0.5*I,    0,   0],\n",
       "[0.5 + 0.5*I,        -0.5,    0,   0],\n",
       "[          0,           0, -0.5,   0],\n",
       "[          0,           0,    0, 0.5]])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "DM4 = QLib.DirectSum(H1,H2)\n",
    "DM4.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1.0\\\\0\\\\0\\\\1.0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[1.0],\n",
       "[  0],\n",
       "[  0],\n",
       "[1.0]])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ket4 = QLib.DirectSum(ket1,ket2)\n",
    "ket4.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & 0.5 & 0 & 0 & 0 & 0\\\\0.5 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & - 0.5 i & 0 & 0\\\\0 & 0 & 0.5 i & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0.5 & 0\\\\0 & 0 & 0 & 0 & 0 & -0.5\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[  0, 0.5,     0,      0,   0,    0],\n",
       "[0.5,   0,     0,      0,   0,    0],\n",
       "[  0,   0,     0, -0.5*I,   0,    0],\n",
       "[  0,   0, 0.5*I,      0,   0,    0],\n",
       "[  0,   0,     0,      0, 0.5,    0],\n",
       "[  0,   0,     0,      0,   0, -0.5]])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "DM5 = QLib.DirectSumMultiple(Sx,Sy,Sz)\n",
    "DM5.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1.0\\\\0\\\\0\\\\1.0\\\\1.0\\\\0\\\\0\\\\1.0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[1.0],\n",
       "[  0],\n",
       "[  0],\n",
       "[1.0],\n",
       "[1.0],\n",
       "[  0],\n",
       "[  0],\n",
       "[1.0]])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ket5 = QLib.DirectSumMultiple(ket1,ket2,ket4)\n",
    "ket5.matrix"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Block Extractor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 1)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ket1.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 1)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ket2.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4, 1)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ket4.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0\\\\1.0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[  0],\n",
       "[1.0]])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ket10 = QLib.BlockExtract(ket5,1,[(2,1),(2,1),(4,1)])\n",
    "ket10.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0.5 & 0\\\\0 & -0.5\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[0.5,    0],\n",
       "[  0, -0.5]])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "DM10 = QLib.BlockExtract(DM5,2,[(2,2),(2,2),(2,2)])\n",
    "DM10.matrix"
   ]
  }
 ],
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