{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "6718709f",
   "metadata": {},
   "source": [
    "# Cartesian Product Operators (Any Spin Half)\n",
    "- Author: Vineeth Francis Thalakottoor\n",
    "- Email: vineeth.thalakottoor@ens.psl.eu or vineethfrancis.physics@gmail.com"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "27a57f94",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the source path\n",
    "SourcePath = '/media/HD2/Vineeth/PostDoc_Simulations/Github/PyOR_V1/PyOR_Combined/PyOR/Source_Doc'\n",
    "\n",
    "# Add source path\n",
    "import sys\n",
    "sys.path.append(SourcePath)\n",
    "import time\n",
    "%matplotlib ipympl\n",
    "\n",
    "# Import PyOR package\n",
    "from PyOR_QuantumSystem import QuantumSystem as QunS\n",
    "from PyOR_Hamiltonian import Hamiltonian\n",
    "from PyOR_DensityMatrix import DensityMatrix\n",
    "from PyOR_QuantumObject import QunObj\n",
    "from PyOR_HardPulse import HardPulse\n",
    "from PyOR_Basis import Basis\n",
    "from PyOR_Evolution import Evolutions\n",
    "from PyOR_Plotting import Plotting\n",
    "import PyOR_SignalProcessing as Spro\n",
    "from PyOR_Commutators import Commutators\n",
    "from PyOR_QuantumLibrary import QuantumLibrary\n",
    "from PyOR_Relaxation import RelaxationProcess"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ab0e39a3",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the spin system\n",
    "#Spin_list = {\"A\" : \"H1\",\"B\" : \"H1\",\"C\" : \"H1\"}\n",
    "Spin_list = {\"A\" : \"H1\",\"B\" : \"H1\"}\n",
    "\n",
    "QS = QunS(Spin_list,PrintDefault=False)\n",
    "\n",
    "# initialize the system\n",
    "QS.Initialize()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "6f86d849",
   "metadata": {},
   "source": [
    "## Product Operator Basis: Spherical Tensors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "efb23439",
   "metadata": {},
   "outputs": [],
   "source": [
    "BS = Basis(QS)\n",
    "\n",
    "Basis_car, Dic_car = BS.ProductOperators_SpinHalf_Cartesian()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "73333478",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Id1 Id2 ',\n",
       " 'Id1 Ix2 ',\n",
       " 'Id1 Iy2 ',\n",
       " 'Id1 Iz2 ',\n",
       " 'Ix1 Id2 ',\n",
       " 'Ix1 Ix2 ',\n",
       " 'Ix1 Iy2 ',\n",
       " 'Ix1 Iz2 ',\n",
       " 'Iy1 Id2 ',\n",
       " 'Iy1 Ix2 ',\n",
       " 'Iy1 Iy2 ',\n",
       " 'Iy1 Iz2 ',\n",
       " 'Iz1 Id2 ',\n",
       " 'Iz1 Ix2 ',\n",
       " 'Iz1 Iy2 ',\n",
       " 'Iz1 Iz2 ']"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Dic_car"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "d0632fe6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0.5 & 0 & 0 & 0\\\\0 & 0.5 & 0 & 0\\\\0 & 0 & 0.5 & 0\\\\0 & 0 & 0 & 0.5\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[0.5,   0,   0,   0],\n",
       "[  0, 0.5,   0,   0],\n",
       "[  0,   0, 0.5,   0],\n",
       "[  0,   0,   0, 0.5]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Basis_car[0].matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "41a46a96",
   "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": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Basis_car[1].matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "9a02a813",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & - 0.5 i & 0 & 0\\\\0.5 i & 0 & 0 & 0\\\\0 & 0 & 0 & - 0.5 i\\\\0 & 0 & 0.5 i & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[    0, -0.5*I,     0,      0],\n",
       "[0.5*I,      0,     0,      0],\n",
       "[    0,      0,     0, -0.5*I],\n",
       "[    0,      0, 0.5*I,      0]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Basis_car[2].matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "cc6ad84e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0.5 & 0 & 0 & 0\\\\0 & -0.5 & 0 & 0\\\\0 & 0 & 0.5 & 0\\\\0 & 0 & 0 & -0.5\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[0.5,    0,   0,    0],\n",
       "[  0, -0.5,   0,    0],\n",
       "[  0,    0, 0.5,    0],\n",
       "[  0,    0,   0, -0.5]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Basis_car[3].matrix"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "90e59b54",
   "metadata": {},
   "source": [
    "### String Index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "5b50848d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['', 'Ix2', 'Iy2', 'Iz2', 'Ix1', 'Ix1Ix2', 'Ix1Iy2', 'Ix1Iz2', 'Iy1', 'Iy1Ix2', 'Iy1Iy2', 'Iy1Iz2', 'Iz1', 'Iz1Ix2', 'Iz1Iy2', 'Iz1Iz2']\n"
     ]
    }
   ],
   "source": [
    "B_car = BS.String_to_Matrix(Dic_car, Basis_car)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "0577a8bb",
   "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": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B_car[\"Ix2\"].matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "a417da06",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0.5 & 0 & 0 & 0\\\\0 & 0.5 & 0 & 0\\\\0 & 0 & 0.5 & 0\\\\0 & 0 & 0 & 0.5\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[0.5,   0,   0,   0],\n",
       "[  0, 0.5,   0,   0],\n",
       "[  0,   0, 0.5,   0],\n",
       "[  0,   0,   0, 0.5]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B_car[''].matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1b3a2cd2",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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