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   "source": [
    "# PyOR Quantum\n",
    "## Author: Vineeth Thalakottoor\n",
    "## Introduction to Zeeman States"
   ]
  },
  {
   "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/PyOR/Source_Doc'\n",
    "\n",
    "# Add source path\n",
    "import sys\n",
    "sys.path.append(SourcePath)\n",
    "\n",
    "# Import PyOR package\n",
    "from PyOR_QuantumSystem import QuantumSystem as QunS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the spin system\n",
    "Spin_list = {\"A\" : \"H1\",\"B\" : \"H1\",\"C\" : \"H1\"}\n",
    "QS = QunS(Spin_list,PrintDefault=False)\n",
    "\n",
    "# initialize the system\n",
    "QS.Initialize()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1.0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[1.0],\n",
       "[  0],\n",
       "[  0],\n",
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       "[  0],\n",
       "[  0],\n",
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       "[  0]])"
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     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X1 = QS.State({\"A\": 1/2,\"B\": 1/2,\"C\": 1/2})\n",
    "X1.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0\\\\1.0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[  0],\n",
       "[1.0],\n",
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       "[  0],\n",
       "[  0]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X2 = QS.State({\"A\": 1/2,\"B\": 1/2,\"C\": -1/2})\n",
    "X2.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0\\\\0\\\\1.0\\\\0\\\\0\\\\0\\\\0\\\\0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[  0],\n",
       "[  0],\n",
       "[1.0],\n",
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       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X3 = QS.State({\"A\": 1/2,\"B\": -1/2,\"C\": 1/2})\n",
    "X3.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0\\\\0\\\\0\\\\1.0\\\\0\\\\0\\\\0\\\\0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[1.0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X4 = QS.State({\"A\": 1/2,\"B\": -1/2,\"C\": -1/2})\n",
    "X4.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0\\\\0\\\\0\\\\0\\\\1.0\\\\0\\\\0\\\\0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[1.0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X5 = QS.State({\"A\": -1/2,\"B\": 1/2,\"C\": 1/2})\n",
    "X5.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0\\\\0\\\\0\\\\0\\\\0\\\\1.0\\\\0\\\\0\\end{matrix}\\right]$"
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       "Matrix([\n",
       "[  0],\n",
       "[  0],\n",
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       "[  0],\n",
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       "[  0],\n",
       "[  0]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X6 = QS.State({\"A\": -1/2,\"B\": 1/2,\"C\": -1/2})\n",
    "X6.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\1.0\\\\0\\end{matrix}\\right]$"
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      "text/plain": [
       "Matrix([\n",
       "[  0],\n",
       "[  0],\n",
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       "[  0],\n",
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       "[1.0],\n",
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      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X7 = QS.State({\"A\": -1/2,\"B\": -1/2,\"C\": 1/2})\n",
    "X7.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\1.0\\end{matrix}\\right]$"
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       "Matrix([\n",
       "[  0],\n",
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       "[  0],\n",
       "[1.0]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X8 = QS.State({\"A\": -1/2,\"B\": -1/2,\"C\": -1/2})\n",
    "X8.matrix"
   ]
  }
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