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   "metadata": {},
   "source": [
    "# PyOR Quantum\n",
    "## Author: Vineeth Thalakottoor\n",
    "## Introduction to kets and bras"
   ]
  },
  {
   "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_QuantumLibrary import QuantumLibrary\n",
    "QLib = QuantumLibrary()"
   ]
  },
  {
   "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"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1.0\\\\0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[1.0],\n",
       "[  0]])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ket1 = QLib.Basis_Ket(2,0, PrintDefault=True)\n",
    "ket1.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Quantum object initialized: shape=(2, 1), type='ket', dtype=complex128\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0\\\\1.0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[  0],\n",
       "[1.0]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ket2 = QLib.Basis_Ket(2,1, PrintDefault=True)\n",
    "ket2.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bra1 = QLib.Basis_Bra(2,0, PrintDefault=True)\n",
    "bra1.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Quantum object initialized: shape=(1, 2), type='bra', dtype=complex128\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & 1.0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([[0, 1.0]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bra2 = QLib.Basis_Bra(2,1, PrintDefault=True)\n",
    "bra2.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "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": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a state\n",
    "psi1 = 1 * ket1 + 2 * ket2\n",
    "psi1.matrix"
   ]
  }
 ],
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