qiskit/density_matrices.ipynb

{
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  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy import pi\n",
    "from qiskit import QuantumCircuit, Aer\n",
    "from qiskit.quantum_info import DensityMatrix\n",
    "from qiskit.visualization import plot_bloch_multivector, plot_state_city\n",
    "from qiskit_textbook.tools import array_to_latex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def show_state(qc):\n",
    "    display(qc.draw())\n",
    "    sim = Aer.get_backend(\"aer_simulator\")\n",
    "    qc.save_statevector()\n",
    "    result = statevector = sim.run(qc).result()\n",
    "    statevector = result.get_statevector()\n",
    "    display(plot_state_city(statevector))\n",
    "    density_matrix = DensityMatrix(statevector)\n",
    "    print(\"Density matrix = \", density_matrix.data)\n",
    "    display(plot_bloch_multivector(statevector))\n",
    "    array_to_latex(statevector, pretext=\"\\\\text{Statevector} = \")\n",
    "    None"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Density matrix for state $\\ket{0}$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "<Figure size 1500x500 with 2 Axes>"
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      "Density matrix =  [[1.+0.j 0.+0.j]\n",
      " [0.+0.j 0.+0.j]]\n"
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      "text/plain": [
       "<Figure size 480x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \n",
       "\\text{Statevector} = \\begin{bmatrix}\n",
       "1 \\\\\n",
       "0\n",
       "\\end{bmatrix}\n",
       "$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qc = QuantumCircuit(1)\n",
    "show_state(qc)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Density matrix for state $\\ket{+}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
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      "text/latex": [
       "$\\displaystyle \n",
       "\\text{Statevector} = \\begin{bmatrix}\n",
       "\\tfrac{1}{\\sqrt{2}} \\\\\n",
       "\\tfrac{1}{\\sqrt{2}}\n",
       "\\end{bmatrix}\n",
       "$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qc = QuantumCircuit(1)\n",
    "qc.h(0)\n",
    "show_state(qc)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Density matrix for state $\\ket{\\Phi^{+}}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "<Figure size 960x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \n",
       "\\text{Statevector} = \\begin{bmatrix}\n",
       "\\tfrac{1}{\\sqrt{2}} \\\\\n",
       "0 \\\\\n",
       "0 \\\\\n",
       "\\tfrac{1}{\\sqrt{2}}\n",
       "\\end{bmatrix}\n",
       "$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qc = QuantumCircuit(2)\n",
    "qc.h(0)\n",
    "qc.cnot(0, 1)\n",
    "show_state(qc)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Density matrix for state $\\ket{\\Psi^{+}}$"
   ]
  },
  {
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      "text/plain": [
       "<Figure size 960x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \n",
       "\\text{Statevector} = \\begin{bmatrix}\n",
       "0 \\\\\n",
       "\\tfrac{1}{\\sqrt{2}} \\\\\n",
       "\\tfrac{1}{\\sqrt{2}} \\\\\n",
       "0\n",
       "\\end{bmatrix}\n",
       "$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qc = QuantumCircuit(2)\n",
    "qc.h(0)\n",
    "qc.cnot(0, 1)\n",
    "qc.x(0)\n",
    "show_state(qc)"
   ]
  }
 ],
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