docs/tutorials/2_simulating_qutrit_circuits.ipynb

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    "# Simulating Qutrit Circuits\n",
    "\n",
    "The `QutritRestlessSimulator` supports circuits with qutrit instructions. These instructions can be\n",
    "unitary or general completely-positive trace-preserving maps. These two types are represented by the\n",
    "`QutritUnitaryGate` and `QutritQuantumChannelOperation` classes respectively.\n",
    "\n",
    "This tutorial covers how to create qutrit circuits and how to simulate them. We use the same types\n",
    "of circuits as in the introductory tutorial but with a leaky initial $R_X(\\pi/2)$ gate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from qiskit import QuantumCircuit\n",
    "from qiskit.circuit.library import RXGate\n",
    "from qiskit.quantum_info import Kraus\n",
    "\n",
    "from restless_simulator.circuit import QutritQuantumChannelOperation, QutritUnitaryGate\n",
    "from restless_simulator.simulator import QutritRestlessSimulator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create simulator\n",
    "simulator = QutritRestlessSimulator()"
   ]
  },
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   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Creating Qutrit Circuits\n",
    "\n",
    "Qutrit circuits are standard Qiskit `QuantumCircuit` instances but with special qutrit\n",
    "instructions, which we add using `QuantumCircuit.append`. The simulator supports mixed instructions,\n",
    "allowing for qubit and qutrit instructions to coexist in the same circuit. Qubit instructions will\n",
    "be converted from their $2\\times{}2$ unitaries to ideal $3\\times{}3$ unitaries."
   ]
  },
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   "source": [
    "In this section we will look at creating a _leaky_ variant of the circuit in the `introduction to\n",
    "the simulator` tutorial, i.e., a leaky $R_X(\\pi/2)$ gate followed by a sequence of ideal $R_X(\\pi/3)$\n",
    "gates. The leaky gate will reduce the contrast of our measurements as the $|2\\rangle$ population\n",
    "will now be non-zero. The $R_X(\\pi/3)$ gates will not interact with the $|2\\rangle$-state population\n",
    "as they are ideal. The default measurement assignment for the simulator assigns the `\"1\"` label to\n",
    "the $|2\\rangle$ state, which means that by default it cannot distinguish between $|1\\rangle$ and\n",
    "$|2\\rangle$. This can be changed by setting the `meas_assignment_mat` option of the simulator.\n",
    "\n",
    "First we create a NumPy array of our leaky unitary gate as an ideal $R_X(\\pi/2)$ rotation between\n",
    "$|0\\rangle$ and $|1\\rangle$ and a small rotation from $|1\\rangle$ into the $|2\\rangle$ state. This\n",
    "final rotation is controlled by the `leakage_rotation` variable.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Variable to control leakage\n",
    "leakage_rotation = np.pi / 16\n",
    "# Construct leaky gate as two rotations.\n",
    "leaky_unitary = (\n",
    "    # very small rotation from |1> to |2>\n",
    "    np.array(\n",
    "        [\n",
    "            [1, 0, 0],\n",
    "            [0, np.cos(leakage_rotation / 2), -1j * np.sin(leakage_rotation / 2)],\n",
    "            [0, -1j * np.sin(leakage_rotation / 2), np.cos(leakage_rotation / 2)],\n",
    "        ],\n",
    "    )\n",
    "    # X-pi/2 rotation between |0> and |1>\n",
    "    @ np.array(\n",
    "        [\n",
    "            [np.cos(np.pi / 4), -1j * np.sin(np.pi / 4), 0],\n",
    "            [-1j * np.sin(np.pi / 4), np.cos(np.pi / 4), 0],\n",
    "            [0, 0, 1],\n",
    "        ]\n",
    "    )\n",
    ")\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we have our leaky unitary, we create an instance of `QutritUnitaryGate` with our unitary\n",
    "matrix. We then construct leaky circuits and use our leaky gate as the first gate. We also create\n",
    "circuits with an ideal $R_X(\\pi/2)$ gate against which we will compare our measurements.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "leaky_gate = QutritUnitaryGate(leaky_unitary, label=\"U(pi/2)\")\n",
    "ideal_gate = RXGate(np.pi / 2)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "N_CIRCUITS = 10\n",
    "leaky_circuits = []\n",
    "ideal_circuits = []\n",
    "for n in range(N_CIRCUITS):\n",
    "    # Create leaky circuit\n",
    "    nth_circ = QuantumCircuit(1)\n",
    "    # Add leaky gate to qubit/qutrit 0.\n",
    "    nth_circ.append(\n",
    "        leaky_gate,\n",
    "        [0],\n",
    "    )\n",
    "    # Add ideal qubit RX(pi/3) gates.\n",
    "    for _ in range(n):\n",
    "        nth_circ.rx(np.pi / 3, 0)\n",
    "    leaky_circuits.append(nth_circ)\n",
    "\n",
    "    # Create ideal circuit\n",
    "    nth_ideal_circ = QuantumCircuit(1)\n",
    "    nth_ideal_circ.append(\n",
    "        ideal_gate,\n",
    "        [0],\n",
    "    )\n",
    "    for _ in range(n):\n",
    "        nth_ideal_circ.rx(np.pi / 3, 0)\n",
    "    ideal_circuits.append(nth_ideal_circ)\n"
   ]
  },
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   "attachments": {},
   "cell_type": "markdown",
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   "source": [
    "Here we can compare the ideal and leaky circuits. Notice that only the first gate is different."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">   ┌─────────┐┌─────────┐┌─────────┐┌─────────┐┌─────────┐┌─────────┐»\n",
       "q: ┤ Rx(π/2) ├┤ Rx(π/3) ├┤ Rx(π/3) ├┤ Rx(π/3) ├┤ Rx(π/3) ├┤ Rx(π/3) ├»\n",
       "   └─────────┘└─────────┘└─────────┘└─────────┘└─────────┘└─────────┘»\n",
       "«   ┌─────────┐┌─────────┐┌─────────┐┌─────────┐\n",
       "«q: ┤ Rx(π/3) ├┤ Rx(π/3) ├┤ Rx(π/3) ├┤ Rx(π/3) ├\n",
       "«   └─────────┘└─────────┘└─────────┘└─────────┘</pre>"
      ],
      "text/plain": [
       "   ┌─────────┐┌─────────┐┌─────────┐┌─────────┐┌─────────┐┌─────────┐»\n",
       "q: ┤ Rx(π/2) ├┤ Rx(π/3) ├┤ Rx(π/3) ├┤ Rx(π/3) ├┤ Rx(π/3) ├┤ Rx(π/3) ├»\n",
       "   └─────────┘└─────────┘└─────────┘└─────────┘└─────────┘└─────────┘»\n",
       "«   ┌─────────┐┌─────────┐┌─────────┐┌─────────┐\n",
       "«q: ┤ Rx(π/3) ├┤ Rx(π/3) ├┤ Rx(π/3) ├┤ Rx(π/3) ├\n",
       "«   └─────────┘└─────────┘└─────────┘└─────────┘"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ideal_circuits[-1].draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">   ┌─────────┐┌─────────┐┌─────────┐┌─────────┐┌─────────┐┌─────────┐»\n",
       "q: ┤ U(pi/2) ├┤ Rx(π/3) ├┤ Rx(π/3) ├┤ Rx(π/3) ├┤ Rx(π/3) ├┤ Rx(π/3) ├»\n",
       "   └─────────┘└─────────┘└─────────┘└─────────┘└─────────┘└─────────┘»\n",
       "«   ┌─────────┐┌─────────┐┌─────────┐┌─────────┐\n",
       "«q: ┤ Rx(π/3) ├┤ Rx(π/3) ├┤ Rx(π/3) ├┤ Rx(π/3) ├\n",
       "«   └─────────┘└─────────┘└─────────┘└─────────┘</pre>"
      ],
      "text/plain": [
       "   ┌─────────┐┌─────────┐┌─────────┐┌─────────┐┌─────────┐┌─────────┐»\n",
       "q: ┤ U(pi/2) ├┤ Rx(π/3) ├┤ Rx(π/3) ├┤ Rx(π/3) ├┤ Rx(π/3) ├┤ Rx(π/3) ├»\n",
       "   └─────────┘└─────────┘└─────────┘└─────────┘└─────────┘└─────────┘»\n",
       "«   ┌─────────┐┌─────────┐┌─────────┐┌─────────┐\n",
       "«q: ┤ Rx(π/3) ├┤ Rx(π/3) ├┤ Rx(π/3) ├┤ Rx(π/3) ├\n",
       "«   └─────────┘└─────────┘└─────────┘└─────────┘"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "leaky_circuits[-1].draw()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulating Qutrit Circuits"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We simulate our circuits in exactly the same way as in the first tutorial \"Simulating Circuits with\n",
    "the Restless Simulator\". As we have not modified the measurement assignment matrix, our measurements\n",
    "default to qubit discrimination."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "leaky_job = simulator.run(leaky_circuits)\n",
    "ideal_job = simulator.run(ideal_circuits)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Results"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To plot the results we use the restless post-processing functions provided in the `utils` module of\n",
    "the restless simulator package."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "from restless_simulator.utils import (\n",
    "    extract_memory,\n",
    "    restless_memory_to_memory,\n",
    "    memory_to_probabilities,\n",
    ")\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To compare against the expected results, we also compute the expected probabilities as was done in the introductory tutorial."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "expected_probs = (\n",
    "    0.5 * np.cos(np.pi / 3 * np.arange(N_CIRCUITS, step=0.1) + np.pi / 2) + 0.5\n",
    ")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, the measurements with a leaky initial $R_X(\\pi/2)$ gate contaminate the measurement\n",
    "results and give values that deviate from the ideal. In the next tutorial, \"Standard Circuit\n",
    "Execution with the Restless Simulator\", you will see how the simulator can be used with standard\n",
    "circuit execution and how leakage accumulates during restless circuit execution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Probability to Measure $|0\\\\rangle$')"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(\n",
    "    range(N_CIRCUITS),\n",
    "    memory_to_probabilities(restless_memory_to_memory(extract_memory(leaky_job))),\n",
    "    label=\"Leaky Initial Gate\",\n",
    "    marker=\"o\",\n",
    "    color=\"g\",\n",
    ")\n",
    "plt.scatter(\n",
    "    range(N_CIRCUITS),\n",
    "    memory_to_probabilities(restless_memory_to_memory(extract_memory(ideal_job))),\n",
    "    label=\"Ideal Initial Gate\",\n",
    "    marker=\"x\",\n",
    "    color=\"r\",\n",
    ")\n",
    "plt.plot(np.arange(N_CIRCUITS, step=0.1), expected_probs, linestyle=\"--\", label=\"Ideal Probabilities\")\n",
    "plt.legend(loc=\"lower center\", bbox_to_anchor=(0.5, 1.0), frameon=False)\n",
    "plt.xlabel(\"Number of $R_X(\\\\pi/3)$ Gates\")\n",
    "plt.ylabel(\"Probability to Measure $|0\\\\rangle$\")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "qiskit",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.13"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}