mitigation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***Introduction***\n",
    "\n",
    "To begin with we need to imports modules from Cirq and Mitiq libraries to facilitate the simulation of quantum circuits and apply error mitigation strategies such as Zero-Noise Extrapolation (ZNE), Probabilistic Error Cancellation (PEC), and Dynamical Decoupling (DDD).\n",
    "\n",
    "Additionally, it imports specific functions for handling noise models, converting circuits to Mitiq format, and representing operations with local depolarizing noise. These functionalities are crucial for optimizing the performance and accuracy of quantum computations in the presence of noise."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import cirq\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from cirq import DensityMatrixSimulator, depolarize, amplitude_damp # selecting simulator and noise\n",
    "from mitiq.interface import convert_to_mitiq\n",
    "from mitiq.pec.representations.depolarizing import represent_operations_in_circuit_with_local_depolarizing_noise\n",
    "\n",
    "from mitiq import pec, zne, ddd\n",
    "from mitiq.zne.scaling import fold_gates_at_random\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```execute```\n",
    "\n",
    "is the executor with depolarizing noise and amplitude damping noise.\n",
    "\n",
    "\n",
    "- Args:\n",
    "\n",
    "    circuit: The input quantum circuit to be executed.\n",
    "    \n",
    "    noise_level: The level of depolarizing noise to be applied to the circuit, defaults to 0.2.\n",
    "\n",
    "- Returns:\n",
    "\n",
    "    The real part of the matrix element (0,0) of the final density matrix, representing the expectation value of the |0⟩⟨0| state prepared by the circuit executed with depolarizing noise.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def execute(circuit, noise_level=0.2, damp=0.1):\n",
    "    \"\"\"Returns Tr[ρ |0⟩⟨0|] (expectation value)where ρ is the state prepared by the circuit\n",
    "    executed with depolarizing noise.\n",
    "    \"\"\"\n",
    "    mitiq_circuit, _ = convert_to_mitiq(circuit)\n",
    "    noisy_circuit = mitiq_circuit.with_noise(depolarize(p=noise_level))\n",
    "    noisy_circuit = noisy_circuit.with_noise(amplitude_damp(gamma=damp))\n",
    "\n",
    "    return DensityMatrixSimulator().simulate(noisy_circuit).final_density_matrix[0, 0].real #real value of matrix element (0,0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```launch:```\n",
    "\n",
    "helper method in style of a closure that allows launching cascading different types of mitigations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def launch(parent_executor, executor, circuit, **executor_args):\n",
    "   executor = parent_executor(executor=executor, **executor_args)\n",
    "   return executor, executor(circuit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "keys = [\"PEC\", \"ZNE\", \"DDD\", \"DDD_PEC\", \"ZNE_PEC\", \"DDD_PEC_ZNE\"]\n",
    "\n",
    "def calculate(executor, circuit, reps, factory, rule):\n",
    "   values = [0] * 6\n",
    "   pec_executor, values[0] = launch(pec.mitigate_executor, executor, circuit, representations= reps)\n",
    "   _, values[1] = launch(zne.mitigate_executor, executor, circuit, factory=factory)\n",
    "   _, values[2] = launch(ddd.mitigate_executor, executor, circuit, rule=rule)\n",
    "   _, values[3] = launch(ddd.mitigate_executor,pec_executor, circuit, rule = rule)\n",
    "   zne_pec_executor, values[4] = launch(zne.mitigate_executor, pec_executor, circuit, factory=factory)\n",
    "   _, values[5] = launch(ddd.mitigate_executor, zne_pec_executor, circuit, rule=rule)\n",
    "   return values\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Simple circuit that equates to Identity operation (via two X gates)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/homebrew/anaconda3/envs/qrize/lib/python3.11/site-packages/mitiq/zne/inference.py:96: UserWarning: The input circuit is very short. This may reduce the accuracy of noise scaling.\n",
      "  warnings.warn(\n",
      "/opt/homebrew/anaconda3/envs/qrize/lib/python3.11/site-packages/mitiq/zne/inference.py:96: UserWarning: The input circuit is very short. This may reduce the accuracy of noise scaling.\n",
      "  warnings.warn(\n",
      "/opt/homebrew/anaconda3/envs/qrize/lib/python3.11/site-packages/mitiq/zne/inference.py:96: UserWarning: The input circuit is very short. This may reduce the accuracy of noise scaling.\n",
      "  warnings.warn(\n"
     ]
    }
   ],
   "source": [
    "a0 = cirq.q(\"a\")\n",
    "ops4 = [cirq.X(a0), cirq.X(a0)]\n",
    "circuitA = cirq.Circuit(ops4)\n",
    "\n",
    "noise_level = 0.2\n",
    "factory = zne.RichardsonFactory([1.0, 2.0])\n",
    "\n",
    "noisy_valueA= execute(circuitA, noise_level)\n",
    "ideal_valueA= execute(circuitA, noise_level=0.0,damp=0.0)\n",
    "rule = ddd.rules.xx\n",
    "repsA = represent_operations_in_circuit_with_local_depolarizing_noise(circuitA, noise_level)\n",
    "\n",
    "values = calculate(execute, circuitA, repsA, factory, rule)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Different Mitigation strategies and combinations compared against each other"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ideal value 1.0\n",
      "without mitigation 0.73027\n",
      "PEC mitigation   0.91913\n",
      "ZNE mitigation   0.84776\n",
      "DDD mitigation   0.73027\n",
      "DDD_PEC mitigation   0.90341\n",
      "ZNE_PEC mitigation   0.93408\n",
      "DDD_PEC_ZNE mitigation   1.00285\n"
     ]
    }
   ],
   "source": [
    "print(\"ideal value\", ideal_valueA)\n",
    "print(f\"without mitigation {noisy_valueA :.5f}\")\n",
    "for key,value in zip(keys, values):\n",
    "   print(f\"{key} mitigation   {value :.5f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.9191336124860907, 0.8477624058723449, 0.7302666306495667, 0.903408575476367, 0.9340829203466832, 1.002850580650994]\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "# Creating the bar chart\n",
    "def plot_it(keys, values):\n",
    "   plt.figure(figsize=(10, 6))\n",
    "   plt.bar(keys, values, color='skyblue')\n",
    "   plt.xlabel('Strategy')\n",
    "   plt.ylabel('Value')\n",
    "   plt.title('Mitigation values')\n",
    "\n",
    "   # Adding a horizontal line\n",
    "   plt.axhline(y=noisy_valueA, color='r', linestyle='--', label=f'Noisey Value ({noisy_valueA:.2f})')\n",
    "   plt.legend()  # Display a legend\n",
    "\n",
    "   plt.show()\n",
    "print(values)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "ZNE_PEC combination stack as the best combination for the combo of amplitude dampening and noise errors. This can easily vary for different scripts and needs more analysis before a claim can be made"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_it(keys, values)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A larger circuit that takes over 4 hrs to execute."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/homebrew/anaconda3/envs/qrize/lib/python3.11/site-packages/mitiq/zne/inference.py:96: UserWarning: The input circuit is very short. This may reduce the accuracy of noise scaling.\n",
      "  warnings.warn(\n",
      "/opt/homebrew/anaconda3/envs/qrize/lib/python3.11/site-packages/mitiq/zne/inference.py:96: UserWarning: The input circuit is very short. This may reduce the accuracy of noise scaling.\n",
      "  warnings.warn(\n",
      "/opt/homebrew/anaconda3/envs/qrize/lib/python3.11/site-packages/mitiq/pec/pec.py:123: LargeSampleWarning: The number of PEC samples is very large. It may take several minutes. It may be necessary to reduce 'precision' or 'num_samples'.\n",
      "  warnings.warn(_LARGE_SAMPLE_WARN, LargeSampleWarning)\n",
      "/opt/homebrew/anaconda3/envs/qrize/lib/python3.11/site-packages/mitiq/zne/inference.py:96: UserWarning: The input circuit is very short. This may reduce the accuracy of noise scaling.\n",
      "  warnings.warn(\n",
      "/opt/homebrew/anaconda3/envs/qrize/lib/python3.11/site-packages/mitiq/pec/pec.py:123: LargeSampleWarning: The number of PEC samples is very large. It may take several minutes. It may be necessary to reduce 'precision' or 'num_samples'.\n",
      "  warnings.warn(_LARGE_SAMPLE_WARN, LargeSampleWarning)\n"
     ]
    }
   ],
   "source": [
    "a0 = cirq.q(\"a\")\n",
    "ops1 = [cirq.H(a0), cirq.H(a0), cirq.H(a0), cirq.H(a0)]\n",
    "circuitA = cirq.Circuit(ops1)\n",
    "\n",
    "noise_level = 0.2\n",
    "factory = zne.RichardsonFactory([1.0, 2.0])\n",
    "\n",
    "noisy_valueA= execute(circuitA, noise_level)\n",
    "ideal_valueA= execute(circuitA, noise_level=0.0, damp=0.0)\n",
    "rule = ddd.rules.xx\n",
    "repsA = represent_operations_in_circuit_with_local_depolarizing_noise(circuitA, noise_level)\n",
    "\n",
    "values = calculate(execute, circuitA, repsA, factory, rule)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_it(keys, values)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "qrize",
   "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": "3.11.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}