part1_zne.ipynb

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    "# Mitiq Tutorial\n",
    "\n",
    "Before running this tutorial, make sure you have `mitiq` installed.\n",
    "\n",
    "```bash\n",
    "pip install mitiq\n",
    "```\n",
    "\n",
    "Use `pip list | grep mitiq` to ensure it is installed.\n",
    "\n",
    "\n",
    "# Goals\n",
    "\n",
    "- learn how to apply ZNE on a basic workflow\n",
    "- explore other QEM methods via calibration"
   ]
  },
  {
   "cell_type": "code",
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   "source": [
    "# if you're using GitHub codespaces, you can use this to install directly in the notebook\n",
    "%pip install mitiq"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Executors\n",
    "\n",
    "Executors are python functions that consume a quantum circuit, and output an expectation value.\n",
    "A type signature might look something like `Circuit -> float`.\n",
    "That said, executors can have additional arguments used to control other parts of the execution process.\n",
    "The circuit must be the first argument, however."
   ]
  },
  {
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   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import cirq\n",
    "\n",
    "\n",
    "def execute(circuit, noise_level=0.005):\n",
    "    \"\"\"Returns Tr[ρ |0⟩⟨0|] where ρ is the state prepared by the circuit\n",
    "    with depolarizing noise.\"\"\"\n",
    "    # add depolarizing noise\n",
    "    return (\n",
    "        cirq.DensityMatrixSimulator()\n",
    "        .simulate(circuit)\n",
    "        .final_density_matrix[0, 0]\n",
    "        .real\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ZNE\n",
    "\n",
    "First, we define a simple circuit to work with."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   "source": [
    "a, b, c = cirq.LineQubit.range(3)\n",
    "\n",
    "circuit = cirq.Circuit([\n",
    "    cirq.H(a),\n",
    "    cirq.CNOT(a, b),\n",
    "    cirq.CNOT(b, c),\n",
    "    cirq.S(a),\n",
    "])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print(circuit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Unitary Folding\n",
    "\n",
    "Making the circuit longer, and hence noisier."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from mitiq.zne.scaling import fold_gates_at_random, fold_global\n",
    "\n",
    "\n",
    "folded_circuit = \"...\"\n",
    "\n",
    "print(folded_circuit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Extrapolation\n",
    "\n",
    "Computing the Zero-Noise limit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Randomized Benchmarking circuits are circuits that are in effect, equivalent to the identity. Hence, the ideal probability that the end state is $|00\\cdots 0\\rangle$ is 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from mitiq.benchmarks import generate_rb_circuits\n",
    "\n",
    "circuit = generate_rb_circuits(2, num_cliffords=20)[0]\n",
    "\n",
    "# print(circuit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from mitiq import zne\n",
    "\n",
    "\n",
    "true_value = execute(circuit, noise_level=0.0)\n",
    "noisy_value = execute(circuit)\n",
    "zne_value = zne.execute_with_zne(circuit, execute)\n",
    "\n",
    "print(f\"Error w/o  Mitiq: {abs((true_value - noisy_value) / true_value):.3f}\")\n",
    "print(f\"Error w Mitiq:    {abs((true_value - zne_value) / true_value):.3f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise\n",
    "\n",
    "Keeping the circuit the same, can you get a smaller error by modifying some of the ZNE options?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from mitiq.zne.scaling import fold_global, fold_gates_at_random, identity_insertion\n",
    "from mitiq.zne.inference import (\n",
    "    LinearFactory,\n",
    "    RichardsonFactory,\n",
    "    PolyFactory,\n",
    "    ExpFactory,\n",
    ")\n",
    "\n",
    "inference_method = ...  # this will include scale factors, which you can play with!\n",
    "noise_scaling_method = ...\n",
    "\n",
    "zne_value = zne.execute_with_zne(\n",
    "    circuit,\n",
    "    execute,\n",
    "    factory=inference_method,\n",
    "    scale_noise=noise_scaling_method,\n",
    ")\n",
    "\n",
    "print(f\"Error w/o  Mitiq: {abs((true_value - noisy_value) / true_value):.3f}\")\n",
    "print(f\"Error w Mitiq:    {abs((true_value - zne_value) / true_value):.3f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calibration\n",
    "\n",
    "When you want to explore more options"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from mitiq import MeasurementResult\n",
    "\n",
    "\n",
    "def execute_with_depolarizing(circuit, noise_level=0.001):\n",
    "    \"\"\"Return bitstrings outcomes from circuit executions performed by\n",
    "    a density matrix simulation with depolarizing noise.\"\"\"\n",
    "    circuit = circuit.with_noise(cirq.depolarize(p=noise_level))\n",
    "    result = cirq.DensityMatrixSimulator().run(circuit, repetitions=100)\n",
    "    bitstrings = np.column_stack(list(result.measurements.values()))\n",
    "    return MeasurementResult(bitstrings)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from mitiq import Calibrator\n",
    "\n",
    "\n",
    "cal = Calibrator(...)\n",
    "# run the calibration experiments\n",
    "..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "cal.best_strategy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from mitiq.calibration import PECSettings\n",
    "\n",
    "# run calibrator with PEC\n",
    "cal = Calibrator(execute_with_depolarizing, frontend=\"cirq\", settings=PECSettings)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "cal.run(log=True)"
   ]
  }
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