{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# AIM: Logical Anderson Impurity Model on Sqale using CUDA-Q "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "beautiful-navigation",
   "metadata": {},
   "source": [
    "[![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/Infleqtion/client-superstaq/blob/main/docs/source/apps/cudaq_logical_aim.ipynb) [![Launch Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/Infleqtion/client-superstaq/HEAD?labpath=docs/source/apps/cudaq_logical_aim.ipynb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ground state quantum chemistry—computing total energies of molecular configurations to within chemical accuracy—is perhaps the most highly-touted industrial application of fault-tolerant quantum computers. Strongly correlated materials, for example, are particularly interesting, and tools like dynamical mean-field theory (DMFT) allow one to account for the effect of their strong, localized electronic correlations. These DMFT models help predict material properties by approximating the system as a single site impurity inside a “bath” that encompasses the rest of the system. Simulating such dynamics can be a tough task using classical methods, but can be done efficiently on a quantum computer via quantum simulation.\n",
    "\n",
    "In this notebook, we showcase a workflow for preparing the ground state of the minimal single-impurity Anderson model (SIAM) using the Hamiltonian Variational Ansatz for a range of realistic parameters. As a first step towards running DMFT on a fault-tolerant quantum computer, we will use logical qubits encoded in the `[[4, 2, 2]]` code. Using this workflow, we will obtain the ground state energy estimates via noisy simulation, and then also execute the corresponding optimized circuits on Infleqtion's gate-based neutral-atom quantum computer, making the benefits of logical qubits apparent. More details can be found in our [paper](https://arxiv.org/abs/2412.07670)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This demo notebook uses CUDA-Q (`cudaq`) and a CUDA-QX library, `cudaq-solvers`; let us first begin by importing (and installing as needed) these packages:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from __future__ import annotations\n",
    "\n",
    "try:\n",
    "    import cudaq\n",
    "    import cudaq_solvers as solvers\n",
    "    import matplotlib.pyplot as plt\n",
    "except ImportError:\n",
    "    print(\"Installing required packages...\")\n",
    "    %pip install --quiet 'cudaq-solvers' 'matplotlib'\n",
    "    print(\"Installed `cudaq`, `cudaq-solvers`, and `matplotlib` packages.\")\n",
    "    print(\"You may need to restart the kernel to import newly installed packages.\")\n",
    "    import cudaq\n",
    "    import cudaq_solvers as solvers\n",
    "    import matplotlib.pyplot as plt\n",
    "\n",
    "import os\n",
    "from collections.abc import Mapping, Sequence\n",
    "\n",
    "import numpy as np\n",
    "from scipy.optimize import minimize"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Performing logical Variational Quantum Eigensolver (VQE) with CUDA-QX"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To prepare our ground state quantum Anderson impurity model circuits (referred to as AIM circuits in this notebook for short), we use VQE to train an ansatz to minimize a Hamiltonian and obtain optimal angles that can be used to set the AIM circuits. As described in our [paper](https://arxiv.org/abs/2412.07670), the associated restricted Hamiltonian for our SIAM can be reduced to,\n",
    "$$  \n",
    "\\begin{equation}\n",
    "H_{(U, V)} = U (Z_0 Z_2 - 1) / 4 + V (X_0 + X_2),\n",
    "\\end{equation}\n",
    "$$\n",
    "where $U$ is the Coulomb interaction and $V$ the hybridization strength. In this notebook workflow, we will optimize over a 2-dimensional grid of Hamiltonian parameter values, namely $U\\in \\{1, 5, 9\\}$ and $V\\in \\{-9, -1, 7\\}$ (with all values assumed to be in units of eV), to ensure that the ansatz is generally trainable and expressive, and obtain 9 different circuit layers identified by the key $(U, V)$. We will simulate the VQE on GPU (or optionally on CPU if you do not have GPU access), enabled by CUDA-Q, in the absence of noise:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "if cudaq.num_available_gpus() == 0:\n",
    "    cudaq.set_target(\"qpp-cpu\", option=\"fp64\")\n",
    "else:\n",
    "    cudaq.set_target(\"nvidia\", option=\"fp64\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This workflow can be easily defined in CUDA-Q as shown in the cell below, using the CUDA-QX Solvers library (which accelerates quantum algorithms like the VQE):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ansatz(n_qubits: int) -> cudaq.Kernel:\n",
    "    # Create a CUDA-Q parameterized kernel\n",
    "    paramterized_ansatz, variational_angles = cudaq.make_kernel(list)\n",
    "    qubits = paramterized_ansatz.qalloc(n_qubits)\n",
    "\n",
    "    # Using |+> as the initial state:\n",
    "    paramterized_ansatz.h(qubits[0])\n",
    "    paramterized_ansatz.cx(qubits[0], qubits[1])\n",
    "\n",
    "    paramterized_ansatz.rx(variational_angles[0], qubits[0])\n",
    "    paramterized_ansatz.cx(qubits[0], qubits[1])\n",
    "    paramterized_ansatz.rz(variational_angles[1], qubits[1])\n",
    "    paramterized_ansatz.cx(qubits[0], qubits[1])\n",
    "    return paramterized_ansatz\n",
    "\n",
    "\n",
    "def run_logical_vqe(cudaq_hamiltonian: cudaq.SpinOperator) -> tuple[float, list[float]]:\n",
    "    # Set seed for easier reproduction\n",
    "    rng = np.random.default_rng(42)\n",
    "\n",
    "    # Initial angles for the optimizer\n",
    "    init_angles = rng.random(2) * 1e-1\n",
    "\n",
    "    # Obtain CUDA-Q Ansatz\n",
    "    num_qubits = cudaq_hamiltonian.get_qubit_count()\n",
    "    variational_kernel = ansatz(num_qubits)\n",
    "\n",
    "    # Perform VQE optimization\n",
    "    energy, params, _ = solvers.vqe(\n",
    "        variational_kernel,\n",
    "        cudaq_hamiltonian,\n",
    "        init_angles,\n",
    "        optimizer=minimize,\n",
    "        method=\"SLSQP\",\n",
    "        tol=1e-10,\n",
    "    )\n",
    "    return energy, params"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Constructing circuits in the `[[4,2,2]]` encoding"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `[[4,2,2]]` code is a quantum error detection code that uses four physical qubits to encode two logical qubits. In this notebook, we will construct two variants of quantum circuits: physical (bare, unencoded) and logical (encoded). These circuits will be informed by the Hamiltonian Variational Ansatz described earlier. To measure all the terms in our Hamiltonian, we will measure the data qubits in both the $Z$- and $X$-basis, as allowed by the `[[4,2,2]]` logical gateset. Full details on the circuit constructions are outlined in our [paper](https://arxiv.org/abs/2412.07670)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below, we create functions to build our CUDA-Q AIM circuits, both physical and logical versions. As we consider noisy simulation in this notebook, we will include some noisy gates. Here, for simplicity, we will just register a custom identity gate -- to be later used as a noisy operation to model readout error: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "cudaq.register_operation(\"meas_id\", np.identity(2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def aim_physical_circuit(\n",
    "    angles: list[float], basis: str, *, ignore_meas_id: bool = False\n",
    ") -> cudaq.Kernel:\n",
    "    kernel = cudaq.make_kernel()\n",
    "    qubits = kernel.qalloc(2)\n",
    "\n",
    "    # Bell state prep\n",
    "    kernel.h(qubits[0])\n",
    "    kernel.cx(qubits[0], qubits[1])\n",
    "\n",
    "    # Rx Gate\n",
    "    kernel.rx(angles[0], qubits[0])\n",
    "\n",
    "    # ZZ rotation\n",
    "    kernel.cx(qubits[0], qubits[1])\n",
    "    kernel.rz(angles[1], qubits[1])\n",
    "    kernel.cx(qubits[0], qubits[1])\n",
    "\n",
    "    if basis == \"z_basis\":\n",
    "        if not ignore_meas_id:\n",
    "            kernel.for_loop(\n",
    "                start=0,\n",
    "                stop=2,\n",
    "                function=lambda q_idx: getattr(kernel, \"meas_id\")(qubits[q_idx]),  # noqa: B009\n",
    "            )\n",
    "        kernel.mz(qubits)\n",
    "    elif basis == \"x_basis\":\n",
    "        kernel.h(qubits)\n",
    "        if not ignore_meas_id:\n",
    "            kernel.for_loop(\n",
    "                start=0,\n",
    "                stop=2,\n",
    "                function=lambda q_idx: getattr(kernel, \"meas_id\")(qubits[q_idx]),  # noqa: B009\n",
    "            )\n",
    "        kernel.mz(qubits)\n",
    "    else:\n",
    "        raise ValueError(\"Unsupported basis provided:\", basis)\n",
    "    return kernel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def aim_logical_circuit(\n",
    "    angles: list[float], basis: str, *, ignore_meas_id: bool = False\n",
    ") -> cudaq.Kernel:\n",
    "    kernel = cudaq.make_kernel()\n",
    "    qubits = kernel.qalloc(6)\n",
    "\n",
    "    kernel.for_loop(start=0, stop=3, function=lambda idx: kernel.h(qubits[idx]))\n",
    "    kernel.cx(qubits[1], qubits[4])\n",
    "    kernel.cx(qubits[2], qubits[3])\n",
    "    kernel.cx(qubits[0], qubits[1])\n",
    "    kernel.cx(qubits[0], qubits[3])\n",
    "\n",
    "    # Rx teleportation\n",
    "    kernel.rx(angles[0], qubits[0])\n",
    "\n",
    "    kernel.cx(qubits[0], qubits[1])\n",
    "    kernel.cx(qubits[0], qubits[3])\n",
    "    kernel.h(qubits[0])\n",
    "\n",
    "    if basis == \"z_basis\":\n",
    "        if not ignore_meas_id:\n",
    "            kernel.for_loop(\n",
    "                start=0,\n",
    "                stop=5,\n",
    "                function=lambda idx: getattr(kernel, \"meas_id\")(qubits[idx]),  # noqa: B009\n",
    "            )\n",
    "        kernel.mz(qubits)\n",
    "    elif basis == \"x_basis\":\n",
    "        # ZZ rotation and teleportation\n",
    "        kernel.cx(qubits[3], qubits[5])\n",
    "        kernel.cx(qubits[2], qubits[5])\n",
    "        kernel.rz(angles[1], qubits[5])\n",
    "        kernel.cx(qubits[1], qubits[5])\n",
    "        kernel.cx(qubits[4], qubits[5])\n",
    "        kernel.for_loop(start=1, stop=5, function=lambda idx: kernel.h(qubits[idx]))\n",
    "        if not ignore_meas_id:\n",
    "            kernel.for_loop(\n",
    "                start=0,\n",
    "                stop=6,\n",
    "                function=lambda idx: getattr(kernel, \"meas_id\")(qubits[idx]),  # noqa: B009\n",
    "            )\n",
    "        kernel.mz(qubits)\n",
    "    else:\n",
    "        raise ValueError(\"Unsupported basis provided:\", basis)\n",
    "    return kernel"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the circuit definitions above, we can now define a function that automatically runs the VQE and constructs a dictionary containing all the AIM circuits we want to submit to hardware (or noisily simulate):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate_circuit_set(ignore_meas_id: bool = False) -> object:\n",
    "    u_vals = [1, 5, 9]\n",
    "    v_vals = [-9, -1, 7]\n",
    "    circuit_dict = {}\n",
    "    for u in u_vals:\n",
    "        for v in v_vals:\n",
    "            qubit_hamiltonian = (\n",
    "                0.25 * u * cudaq.spin.z(0) * cudaq.spin.z(1)\n",
    "                - 0.25 * u\n",
    "                + v * cudaq.spin.x(0)\n",
    "                + v * cudaq.spin.x(1)\n",
    "            )\n",
    "            _, opt_params = run_logical_vqe(qubit_hamiltonian)\n",
    "            angles = [float(angle) for angle in opt_params]\n",
    "            print(f\"Computed optimal angles={angles} for U={u}, V={v}\")\n",
    "\n",
    "            tmp_physical_dict = {}\n",
    "            tmp_logical_dict = {}\n",
    "            for basis in (\"z_basis\", \"x_basis\"):\n",
    "                tmp_physical_dict[basis] = aim_physical_circuit(\n",
    "                    angles, basis, ignore_meas_id=ignore_meas_id\n",
    "                )\n",
    "                tmp_logical_dict[basis] = aim_logical_circuit(\n",
    "                    angles, basis, ignore_meas_id=ignore_meas_id\n",
    "                )\n",
    "\n",
    "            circuit_dict[f\"{u}:{v}\"] = {\n",
    "                \"physical\": tmp_physical_dict,\n",
    "                \"logical\": tmp_logical_dict,\n",
    "            }\n",
    "    print(\"\\nFinished building optimized circuits!\")\n",
    "    return circuit_dict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computed optimal angles=[1.5846845738799267, 1.5707961678256028] for U=1, V=-9\n",
      "Computed optimal angles=[4.588033710930825, 4.712388365176642] for U=1, V=-1\n",
      "Computed optimal angles=[-1.588651490745171, 1.5707962742876598] for U=1, V=7\n",
      "Computed optimal angles=[1.64012940802256, 1.5707963354922125] for U=5, V=-9\n",
      "Computed optimal angles=[2.1293956916868737, 1.5707963294715355] for U=5, V=-1\n",
      "Computed optimal angles=[-1.6598458659836037, 1.570796331040382] for U=5, V=7\n",
      "Computed optimal angles=[1.695151467539617, 1.5707960973500679] for U=9, V=-9\n",
      "Computed optimal angles=[2.4149519241823376, 1.5707928509325972] for U=9, V=-1\n",
      "Computed optimal angles=[-1.7301462729177735, 1.570796033796985] for U=9, V=7\n",
      "\n",
      "Finished building optimized circuits!\n"
     ]
    }
   ],
   "source": [
    "sim_circuit_dict = generate_circuit_set()\n",
    "circuit_layers = sim_circuit_dict.keys()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Setting up submission and decoding workflow "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this section, we define various helper functions that will play a role in generating the associated energies of the AIM circuits based on the circuit samples (in the different bases), as well as decode the logical circuits with post-selection informed by the `[[4,2,2]]` code:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def _num_qubits(counts: Mapping[str, float]) -> int:\n",
    "    for key in counts:\n",
    "        if key.isdecimal():\n",
    "            return len(key)\n",
    "    return 0\n",
    "\n",
    "\n",
    "def process_counts(\n",
    "    counts: Mapping[str, float],\n",
    "    data_qubits: Sequence[int],\n",
    "    flag_qubits: Sequence[int] = (),\n",
    ") -> dict[str, float]:\n",
    "    new_data: dict[str, float] = {}\n",
    "    for key, val in counts.items():\n",
    "        if not all(key[i] == \"0\" for i in flag_qubits):\n",
    "            continue\n",
    "\n",
    "        new_key = \"\".join(key[i] for i in data_qubits)\n",
    "\n",
    "        if not set(\"01\").issuperset(new_key):\n",
    "            continue\n",
    "\n",
    "        new_data.setdefault(new_key, 0)\n",
    "        new_data[new_key] += val\n",
    "\n",
    "    return new_data\n",
    "\n",
    "\n",
    "def decode(counts: Mapping[str, float]) -> dict[str, float]:\n",
    "    \"\"\"Decode physical counts into logical counts. Should be called after `process_counts`.\"\"\"\n",
    "    if not counts:\n",
    "        return {}\n",
    "\n",
    "    num_qubits = _num_qubits(counts)\n",
    "    assert num_qubits % 4 == 0\n",
    "\n",
    "    physical_to_logical = {\n",
    "        \"0000\": \"00\",\n",
    "        \"1111\": \"00\",\n",
    "        \"0011\": \"01\",\n",
    "        \"1100\": \"01\",\n",
    "        \"0101\": \"10\",\n",
    "        \"1010\": \"10\",\n",
    "        \"0110\": \"11\",\n",
    "        \"1001\": \"11\",\n",
    "    }\n",
    "\n",
    "    new_data: dict[str, float] = {}\n",
    "    for key, val in counts.items():\n",
    "        physical_keys = [key[i : i + 4] for i in range(0, num_qubits, 4)]\n",
    "        logical_keys = [physical_to_logical.get(physical_key) for physical_key in physical_keys]\n",
    "        if None not in logical_keys:\n",
    "            new_key = \"\".join(logical_keys)\n",
    "            new_data.setdefault(new_key, 0)\n",
    "            new_data[new_key] += val\n",
    "\n",
    "    return new_data\n",
    "\n",
    "\n",
    "def ev_x(counts: Mapping[str, float]) -> float:\n",
    "    ev = 0.0\n",
    "\n",
    "    for k, val in counts.items():\n",
    "        ev += val * ((-1) ** int(k[0]) + (-1) ** int(k[1]))\n",
    "\n",
    "    total = sum(counts.values())\n",
    "    ev /= total\n",
    "    return ev\n",
    "\n",
    "\n",
    "def ev_xx(counts: Mapping[str, float]) -> float:\n",
    "    ev = 0.0\n",
    "\n",
    "    for k, val in counts.items():\n",
    "        ev += val * (-1) ** k.count(\"1\")\n",
    "\n",
    "    total = sum(counts.values())\n",
    "    ev /= total\n",
    "    return ev\n",
    "\n",
    "\n",
    "def ev_zz(counts: Mapping[str, float]) -> float:\n",
    "    ev = 0.0\n",
    "\n",
    "    for k, val in counts.items():\n",
    "        ev += val * (-1) ** k.count(\"1\")\n",
    "\n",
    "    total = sum(counts.values())\n",
    "    ev /= total\n",
    "    return ev\n",
    "\n",
    "\n",
    "def aim_logical_energies(\n",
    "    data_ordering: object, counts_list: Sequence[dict[str, float]]\n",
    ") -> tuple[dict[tuple[int, int], float], dict[tuple[int, int], float]]:\n",
    "    counts_data = {\n",
    "        data_ordering[i]: decode(\n",
    "            process_counts(\n",
    "                counts,\n",
    "                data_qubits=[1, 2, 3, 4],\n",
    "                flag_qubits=[0, 5],\n",
    "            )\n",
    "        )\n",
    "        for i, counts in enumerate(counts_list)\n",
    "    }\n",
    "    return _aim_energies(counts_data)\n",
    "\n",
    "\n",
    "def aim_physical_energies(\n",
    "    data_ordering: object, counts_list: Sequence[dict[str, float]]\n",
    ") -> tuple[dict[tuple[int, int], float], dict[tuple[int, int], float]]:\n",
    "    counts_data = {\n",
    "        data_ordering[i]: process_counts(\n",
    "            counts,\n",
    "            data_qubits=[0, 1],\n",
    "        )\n",
    "        for i, counts in enumerate(counts_list)\n",
    "    }\n",
    "    return _aim_energies(counts_data)\n",
    "\n",
    "\n",
    "def _aim_energies(\n",
    "    counts_data: Mapping[tuple[int, int, str], dict[str, float]],\n",
    ") -> tuple[dict[tuple[int, int], float], dict[tuple[int, int], float]]:\n",
    "    evxs: dict[tuple[int, int], float] = {}\n",
    "    evxxs: dict[tuple[int, int], float] = {}\n",
    "    evzzs: dict[tuple[int, int], float] = {}\n",
    "    totals: dict[tuple[int, int], float] = {}\n",
    "\n",
    "    for key, counts in counts_data.items():\n",
    "        h_params, basis = key\n",
    "        key_a, key_b = h_params.split(\":\")\n",
    "        u, v = int(key_a), int(key_b)\n",
    "        if basis.startswith(\"x\"):\n",
    "            evxs[u, v] = ev_x(counts)\n",
    "            evxxs[u, v] = ev_xx(counts)\n",
    "        else:\n",
    "            evzzs[u, v] = ev_zz(counts)\n",
    "\n",
    "        totals.setdefault((u, v), 0)\n",
    "        totals[u, v] += sum(counts.values())\n",
    "\n",
    "    energies = {}\n",
    "    uncertainties = {}\n",
    "    for u, v in evxs.keys() & evzzs.keys():\n",
    "        string_key = f\"{u}:{v}\"\n",
    "        energies[string_key] = u * (evzzs[u, v] - 1) / 4 + v * evxs[u, v]\n",
    "\n",
    "        uncertainty_xx = 2 * v**2 * (1 + evxxs[u, v]) - u * v * evxs[u, v] / 2\n",
    "        uncertainty_zz = u**2 * (1 - evzzs[u, v]) / 2\n",
    "\n",
    "        uncertainties[string_key] = np.sqrt(\n",
    "            (uncertainty_zz + uncertainty_xx - energies[string_key] ** 2) / (totals[u, v] / 2)\n",
    "        )\n",
    "\n",
    "    return energies, uncertainties\n",
    "\n",
    "\n",
    "def _get_energy_diff(\n",
    "    bf_energies: dict[str, float],\n",
    "    physical_energies: dict[str, float],\n",
    "    logical_energies: dict[str, float],\n",
    ") -> tuple[list[float], list[float]]:\n",
    "    physical_energy_diff = []\n",
    "    logical_energy_diff = []\n",
    "\n",
    "    # Data ordering following `bf_energies` keys\n",
    "    for layer, bf_energy in bf_energies.items():\n",
    "        physical_sim_energy = physical_energies[layer]\n",
    "        logical_sim_energy = logical_energies[layer]\n",
    "        true_energy = bf_energy\n",
    "        u, v = layer.split(\":\")\n",
    "        print(f\"Layer=({u}, {v}) has brute-force energy of: {true_energy}\")\n",
    "        print(f\"Physical circuit of layer=({u}, {v}) got an energy of: {physical_sim_energy}\")\n",
    "        print(f\"Logical circuit of layer=({u}, {v}) got an energy of: {logical_sim_energy}\")\n",
    "        print(\"-\" * 72)\n",
    "\n",
    "        if logical_sim_energy < physical_sim_energy:\n",
    "            print(\"Logical circuit achieved the lower energy!\")\n",
    "        else:\n",
    "            print(\"Physical circuit achieved the lower energy\")\n",
    "        print(\"-\" * 72, \"\\n\")\n",
    "\n",
    "        physical_energy_diff.append(\n",
    "            -1 * (true_energy - physical_sim_energy)\n",
    "        )  # Multiply by -1 since negative energies\n",
    "        logical_energy_diff.append(-1 * (true_energy - logical_sim_energy))\n",
    "    return physical_energy_diff, logical_energy_diff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def submit_aim_circuits(\n",
    "    circuit_dict: object,\n",
    "    *,\n",
    "    folder_path: str = \"future_aim_results\",\n",
    "    shots_count: int = 1000,\n",
    "    noise_model: cudaq.mlir._mlir_libs._quakeDialects.cudaq_runtime.NoiseModel | None = None,\n",
    "    run_async: bool = False,\n",
    ") -> dict[str, list[dict[str, int]]] | None:\n",
    "    if run_async:\n",
    "        os.makedirs(folder_path, exist_ok=True)\n",
    "    else:\n",
    "        aim_results = {\"physical\": [], \"logical\": []}\n",
    "\n",
    "    for layer in circuit_dict.keys():\n",
    "        if run_async:\n",
    "            print(f\"Posting circuits associated with layer=('{layer}')\")\n",
    "        else:\n",
    "            print(f\"Running circuits associated with layer=('{layer}')\")\n",
    "\n",
    "        for basis in (\"z_basis\", \"x_basis\"):\n",
    "            if run_async:\n",
    "                u, v = layer.split(\":\")\n",
    "\n",
    "                tmp_physical_results = cudaq.sample_async(\n",
    "                    circuit_dict[layer][\"physical\"][basis], shots_count=shots_count\n",
    "                )\n",
    "                with open(\n",
    "                    f\"{folder_path}/physical_{basis}_job_u={u}_v={v}_result.txt\", \"w\"\n",
    "                ) as file:\n",
    "                    file.write(str(tmp_physical_results))\n",
    "\n",
    "                tmp_logical_results = cudaq.sample_async(\n",
    "                    circuit_dict[layer][\"logical\"][basis], shots_count=shots_count\n",
    "                )\n",
    "                with open(f\"{folder_path}/logical_{basis}_job_u={u}_v={v}_result.txt\", \"w\") as file:\n",
    "                    file.write(str(tmp_logical_results))\n",
    "            else:\n",
    "                tmp_physical_results = cudaq.sample(\n",
    "                    circuit_dict[layer][\"physical\"][basis],\n",
    "                    shots_count=shots_count,\n",
    "                    noise_model=noise_model,\n",
    "                )\n",
    "                tmp_logical_results = cudaq.sample(\n",
    "                    circuit_dict[layer][\"logical\"][basis],\n",
    "                    shots_count=shots_count,\n",
    "                    noise_model=noise_model,\n",
    "                )\n",
    "                aim_results[\"physical\"].append({k: v for k, v in tmp_physical_results.items()})\n",
    "                aim_results[\"logical\"].append({k: v for k, v in tmp_logical_results.items()})\n",
    "    if not run_async:\n",
    "        print(\"\\nCompleted all circuit sampling!\")\n",
    "        return aim_results\n",
    "    print(\"\\nAll circuits submitted for async sampling!\")\n",
    "    return None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def _get_async_results(\n",
    "    layers: object, *, folder_path: str = \"future_aim_results\"\n",
    ") -> dict[str, list[dict[str, int]]]:\n",
    "    aim_results = {\"physical\": [], \"logical\": []}\n",
    "    for layer in layers:\n",
    "        print(f\"Retrieving all circuits counts associated with layer=('{layer}')\")\n",
    "        u, v = layer.split(\":\")\n",
    "        for basis in (\"z_basis\", \"x_basis\"):\n",
    "            with open(f\"{folder_path}/physical_{basis}_job_u={u}_v={v}_result.txt\") as file:\n",
    "                tmp_physical_results = cudaq.AsyncSampleResult(str(file.read()))\n",
    "            physical_counts = tmp_physical_results.get()\n",
    "\n",
    "            with open(f\"{folder_path}/logical_{basis}_job_u={u}_v={v}_result.txt\") as file:\n",
    "                tmp_logical_results = cudaq.AsyncSampleResult(str(file.read()))\n",
    "            logical_counts = tmp_logical_results.get()\n",
    "\n",
    "            aim_results[\"physical\"].append({k: v for k, v in physical_counts.items()})\n",
    "            aim_results[\"logical\"].append({k: v for k, v in logical_counts.items()})\n",
    "\n",
    "    print(\"\\nObtained all circuit samples!\")\n",
    "    return aim_results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Running a CUDA-Q noisy simulation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this section, we will first explore the performance of the physical and logical circuits under the influence of a device noise model. This will help us predict experimental results, as well as understand the dominant error sources at play. Such a simulation can be achieved via CUDA-Q's density matrix simulator: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "cudaq.reset_target()\n",
    "cudaq.set_target(\"density-matrix-cpu\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_device_noise(\n",
    "    depolar_prob_1q: float,\n",
    "    depolar_prob_2q: float,\n",
    "    *,\n",
    "    readout_error_prob: float | None = None,\n",
    "    custom_gates: list[str] | None = None,\n",
    ") -> cudaq.mlir._mlir_libs._quakeDialects.cudaq_runtime.NoiseModel:\n",
    "    noise = cudaq.NoiseModel()\n",
    "    depolar_noise = cudaq.DepolarizationChannel(depolar_prob_1q)\n",
    "\n",
    "    noisy_ops = [\"z\", \"s\", \"x\", \"h\", \"rx\", \"rz\"]\n",
    "    for op in noisy_ops:\n",
    "        noise.add_all_qubit_channel(op, depolar_noise)\n",
    "\n",
    "    if custom_gates:\n",
    "        custom_depolar_channel = cudaq.DepolarizationChannel(depolar_prob_1q)\n",
    "        for op in custom_gates:\n",
    "            noise.add_all_qubit_channel(op, custom_depolar_channel)\n",
    "\n",
    "    # Two qubit depolarization error\n",
    "    p_0 = 1 - depolar_prob_2q\n",
    "    p_1 = np.sqrt((1 - p_0**2) / 3)\n",
    "\n",
    "    k0 = np.array(\n",
    "        [[p_0, 0.0, 0.0, 0.0], [0.0, p_0, 0.0, 0.0], [0.0, 0.0, p_0, 0.0], [0.0, 0.0, 0.0, p_0]],\n",
    "        dtype=np.complex128,\n",
    "    )\n",
    "    k1 = np.array(\n",
    "        [[0.0, 0.0, p_1, 0.0], [0.0, 0.0, 0.0, p_1], [p_1, 0.0, 0.0, 0.0], [0.0, p_1, 0.0, 0.0]],\n",
    "        dtype=np.complex128,\n",
    "    )\n",
    "    k2 = np.array(\n",
    "        [\n",
    "            [0.0, 0.0, -1j * p_1, 0.0],\n",
    "            [0.0, 0.0, 0.0, -1j * p_1],\n",
    "            [1j * p_1, 0.0, 0.0, 0.0],\n",
    "            [0.0, 1j * p_1, 0.0, 0.0],\n",
    "        ],\n",
    "        dtype=np.complex128,\n",
    "    )\n",
    "    k3 = np.array(\n",
    "        [[p_1, 0.0, 0.0, 0.0], [0.0, p_1, 0.0, 0.0], [0.0, 0.0, -p_1, 0.0], [0.0, 0.0, 0.0, -p_1]],\n",
    "        dtype=np.complex128,\n",
    "    )\n",
    "    kraus_channel = cudaq.KrausChannel([k0, k1, k2, k3])\n",
    "\n",
    "    noise.add_all_qubit_channel(\"cz\", kraus_channel)\n",
    "    noise.add_all_qubit_channel(\"cx\", kraus_channel)\n",
    "\n",
    "    if readout_error_prob is not None:\n",
    "        # Readout error modeled with a Bit flip channel on identity before measurement\n",
    "        bit_flip = cudaq.BitFlipChannel(readout_error_prob)\n",
    "        noise.add_all_qubit_channel(\"meas_id\", bit_flip)\n",
    "    return noise"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, with our example noise model defined above, we can synchronously & noisily sample all of our AIM circuits by passing `noise_model=cudaq_noise_model` to the workflow containing function `submit_aim_circuits()`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Example parameters that can model execution on hardware at the high, simulation, level:\n",
    "# Take single-qubit gate depolarization rate: ~0.2% or better (fidelity ≥99.8%)\n",
    "# Take two-qubit gate depolarization rate: ~1-2% (fidelity ~98-99%)\n",
    "cudaq_noise_model = get_device_noise(0.002, 0.02, readout_error_prob=0.02)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running circuits associated with layer=('1:-9')\n",
      "Running circuits associated with layer=('1:-1')\n",
      "Running circuits associated with layer=('1:7')\n",
      "Running circuits associated with layer=('5:-9')\n",
      "Running circuits associated with layer=('5:-1')\n",
      "Running circuits associated with layer=('5:7')\n",
      "Running circuits associated with layer=('9:-9')\n",
      "Running circuits associated with layer=('9:-1')\n",
      "Running circuits associated with layer=('9:7')\n",
      "\n",
      "Completed all circuit sampling!\n"
     ]
    }
   ],
   "source": [
    "aim_sim_data = submit_aim_circuits(sim_circuit_dict, noise_model=cudaq_noise_model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_ordering = []\n",
    "for key in circuit_layers:\n",
    "    for basis in (\"z_basis\", \"x_basis\"):\n",
    "        data_ordering.append((key, basis))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "sim_physical_energies, sim_physical_uncertainties = aim_physical_energies(\n",
    "    data_ordering, aim_sim_data[\"physical\"]\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "sim_logical_energies, sim_logical_uncertainties = aim_logical_energies(\n",
    "    data_ordering, aim_sim_data[\"logical\"]\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To analyze our simulated energy results in the above cells, we will compare them to the brute-force computed exact ground state energies for the AIM Hamiltonian. For simplicity, these are already stored in the dictionary `bf_energies` below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "bf_energies = {\n",
    "    \"1:-9\": -18.251736027394713,\n",
    "    \"1:-1\": -2.265564437074638,\n",
    "    \"1:7\": -14.252231964940428,\n",
    "    \"5:-9\": -19.293350575766127,\n",
    "    \"5:-1\": -3.608495283014149,\n",
    "    \"5:7\": -15.305692796870582,\n",
    "    \"9:-9\": -20.39007993367173,\n",
    "    \"9:-1\": -5.260398644698076,\n",
    "    \"9:7\": -16.429650912487233,\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the above metric, we can assess the performance of the logical circuits against the physical circuits by considering how far away the respective energies are from the brute-force expected energies. The cell below computes these energy deviations:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Layer=(1, -9) has brute-force energy of: -18.251736027394713\n",
      "Physical circuit of layer=(1, -9) got an energy of: -15.5275\n",
      "Logical circuit of layer=(1, -9) got an energy of: -17.151020829036916\n",
      "------------------------------------------------------------------------\n",
      "Logical circuit achieved the lower energy!\n",
      "------------------------------------------------------------------------ \n",
      "\n",
      "Layer=(1, -1) has brute-force energy of: -2.265564437074638\n",
      "Physical circuit of layer=(1, -1) got an energy of: -1.9745\n",
      "Logical circuit of layer=(1, -1) got an energy of: -2.1268498061611574\n",
      "------------------------------------------------------------------------\n",
      "Logical circuit achieved the lower energy!\n",
      "------------------------------------------------------------------------ \n",
      "\n",
      "Layer=(1, 7) has brute-force energy of: -14.252231964940428\n",
      "Physical circuit of layer=(1, 7) got an energy of: -11.9755\n",
      "Logical circuit of layer=(1, 7) got an energy of: -13.565638751650726\n",
      "------------------------------------------------------------------------\n",
      "Logical circuit achieved the lower energy!\n",
      "------------------------------------------------------------------------ \n",
      "\n",
      "Layer=(5, -9) has brute-force energy of: -19.293350575766127\n",
      "Physical circuit of layer=(5, -9) got an energy of: -16.6285\n",
      "Logical circuit of layer=(5, -9) got an energy of: -18.38040026051508\n",
      "------------------------------------------------------------------------\n",
      "Logical circuit achieved the lower energy!\n",
      "------------------------------------------------------------------------ \n",
      "\n",
      "Layer=(5, -1) has brute-force energy of: -3.608495283014149\n",
      "Physical circuit of layer=(5, -1) got an energy of: -3.309\n",
      "Logical circuit of layer=(5, -1) got an energy of: -3.5374647301794413\n",
      "------------------------------------------------------------------------\n",
      "Logical circuit achieved the lower energy!\n",
      "------------------------------------------------------------------------ \n",
      "\n",
      "Layer=(5, 7) has brute-force energy of: -15.305692796870582\n",
      "Physical circuit of layer=(5, 7) got an energy of: -13.413\n",
      "Logical circuit of layer=(5, 7) got an energy of: -14.602247392308305\n",
      "------------------------------------------------------------------------\n",
      "Logical circuit achieved the lower energy!\n",
      "------------------------------------------------------------------------ \n",
      "\n",
      "Layer=(9, -9) has brute-force energy of: -20.39007993367173\n",
      "Physical circuit of layer=(9, -9) got an energy of: -17.883\n",
      "Logical circuit of layer=(9, -9) got an energy of: -19.290700765203383\n",
      "------------------------------------------------------------------------\n",
      "Logical circuit achieved the lower energy!\n",
      "------------------------------------------------------------------------ \n",
      "\n",
      "Layer=(9, -1) has brute-force energy of: -5.260398644698076\n",
      "Physical circuit of layer=(9, -1) got an energy of: -4.671\n",
      "Logical circuit of layer=(9, -1) got an energy of: -4.993866818129227\n",
      "------------------------------------------------------------------------\n",
      "Logical circuit achieved the lower energy!\n",
      "------------------------------------------------------------------------ \n",
      "\n",
      "Layer=(9, 7) has brute-force energy of: -16.429650912487233\n",
      "Physical circuit of layer=(9, 7) got an energy of: -14.431\n",
      "Logical circuit of layer=(9, 7) got an energy of: -15.700114086383103\n",
      "------------------------------------------------------------------------\n",
      "Logical circuit achieved the lower energy!\n",
      "------------------------------------------------------------------------ \n",
      "\n"
     ]
    }
   ],
   "source": [
    "sim_physical_energy_diff, sim_logical_energy_diff = _get_energy_diff(\n",
    "    bf_energies, sim_physical_energies, sim_logical_energies\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Both physical and logical circuits were subject to the same noise model, but the `[[4,2,2]]` provides additional information that can help overcome some errors. Visualizing the computed energy differences from the above the cell, our noisy simulation provides a preview of the benefits logical qubits can offer:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 2200x1400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(11, 7), dpi=200)\n",
    "\n",
    "layer_labels = [(int(key.split(\":\")[0]), int(key.split(\":\")[1])) for key in bf_energies.keys()]\n",
    "plot_labels = [str(item) for item in layer_labels]\n",
    "\n",
    "plt.errorbar(\n",
    "    plot_labels,\n",
    "    sim_physical_energy_diff,\n",
    "    yerr=sim_physical_uncertainties.values(),\n",
    "    ecolor=(20 / 255.0, 26 / 255.0, 94 / 255.0),\n",
    "    color=(20 / 255.0, 26 / 255.0, 94 / 255.0),\n",
    "    capsize=4,\n",
    "    elinewidth=1.5,\n",
    "    fmt=\"o\",\n",
    "    markersize=8,\n",
    "    markeredgewidth=1,\n",
    "    label=\"Physical\",\n",
    ")\n",
    "\n",
    "plt.errorbar(\n",
    "    plot_labels,\n",
    "    sim_logical_energy_diff,\n",
    "    yerr=sim_logical_uncertainties.values(),\n",
    "    color=(0, 177 / 255.0, 152 / 255.0),\n",
    "    ecolor=(0, 177 / 255.0, 152 / 255.0),\n",
    "    capsize=4,\n",
    "    elinewidth=1.5,\n",
    "    fmt=\"o\",\n",
    "    markersize=8,\n",
    "    markeredgewidth=1,\n",
    "    label=\"Logical\",\n",
    ")\n",
    "\n",
    "ax.set_xlabel(\"Hamiltonian Parameters (U, V)\", fontsize=18)\n",
    "ax.set_ylabel(\"Energy above true ground state (in eV)\", fontsize=18)\n",
    "ax.set_title(\"CUDA-Q AIM Circuits Simulation (lower is better)\", fontsize=20)\n",
    "ax.legend(loc=\"upper right\", fontsize=18.5)\n",
    "plt.xticks(fontsize=16)\n",
    "plt.yticks(fontsize=16)\n",
    "\n",
    "ax.axhline(y=0, color=\"black\", linestyle=\"--\", linewidth=2)\n",
    "plt.ylim(\n",
    "    top=max(sim_physical_energy_diff) + max(sim_physical_uncertainties.values()) + 0.2, bottom=-0.2\n",
    ")\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Running logical AIM on Infleqtion's hardware "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The entire workflow we've seen thus far can be seamlessly executed on real quantum hardware as well. CUDA-Q has integration with Infleqtion's gate-based neutral atom quantum computer, [Sqale](https://arxiv.org/html/2408.08288v2), allowing execution of CUDA-Q kernels on neutral-atom hardware via Infleqtion’s cross-platform Superstaq compiler API that performs low-level compilation and optimization under the hood. Indeed, the AIM research results seen in [our paper](https://arxiv.org/abs/2412.07670) were obtained via this complete end-to-end workflow.\n",
    "\n",
    "To do so, users can obtain a Superstaq API key from [superstaq.infleqtion.com](https://superstaq.infleqtion.com/) to gain access to Infleqtion's neutral-atom simulator, with [pre-registration](https://www.infleqtion.com/sqale-preregistration) open for access to Infleqtion’s neutral atom QPU."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As a tutorial, let us reproduce the workflow we've run so far but on Infleqtion's QPU. We begin with the same GPU-enhanced VQE to generate the AIM circuits:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "cudaq.reset_target()\n",
    "\n",
    "if cudaq.num_available_gpus() == 0:\n",
    "    cudaq.set_target(\"qpp-cpu\", option=\"fp64\")\n",
    "else:\n",
    "    cudaq.set_target(\"nvidia\", option=\"fp64\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computed optimal angles=[1.5846845738799267, 1.5707961678256028] for U=1, V=-9\n",
      "Computed optimal angles=[4.588033710930825, 4.712388365176642] for U=1, V=-1\n",
      "Computed optimal angles=[-1.588651490745171, 1.5707962742876598] for U=1, V=7\n",
      "Computed optimal angles=[1.64012940802256, 1.5707963354922125] for U=5, V=-9\n",
      "Computed optimal angles=[2.1293956916868737, 1.5707963294715355] for U=5, V=-1\n",
      "Computed optimal angles=[-1.6598458659836037, 1.570796331040382] for U=5, V=7\n",
      "Computed optimal angles=[1.695151467539617, 1.5707960973500679] for U=9, V=-9\n",
      "Computed optimal angles=[2.4149519241823376, 1.5707928509325972] for U=9, V=-1\n",
      "Computed optimal angles=[-1.7301462729177735, 1.570796033796985] for U=9, V=7\n",
      "\n",
      "Finished building optimized circuits!\n"
     ]
    }
   ],
   "source": [
    "device_circuit_dict = generate_circuit_set(\n",
    "    ignore_meas_id=True\n",
    ")  # Setting `ignore_meas_id=True` drops the noisy-identity gate from earlier"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And now, we change backends! Before selecting an Infleqtion machine in CUDA-Q, we must first set our Superstaq API key, like so:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "# os.environ['SUPERSTAQ_API_KEY'] = \"api_key\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we declare the type of execution we would like on Infleqtion's machine based on the keyword options specified:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "cudaq.reset_target()\n",
    "\n",
    "# Note: The Infleqtion target requires `cudaq>0.9.0`\n",
    "\n",
    "# Set the following to run on Infleqtion's Sqale QPU:\n",
    "cudaq.set_target(\"infleqtion\", machine=\"cq_sqale_qpu\")\n",
    "\n",
    "# Set the following to run an ideal dry-run on Infleqtion's Sqale QPU:\n",
    "# cudaq.set_target(\"infleqtion\", machine=\"cq_sqale_qpu\", method=\"dry-run\")\n",
    "\n",
    "# Set the following to run a device-realistic noisy simulation of Infleqtion's Sqale QPU:\n",
    "# cudaq.set_target(\"infleqtion\", machine=\"cq_sqale_qpu\", method=\"noise-sim\")\n",
    "\n",
    "# Set the following to run a local, ideal emulation:\n",
    "# cudaq.set_target(\"infleqtion\", emulate=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With that, we're all set! That simple change instructs our AIM circuits to execute on Infleqtion's QPU (or simulator). Due to the general queue wait time of running on hardware, we optionally recommend enabling the `run_async=True` flag to asynchronously sample the circuits. This will allow the cell to be executed and not wait synchronously until all the jobs are complete, allowing other classical code to be run in the meantime. When using `run_async`, an optional directory to store the job information can be specified with `folder_path` (this will be important to later retrieve the job results from the same directory)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Posting circuits associated with layer=('1:-9')\n",
      "Posting circuits associated with layer=('1:-1')\n",
      "Posting circuits associated with layer=('1:7')\n",
      "Posting circuits associated with layer=('5:-9')\n",
      "Posting circuits associated with layer=('5:-1')\n",
      "Posting circuits associated with layer=('5:7')\n",
      "Posting circuits associated with layer=('9:-9')\n",
      "Posting circuits associated with layer=('9:-1')\n",
      "Posting circuits associated with layer=('9:7')\n",
      "\n",
      "All circuits submitted for async sampling!\n"
     ]
    }
   ],
   "source": [
    "submit_aim_circuits(\n",
    "    device_circuit_dict, folder_path=\"hardware_aim_future_results\", shots_count=1000, run_async=True\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the above cell execution, all the circuits will post to execute on QPU. We can then return at a later time to retrieve the job results with the cell below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Retrieving all circuits counts associated with layer=('1:-9')\n",
      "Retrieving all circuits counts associated with layer=('1:-1')\n",
      "Retrieving all circuits counts associated with layer=('1:7')\n",
      "Retrieving all circuits counts associated with layer=('5:-9')\n",
      "Retrieving all circuits counts associated with layer=('5:-1')\n",
      "Retrieving all circuits counts associated with layer=('5:7')\n",
      "Retrieving all circuits counts associated with layer=('9:-9')\n",
      "Retrieving all circuits counts associated with layer=('9:-1')\n",
      "Retrieving all circuits counts associated with layer=('9:7')\n",
      "\n",
      "Obtained all circuit samples!\n"
     ]
    }
   ],
   "source": [
    "aim_device_data = _get_async_results(circuit_layers, folder_path=\"hardware_aim_future_results\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "physical_energies, physical_uncertainties = aim_physical_energies(\n",
    "    data_ordering, aim_device_data[\"physical\"]\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "logical_energies, logical_uncertainties = aim_logical_energies(\n",
    "    data_ordering, aim_device_data[\"logical\"]\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Layer=(1, -9) has brute-force energy of: -18.251736027394713\n",
      "Physical circuit of layer=(1, -9) got an energy of: -17.626499999999997\n",
      "Logical circuit of layer=(1, -9) got an energy of: -17.69666562801761\n",
      "------------------------------------------------------------------------\n",
      "Logical circuit achieved the lower energy!\n",
      "------------------------------------------------------------------------ \n",
      "\n",
      "Layer=(1, -1) has brute-force energy of: -2.265564437074638\n",
      "Physical circuit of layer=(1, -1) got an energy of: -2.1415\n",
      "Logical circuit of layer=(1, -1) got an energy of: -2.2032104443266585\n",
      "------------------------------------------------------------------------\n",
      "Logical circuit achieved the lower energy!\n",
      "------------------------------------------------------------------------ \n",
      "\n",
      "Layer=(1, 7) has brute-force energy of: -14.252231964940428\n",
      "Physical circuit of layer=(1, 7) got an energy of: -12.9955\n",
      "Logical circuit of layer=(1, 7) got an energy of: -13.76919450035401\n",
      "------------------------------------------------------------------------\n",
      "Logical circuit achieved the lower energy!\n",
      "------------------------------------------------------------------------ \n",
      "\n",
      "Layer=(5, -9) has brute-force energy of: -19.293350575766127\n",
      "Physical circuit of layer=(5, -9) got an energy of: -18.331\n",
      "Logical circuit of layer=(5, -9) got an energy of: -18.85730052910377\n",
      "------------------------------------------------------------------------\n",
      "Logical circuit achieved the lower energy!\n",
      "------------------------------------------------------------------------ \n",
      "\n",
      "Layer=(5, -1) has brute-force energy of: -3.608495283014149\n",
      "Physical circuit of layer=(5, -1) got an energy of: -3.476\n",
      "Logical circuit of layer=(5, -1) got an energy of: -3.5425689231532203\n",
      "------------------------------------------------------------------------\n",
      "Logical circuit achieved the lower energy!\n",
      "------------------------------------------------------------------------ \n",
      "\n",
      "Layer=(5, 7) has brute-force energy of: -15.305692796870582\n",
      "Physical circuit of layer=(5, 7) got an energy of: -14.043500000000002\n",
      "Logical circuit of layer=(5, 7) got an energy of: -14.795918428433312\n",
      "------------------------------------------------------------------------\n",
      "Logical circuit achieved the lower energy!\n",
      "------------------------------------------------------------------------ \n",
      "\n",
      "Layer=(9, -9) has brute-force energy of: -20.39007993367173\n",
      "Physical circuit of layer=(9, -9) got an energy of: -19.4715\n",
      "Logical circuit of layer=(9, -9) got an energy of: -19.96524696701215\n",
      "------------------------------------------------------------------------\n",
      "Logical circuit achieved the lower energy!\n",
      "------------------------------------------------------------------------ \n",
      "\n",
      "Layer=(9, -1) has brute-force energy of: -5.260398644698076\n",
      "Physical circuit of layer=(9, -1) got an energy of: -4.973\n",
      "Logical circuit of layer=(9, -1) got an energy of: -5.207315773582224\n",
      "------------------------------------------------------------------------\n",
      "Logical circuit achieved the lower energy!\n",
      "------------------------------------------------------------------------ \n",
      "\n",
      "Layer=(9, 7) has brute-force energy of: -16.429650912487233\n",
      "Physical circuit of layer=(9, 7) got an energy of: -15.182\n",
      "Logical circuit of layer=(9, 7) got an energy of: -16.241375689575516\n",
      "------------------------------------------------------------------------\n",
      "Logical circuit achieved the lower energy!\n",
      "------------------------------------------------------------------------ \n",
      "\n"
     ]
    }
   ],
   "source": [
    "physical_energy_diff, logical_energy_diff = _get_energy_diff(\n",
    "    bf_energies, physical_energies, logical_energies\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As before, we use the same metric of comparing against the true ground state energies; however, this time, both the physical and logical circuits are fully exposed to real hardware noise. Yet, we expect the use of logical qubits afforded to us by the `[[4,2,2]]` code to achieve energies closer to the true ground state than the bare physical circuits (up to a certain error threshold). And indeed they do! Visually, we can plot the energy deviations of both the physical and logical circuits from the cell above and observe that the logical circuits are able to outperform the physical circuits by obtaining much lower energies, demonstrating the power of error detection and the beginning possibilities of fault-tolerant quantum computation: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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792dnZ2vJkiWFdsbnPlft0h+SIiMjTc9qKw6+tr6Nr4+ZVbXnC/ja+je+fp777LPPTNvt27dXq1atLIvP18a/lfbX77nnnjP90cswDP3000+64447SjWPgrDmRGmh9sxYc8JXUJueY82Jwnj69Xv00UeVnJys8ePHm2Ls37/f5e46l+rSpYvee+89n/2jF2tOlBZqz4w1J3wFtek51pwlRzMIYIMKFSq47EtLS7MhE9/19NNP69ChQ8U6tkGDBoUu1GrUqKElS5bohRde0JQpU4rs7IuJidH06dM1cOBATZgwwfRavXr1ipXTpfI+h41HH9iH2iualbVnN2rPf1Cb1tm0aZO2bNli2mdlt7xEbfkTX6it1q1bq379+jp8+LBz39q1a33mj16sOeEN1F7RWHPCDtSmdVhz4lJW19Yzzzyjtm3b6v/+7/+0a9euQo8NCgrSuHHj9NJLL+nEiRMur3uypvIG1pzwBmqvaKw5YQdq0zqsOa1BMwhgg0qVKsnhcJg6zpKTk23MKPCVK1dOL7/8sh555BHNmTNHP/30k3bs2KGEhARlZmaqdu3aatasmW6++WYNGzbMecHPu1js2LGj23OnpKSYtt29/SKsQ+2VLdSe/6A2rfPpp5+atsPCwvTXv/7V0jmoLf/hK7XVokUL0x+9Tp06Veo5lBbWnJCovbKG2vMf1KZ1WHPiUt6oreuvv14DBgzQggULtHDhQq1atUonT57UuXPnVL16ddWvX1/9+/fXHXfcodjYWEmu66mwsDBL3znsS1hzQqL2yhpqz39Qm9ZhzWkNmkEAG4SEhKhWrVqm53edOHFCbdu2tS+pMqJmzZp68MEH9eCDDxbr+G3btpm2O3Xq5PaceTsw69ev73YMWIPaK1uoPf9BbVojMzNTX3zxhWnf4MGDVbVqVUvnobb8h6/UVt7vwXPnzpXq/HZgzVm2UXtlC7XnP6hNa7DmRF7eqq3g4GDdcMMNuuGGG4p1fN71VJs2bRQWFlaiHHwda86yjdorW6g9/0FtWoM1p3VoBgFs0rBhQ9P/DI4dO2ZjNr4nLi7O7hSUmpqq7du3m/ZdddVVbsfJ+7Vt0KBBifJCyVB7hfOF2rMKtedfqM2SW7BggU6fPm3aZ/WtEyVqy9/4Qm2dP3/etB0VFVXqORTEF/6/x5ozMFF7hfOF2rMKtedfqM2SY82J/PhCba1bt8607cl6ylt84f97rDkDE7VXOF+oPatQe/6F2iw51pzWCbI7AaCsuuKKK0zb+/btsykTFOS7774zPcutTZs2atOmjdtx9u/fb9pu2bJliXOD56i9soPa8y/UZsnlvXViTEyM+vfvb/k81JZ/8YXa2rt3r2k7Ojq61HPwZaw5AxO1V3ZQe/6F2iw51pzIj921lZ6ervnz55v23XXXXaWag69jzRmYqL2yg9rzL9RmybHmtA7NIIBN8j6TMe8tm2C/jz76yLQ9evRot2McOnRIFy5ccG6XL18+IP9n4k+ovbKB2vM/1GbJJCQkaOHChaZ9d9xxh4KDgy2dh9ryP3bX1r59+1z+6NW6detSzcHXseYMTNRe2UDt+R9qs2RYc6IgdtfWnDlzTN8zHTt25LGjebDmDEzUXtlA7fkfarNkWHNai2YQwCZdu3Y1bW/evNmeRJCvefPm6ZdffnFuV69eXbfffrvbcbZs2WLa7tChg0JCeEKXnai9soHa8z/UZsnMnDlTmZmZpn0jR460fB5qy//YXVsvvfSSyz5vvJPDX7HmDFzUXtlA7fkfarNkWHOiIHbWVnJysv7xj3+Y9j366KOlNr8/YM0ZuKi9soHa8z/UZsmw5rQWzSCATVq1aqVatWo5t48fP+5yOyJfFBcXJ4fDYfqYMGGC3WlZateuXbr//vtN+yZPnuzRc3yXL19u2vanX/IEKmqvbKD2/A+1WTKfffaZabtTp05q0aKF5fNQW/6npLVlGIbHc3/55Zcu35u9evUq1vNXfaW2vIk1Z2Cj9soGas//UJslw5oTBbHr57msrCyNHDlSx44dc+675pprdNtttxVrvK/Uljex5gxs1F7ZQO35H2qzZFhzWotmEMAmDofD5cKybNkye5IJYPHx8VqyZEmxj//ll1/Uu3dvnTx50rmvb9++uuOOOzyaP+//TAYOHOhRHFiH2isbqD3/Q216btOmTS6d7HfffbdX5qK2/E9Ja+vXX3/VwIED9dtvv7k175QpU3TnnXea/mjmcDj0+uuvuxXHX7DmRF7UXtlA7fkfatNzrDlRGKt+nvvuu++UlJRUrGPj4+M1bNgwffPNN8595cuX19SpU92e11+w5kRe1F7ZQO35H2rTc6w5rRd49zoB/MiIESP0ySefOLd//PFHjRo1yq0YSUlJmjVrVrGPX7p0qdLS0vJ9rWPHji7PMvN38fHxuuaaa9S0aVMNGTJE1157rdq2bavo6GhJf76rJyEhQb/88ov+85//6PvvvzeNj42Ndevze6mTJ09q06ZNzu0mTZqoXbt2np8MLEPtlY7169dr/fr1+b72+++/u+wrbGF62223qVKlSsWal9rzX9SmZz799FPTdnh4uG699VbL56G2/FdJasswDC1cuFALFy5U48aNddNNN+mqq65S27ZtVbduXQUFBTmP27t3r5YsWaJ3331Xf/zxh0us5557Tp06dbLmpHwMa07kh9orHaw54S5q0zOsOVEUK36eGz9+vA4cOKBBgwZp0KBB6tSpk5o2beqsrdTUVG3cuFHz58/XtGnTlJiY6BwbFBSkGTNmqEmTJtackA9izYn8UHulgzUn3EVteoY1pxcYAGyTlZVlxMTEGJIMSUaFChWM1NRUt2IcPHjQOb6kH88995xH8z3//PMefga8b9OmTfmea1hYmFGtWjUjJCSkwM9H8+bNjcOHD3s89/vvv+83n6eyhtorHc8995xln6ODBw8We15qz39Rm+7LyMgwqlevbpr/5ptv9spc1Jb/KkltLV26tMAacTgcRqVKlYyqVasaQUFBhdbTo48+6lbOdteWu1hzIj/UXulgzQl3UZvuY82J4rDi57k2bdq4fK8HBQUZlStXNiIiIgqsqdDQUOOLL75wO2e7a8tdrDmRH2qvdLDmhLuoTfex5vQOHhMD2Cg4ONh0W77U1FT98MMPNmZUtB07dpi2HQ6Hhg0bZlM2nsvIyNCZM2eUlZXl8prD4dA999yjtWvXql69eh7PMWfOHOe/g4KCdOedd3ocC9ai9gIbtee/qE33LViwQKdPnzbtGzlypFfmorb8l7dqyzAMJSUl6ezZs8rJycn3mBo1amju3Ll688033Yptd21ZhTVn2UbtBTZqz39Rm+5jzYni8FZt5eTk6Pz580pJScn39SuuuEK///67R+8atru2rMKas2yj9gIbtee/qE33seb0DppBAJs9+OCDCg4Odm5Pnz7dxmyKlve5ZjfddJNatmxpTzLF0KhRI40fP16dOnVSSEjhT8aqWLGibr/9dm3YsEHTp09XxYoVPZ73wIEDWrp0qXP7hhtuUMOGDT2OB+tRe4GJ2vN/1KZ7PvvsM9N27dq11bdvX8vnobb8n6e11bZtW7333nsaMWJEsX95HBoaqiuvvFIfffSRDh06pKFDh7qdr9215S7WnCgItReYqD3/R226hzUniqukP8899dRTGjJkiCpXrlzocQ6HQ127dtWnn36qLVu2qEOHDp6ka3ttuYs1JwpC7QUmas//UZvuYc3pHQ7DMAy7kwDKultuuUWzZ8+W9GcH2oEDB9SgQQObs8pf586dtW7dOkl//g9m27ZtuuKKK2zOqnhSU1O1detW7du3T6dOnVJKSorCwsIUHR2t5s2bq0OHDgoNDbVkrqefflovv/yyc/vXX39V9+7dLYkN61B7gYfaCwzUpu+htgKDFbV19uxZ7dq1S0eOHNHJkyeVkpKinJwcRUZGqkqVKmrUqJE6dOigcuXKlShXf64t1pzIi9oLPNReYKA2fQ+1FRisqC3DMLRnzx5nfSUmJkqSIiMjFRsbq44dO6pGjRolztWfa4s1J/Ki9gIPtRcYqE3fU+Zqy74n1ADItWXLFsPhcDifTfX444/bnVK+EhMTjeDgYGeeI0aMsDsln5SammrUqFHD+Xnq0aOH3SmhANReYKH2Age16VuorcBBbQUWatN/UHuBhdoLHNSmb6G2Age1FVioTf9B7QUWai9wUJu+pSzWFo+JAXxA69atNXz4cOf2Bx98oPPnz9uXUAFWrFih7OxsSX92MI4fP97mjHzT9OnTlZCQ4Nx+6aWXbMwGhaH2Agu1FzioTd9CbQUOaiuwUJv+g9oLLNRe4KA2fQu1FTiorcBCbfoPai+wUHuBg9r0LWWxtmgGAXzExIkTnbfuS0pK0jvvvGNzRq4ufV7Y8OHDA/L2UCWVkZGhSZMmObcHDhyoq6++2saMUBRqLzBQe4GH2vQN1FbgobYCA7Xpf6i9wEDtBR5q0zdQW4GH2goM1Kb/ofYCA7UXeKhN31Bma8vuW5MA+J+///3vzlsTRUVFGadPn7Y7JZMuXboYkoygoCBj+/btdqfjk6ZMmeL8GoaFhRl79uyxOyUUA7Xn/6i9wERt2o/aCkzUlv+jNv0Ttef/qL3ARG3aj9oKTNSW/6M2/RO15/+ovcBEbdqvrNaWwzAMwytdJgDclpSUpMsvv1wnTpyQJI0bN06TJ0+2OSsUV1JSkmJjY523mPrHP/6hV155xeasUBzUnn+j9gIXtWkvaitwUVv+jdr0X9Sef6P2Ahe1aS9qK3BRW/6N2vRf1J5/o/YCF7Vpr7JcWzSDAAAAAAAAAAAAAAAABJAguxMAAAAAAAAAAAAAAACAdWgGAQAAAAAAAAAAAAAACCA0gwAAAAAAAAAAAAAAAAQQmkEAAAAAAAAAAAAAAAACCM0gAAAAAAAAAAAAAAAAAYRmEAAAAAAAAAAAAAAAgABCMwgAAAAAAAAAAAAAAEAAoRkEAAAAAAAAAAAAAAAggNA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",
      "text/plain": [
       "<Figure size 2200x1400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(11, 7), dpi=200)\n",
    "\n",
    "plt.errorbar(\n",
    "    plot_labels,\n",
    "    physical_energy_diff,\n",
    "    yerr=physical_uncertainties.values(),\n",
    "    ecolor=(20 / 255.0, 26 / 255.0, 94 / 255.0),\n",
    "    color=(20 / 255.0, 26 / 255.0, 94 / 255.0),\n",
    "    capsize=4,\n",
    "    elinewidth=1.5,\n",
    "    fmt=\"o\",\n",
    "    markersize=8,\n",
    "    markeredgewidth=1,\n",
    "    label=\"Physical\",\n",
    ")\n",
    "plt.errorbar(\n",
    "    plot_labels,\n",
    "    logical_energy_diff,\n",
    "    yerr=logical_uncertainties.values(),\n",
    "    color=(0, 177 / 255.0, 152 / 255.0),\n",
    "    ecolor=(0, 177 / 255.0, 152 / 255.0),\n",
    "    capsize=4,\n",
    "    elinewidth=1.5,\n",
    "    fmt=\"o\",\n",
    "    markersize=8,\n",
    "    markeredgewidth=1,\n",
    "    label=\"Logical\",\n",
    ")\n",
    "\n",
    "ax.set_xlabel(\"Hamiltonian Parameters (U, V)\", fontsize=18)\n",
    "ax.set_ylabel(\"Energy above true ground state (in eV)\", fontsize=18)\n",
    "ax.set_title(\"CUDA-Q AIM Infleqtion Hardware Execution (lower is better)\", fontsize=20)\n",
    "ax.legend(loc=\"upper left\", fontsize=18.5)\n",
    "plt.xticks(fontsize=16)\n",
    "plt.yticks(fontsize=16)\n",
    "\n",
    "ax.axhline(y=0, color=\"black\", linestyle=\"--\", linewidth=2)\n",
    "plt.ylim(top=max(physical_energy_diff) + max(physical_uncertainties.values()) + 0.2, bottom=-0.2)\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.16"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}