{ "cells": [ { "cell_type": "markdown", "id": "d2c31ae8", "metadata": {}, "source": [ "---\n", "title: \"Atténuation des erreurs à grande échelle par amplification probabiliste des erreurs\"\n", "description: \"Réalisez une expérience d'atténuation des erreurs à l'échelle industrielle avec extrapolation sans bruit et amplification probabiliste des erreurs.\"\n", "---\n", "\n", "{/* cspell:ignore mapsto multigraph inds extrap sharex sharey pidx */}\n", "\n", "\n", "\n", "# Atténuation des erreurs à grande échelle par amplification probabiliste des erreurs\n", "\n", "*Durée estimée : 14 minutes sur un processeur Heron r3 (REMARQUE : il s'agit uniquement d'une estimation. (Votre temps d'exécution peut varier.)*\n", "\n" ] }, { "cell_type": "markdown", "id": "8bf80006", "metadata": {}, "source": [ "\n", "\n", "## Résultats d'apprentissage\n", "\n", "À l'issue de ce tutoriel, les utilisateurs devraient être en mesure de :\n", "\n", "* La théorie qui sous-tend *l'extrapolation sans bruit* (ZNE), les différentes méthodes d'amplification du bruit, et les raisons pour lesquelles *l'amplification probabiliste des erreurs* (PEA) est privilégiée pour les expériences à grande échelle.\n", "* Comment mettre en œuvre le ZNE avec la PEA dans la pratique à l'aide de Qiskit.\n", "\n", "\n", "\n", "## Prérequis\n", "\n", "Nous recommandons aux utilisateurs de se familiariser avec les sujets suivants avant de suivre ce tutoriel :\n", "\n", "* [Le module « Atténuation des](/learning/courses/utility-scale-quantum-computing/error-mitigation) erreurs » du cours *sur l'informatique quantique à l'échelle industrielle,* destiné à acquérir les connaissances de base sur l'utilisation de l'atténuation des erreurs dans Qiskit.\n", "* [La leçon «](/learning/courses/utility-scale-quantum-computing/utility-i) Utility-I » du cours *sur l'informatique quantique à l'échelle industrielle,* pour en savoir plus sur l'expérience à l'échelle industrielle citée en exemple dans ce tutoriel.\n", "\n" ] }, { "cell_type": "markdown", "id": "a929ccce", "metadata": {}, "source": [ "\n", "\n", "## Arrière-plan\n", "\n", "Ce tutoriel explique comment mener une expérience d'atténuation des erreurs à l'échelle industrielle avec le service de calcul d' IBM Quantum, en utilisant une version expérimentale de *l'extrapolation sans bruit* (ZNE) associée à *l'amplification probabiliste des erreurs* (PEA).\n", "\n", "![kim\\_nature\\_fig.png](https://quantum.cloud.ibm.com/docs/images/tutorials/utility-scale-error-mitigation-with-probabilistic-error-amplification/e1e67c34-9d4d-4a88-9340-f0b2f3676770.avif)\n", "\n", "**Référence**\n", ": Y. Kim et al. *Preuves de l'utilité de l'informatique quantique avant la mise en place de la tolérance aux pannes.* [Nature 618.7965 (2023)](https://www.nature.com/articles/s41586-023-06096-3)\n", "\n" ] }, { "cell_type": "markdown", "id": "a89ed8dd", "metadata": {}, "source": [ "\n", "\n", "### Extrapolation sans bruit (ZNE)\n", "\n", "L'extrapolation à bruit nul (ZNE) est une technique d'atténuation des erreurs qui supprime les effets d'un bruit *inconnu* pendant l'exécution d'un circuit qui peut être mis à l'échelle d'une manière *connue.*\n", "\n", "Elle suppose que les valeurs attendues s'échelonnent en fonction du bruit selon une fonction connue\n", "\n", "$$\n", "\\langle A(\\lambda) \\rangle = \\langle A(0) \\rangle + \\sum_{k=0}^{m} a_k \\lambda^k + R\n", "$$\n", "\n", "où $\\lambda$ paramètre l'intensité du bruit et peut être amplifié.\n", "\n", "Nous pouvons mettre en œuvre les ZNE en suivant les étapes suivantes :\n", "\n", "1. Amplifier le bruit du circuit pour plusieurs facteurs de bruit $\\lambda_1, \\lambda_2, ... $\n", "2. Exécutez chaque circuit amplifié par le bruit pour mesurer $\\langle A(\\lambda_1)\\rangle, ...$\n", "3. Extrapolation jusqu'à la limite du bruit zéro $\\langle A(0)\\rangle$\n", "\n", "![zne\\_stages.png](https://quantum.cloud.ibm.com/docs/images/tutorials/utility-scale-error-mitigation-with-probabilistic-error-amplification/5e63d706-82d8-4212-b802-c9191ce53341.avif)\n", "\n" ] }, { "cell_type": "markdown", "id": "5db985b9", "metadata": {}, "source": [ "\n", "\n", "#### Amplifier le bruit pour ZNE\n", "\n", "Le principal défi à relever pour réussir la mise en œuvre de ZNE est de disposer d'un modèle précis pour le bruit dans la valeur espérée et d'amplifier le bruit d'une manière connue.\n", "\n", "Il existe trois façons courantes de mettre en œuvre l'amplification des erreurs pour les ZNE.\n", "\n", "| **Étirement des pouls** | **Porte pliante** | **Amplification probabiliste des erreurs** |\n", "| -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ |\n", "| Mise à l'échelle de la durée de l'impulsion par étalonnage | Répétition des portes en cycles d'identité $U\\mapsto U(U^{-1}U)^{\\lambda-1}/2$ | Ajouter du bruit via l'échantillonnage des canaux de Pauli |\n", "| ![zne\\_pulse\\_stretching.png](https://quantum.cloud.ibm.com/docs/images/tutorials/utility-scale-error-mitigation-with-probabilistic-error-amplification/83188b57-e88f-43a1-a7bd-29327f46ecf5.avif) | ![zne\\_gate\\_folding.png](https://quantum.cloud.ibm.com/docs/images/tutorials/utility-scale-error-mitigation-with-probabilistic-error-amplification/e1358d08-2632-4fd2-bf0f-f9384a2d3340.avif) | ![zne\\_pea.png](https://quantum.cloud.ibm.com/docs/images/tutorials/utility-scale-error-mitigation-with-probabilistic-error-amplification/3d69d5bd-70e5-4eeb-aa02-fc0a62043010.avif) |\n", "| Kandala et al. Nature (2019) | Shultz et al. PRA (2022) | Li & Benjamin PRX (2017) |\n", "\n" ] }, { "cell_type": "markdown", "id": "c23e43ee", "metadata": {}, "source": [ "Pour les expériences à l'échelle des services publics, l' *amplification probabiliste des erreurs* (PEA) est la solution la plus intéressante.\n", "\n", "* L'étirement des impulsions suppose que le bruit de la porte est proportionnel à la durée, ce qui n'est généralement pas le cas. L'étalonnage est également coûteux.\n", "* Le pliage des portes nécessite des facteurs d'étirement importants qui limitent considérablement la profondeur des circuits qui peuvent être exécutés.\n", "* La PEA peut être appliquée à n'importe quel circuit pouvant fonctionner avec un facteur de bruit natif ( $\\lambda=1$ ) mais nécessite l'apprentissage du modèle de bruit.\n", "\n", "\n", "\n", "### Apprenez le modèle de bruit pour PEA\n", "\n", "La PEA repose sur le même modèle de bruit basé sur les couches que l' *annulation probabiliste des erreurs* (PEC); cependant, elle évite le surcoût d'échantillonnage qui s'élève de manière exponentielle avec le bruit du circuit.\n", "\n", "| **Etape 1** | **Etape 2** | **Etape 3** |\n", "| ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ | --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |\n", "| Couches de Pauli de portes à deux qubits | Répéter les paires de couches d'identité et apprendre le bruit | Déterminer une fidélité (erreur pour chaque canal de bruit) |\n", "| ![pec\\_pauli\\_twirling.png](https://quantum.cloud.ibm.com/docs/images/tutorials/utility-scale-error-mitigation-with-probabilistic-error-amplification/2eab5ff4-40fa-4a41-9f2c-74f5e22c4643.avif) | ![pec\\_learn\\_layer.png](https://quantum.cloud.ibm.com/docs/images/tutorials/utility-scale-error-mitigation-with-probabilistic-error-amplification/8d0d64c3-65ad-4419-8ac9-4ec9633d39a0.avif) | ![pec\\_curve\\_fitting.png](https://quantum.cloud.ibm.com/docs/images/tutorials/utility-scale-error-mitigation-with-probabilistic-error-amplification/c51bd42d-2463-4c78-807b-d284ca79296f.avif) |\n", "\n", "**Référence** : E. van den Berg, Z. Minev, A. Kandala et K. Temme, *Annulation probabiliste des erreurs avec des modèles de Pauli-Lindblad épars sur des processeurs quantiques bruyants* [arXiv:2201.09866](https://arxiv.org/abs/2201.09866)\n", "\n" ] }, { "cell_type": "markdown", "id": "55b94021", "metadata": {}, "source": [ "\n", "\n", "## Exigences\n", "\n", "Avant de commencer ce tutoriel, assurez-vous d'avoir installé les éléments suivants :\n", "\n", "* Qiskit SDK v2.0 ou version ultérieure, avec prise en charge [de la visualisation](/docs/api/qiskit/visualization)\n", "* Qiskit Runtime v0.22 ou plus tard (`pip install qiskit-ibm-runtime`)\n", "\n" ] }, { "attachments": {}, "cell_type": "markdown", "id": "7db2e559", "metadata": {}, "source": [ "\n", "\n", "## Configuration\n", "\n", "Dans la cellule ci-dessous, nous importons les paquets nécessaires et créons quelques fonctions d'aide pour construire les circuits permettant l'évolution temporelle selon la méthode de Trotter d'un modèle d'Ising à champ transversal en deux dimensions, en respectant la topologie du backend.\n", "\n" ] }, { "cell_type": "code", "execution_count": 1, "id": "779bbc51", "metadata": {}, "outputs": [], "source": [ "from __future__ import annotations\n", "from collections.abc import Sequence\n", "from collections import defaultdict\n", "import numpy as np\n", "import rustworkx\n", "import matplotlib.pyplot as plt\n", "\n", "from qiskit.circuit import QuantumCircuit, Parameter\n", "from qiskit.circuit.library import CXGate, CZGate, ECRGate\n", "from qiskit.providers import Backend\n", "from qiskit.visualization import plot_error_map\n", "from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager\n", "from qiskit.quantum_info import SparsePauliOp\n", "from qiskit.primitives import PubResult\n", "\n", "from qiskit_ibm_runtime import QiskitRuntimeService\n", "from qiskit_ibm_runtime import EstimatorV2 as Estimator\n", "\n", "\n", "\"\"\"Trotter circuit generation\"\"\"\n", "\n", "\n", "def remove_qubit_couplings(\n", " couplings: Sequence[tuple[int, int]], qubits: Sequence[int] | None = None\n", ") -> list[tuple[int, int]]:\n", " \"\"\"Remove qubits from a coupling list.\n", "\n", " Args:\n", " couplings: A sequence of qubit couplings.\n", " qubits: Optional, the qubits to remove.\n", "\n", " Returns:\n", " The input couplings with the specified qubits removed.\n", " \"\"\"\n", " if qubits is None:\n", " return couplings\n", " qubits = set(qubits)\n", " return [edge for edge in couplings if not qubits.intersection(edge)]\n", "\n", "\n", "def coupling_qubits(\n", " *couplings: Sequence[tuple[int, int]],\n", " allowed_qubits: Sequence[int] | None = None,\n", ") -> list[int]:\n", " \"\"\"Return a sorted list of all qubits involved in one or more couplings lists.\n", "\n", " Args:\n", " couplings: one or more coupling lists.\n", " allowed_qubits: Optional, the allowed qubits to include. If None all\n", " qubits are allowed.\n", "\n", " Returns:\n", " The intersection of all qubits in the couplings and the allowed qubits.\n", " \"\"\"\n", " qubits = set()\n", " for edges in couplings:\n", " for edge in edges:\n", " qubits.update(edge)\n", " if allowed_qubits is not None:\n", " qubits = qubits.intersection(allowed_qubits)\n", " return list(qubits)\n", "\n", "\n", "def construct_layer_couplings(\n", " backend: Backend,\n", ") -> list[list[tuple[int, int]]]:\n", " \"\"\"Separate a coupling map into disjoint 2-qubit gate layers.\n", "\n", " Args:\n", " backend: A backend to construct layer couplings for.\n", "\n", " Returns:\n", " A list of disjoint layers of directed couplings for the input coupling map.\n", " \"\"\"\n", " coupling_graph = backend.coupling_map.graph.to_undirected(\n", " multigraph=False\n", " )\n", " edge_coloring = rustworkx.graph_bipartite_edge_color(coupling_graph)\n", "\n", " layers = defaultdict(list)\n", " for edge_idx, color in edge_coloring.items():\n", " layers[color].append(\n", " coupling_graph.get_edge_endpoints_by_index(edge_idx)\n", " )\n", " layers = [sorted(layers[i]) for i in sorted(layers.keys())]\n", "\n", " return layers\n", "\n", "\n", "def entangling_layer(\n", " gate_2q: str,\n", " couplings: Sequence[tuple[int, int]],\n", " qubits: Sequence[int] | None = None,\n", ") -> QuantumCircuit:\n", " \"\"\"Generating a entangling layer for the specified couplings.\n", "\n", " This corresponds to a Trotter layer for a ZZ Ising term with angle Pi/2.\n", "\n", " Args:\n", " gate_2q: The 2-qubit basis gate for the layer, should be \"cx\", \"cz\", or \"ecr\".\n", " couplings: A sequence of qubit couplings to add CX gates to.\n", " qubits: Optional, the physical qubits for the layer. Any couplings involving\n", " qubits not in this list will be removed. If None the range up to the largest\n", " qubit in the couplings will be used.\n", "\n", " Returns:\n", " The QuantumCircuit for the entangling layer.\n", " \"\"\"\n", " # Get qubits and convert to set to order\n", " if qubits is None:\n", " qubits = range(1 + max(coupling_qubits(couplings)))\n", " qubits = set(qubits)\n", "\n", " # Mapping of physical qubit to virtual qubit\n", " qubit_mapping = {q: i for i, q in enumerate(qubits)}\n", "\n", " # Convert couplings to indices for virtual qubits\n", " indices = [\n", " [qubit_mapping[i] for i in edge]\n", " for edge in couplings\n", " if qubits.issuperset(edge)\n", " ]\n", "\n", " # Layer circuit on virtual qubits\n", " circuit = QuantumCircuit(len(qubits))\n", "\n", " # Get 2-qubit basis gate and pre and post rotation circuits\n", " gate2q = None\n", " pre = QuantumCircuit(2)\n", " post = QuantumCircuit(2)\n", "\n", " if gate_2q == \"cx\":\n", " gate2q = CXGate()\n", " # Pre-rotation\n", " pre.sdg(0)\n", " pre.z(1)\n", " pre.sx(1)\n", " pre.s(1)\n", " # Post-rotation\n", " post.sdg(1)\n", " post.sxdg(1)\n", " post.s(1)\n", " elif gate_2q == \"ecr\":\n", " gate2q = ECRGate()\n", " # Pre-rotation\n", " pre.z(0)\n", " pre.s(1)\n", " pre.sx(1)\n", " pre.s(1)\n", " # Post-rotation\n", " post.x(0)\n", " post.sdg(1)\n", " post.sxdg(1)\n", " post.s(1)\n", " elif gate_2q == \"cz\":\n", " gate2q = CZGate()\n", " # Identity pre-rotation\n", " # Post-rotation\n", " post.sdg([0, 1])\n", " else:\n", " raise ValueError(\n", " f\"Invalid 2-qubit basis gate {gate_2q}, should be 'cx', 'cz', or 'ecr'\"\n", " )\n", "\n", " # Add 1Q pre-rotations\n", " for inds in indices:\n", " circuit.compose(pre, qubits=inds, inplace=True)\n", "\n", " # Use barriers around 2-qubit basis gate to specify a layer for PEA noise learning\n", " circuit.barrier()\n", " for inds in indices:\n", " circuit.append(gate2q, (inds[0], inds[1]))\n", " circuit.barrier()\n", "\n", " # Add 1Q post-rotations after barrier\n", " for inds in indices:\n", " circuit.compose(post, qubits=inds, inplace=True)\n", "\n", " # Add physical qubits as metadata\n", " circuit.metadata[\"physical_qubits\"] = tuple(qubits)\n", "\n", " return circuit\n", "\n", "\n", "def trotter_circuit(\n", " theta: Parameter | float,\n", " layer_couplings: Sequence[Sequence[tuple[int, int]]],\n", " num_steps: int,\n", " gate_2q: str | None = \"cx\",\n", " backend: Backend | None = None,\n", " qubits: Sequence[int] | None = None,\n", ") -> QuantumCircuit:\n", " \"\"\"Generate a Trotter circuit for the 2D Ising\n", "\n", " Args:\n", " theta: The angle parameter for X.\n", " layer_couplings: A list of couplings for each entangling layer.\n", " num_steps: the number of Trotter steps.\n", " gate_2q: The 2-qubit basis gate to use in entangling layers.\n", " Can be \"cx\", \"cz\", \"ecr\", or None if a backend is provided.\n", " backend: A backend to get the 2-qubit basis gate from, if provided\n", " will override the basis_gate field.\n", " qubits: Optional, the allowed physical qubits to truncate the\n", " couplings to. If None the range up to the largest\n", " qubit in the couplings will be used.\n", "\n", " Returns:\n", " The Trotter circuit.\n", " \"\"\"\n", " if backend is not None:\n", " try:\n", " basis_gates = backend.configuration().basis_gates\n", " except AttributeError:\n", " basis_gates = backend.basis_gates\n", " for gate in [\"cx\", \"cz\", \"ecr\"]:\n", " if gate in basis_gates:\n", " gate_2q = gate\n", " break\n", "\n", " # If no qubits, get the largest qubit from all layers and\n", " # specify the range so the same one is used for all layers.\n", " if qubits is None:\n", " qubits = range(1 + max(coupling_qubits(layer_couplings)))\n", "\n", " # Generate the entangling layers\n", " layers = [\n", " entangling_layer(gate_2q, couplings, qubits=qubits)\n", " for couplings in layer_couplings\n", " ]\n", "\n", " # Construct the circuit for a single Trotter step\n", " num_qubits = len(qubits)\n", " trotter_step = QuantumCircuit(num_qubits)\n", " trotter_step.rx(theta, range(num_qubits))\n", " for layer in layers:\n", " trotter_step.compose(layer, range(num_qubits), inplace=True)\n", "\n", " # Construct the circuit for the specified number of Trotter steps\n", " circuit = QuantumCircuit(num_qubits)\n", " for _ in range(num_steps):\n", " circuit.rx(theta, range(num_qubits))\n", " for layer in layers:\n", " circuit.compose(layer, range(num_qubits), inplace=True)\n", "\n", " circuit.metadata[\"physical_qubits\"] = tuple(qubits)\n", " return circuit\n", "\n", "\n", "\"\"\"Result visualization functions\"\"\"\n", "\n", "\n", "def plot_trotter_results(\n", " pub_result: PubResult,\n", " angles: Sequence[float],\n", " plot_noise_factors: Sequence[float] | None = None,\n", " plot_extrapolator: Sequence[str] | None = None,\n", " exact: np.ndarray = None,\n", " close: bool = True,\n", "):\n", " \"\"\"Plot average magnetization from ZNE result data.\n", " Args:\n", " pub_result: The Estimator PubResult for the PEA experiment.\n", " angles: The Rx angle values for the experiment.\n", " plot_raw: If provided plot the unextrapolated data for the noise factors.\n", " plot_extrapolator: If provided plot all extrapolators, if False only plot\n", " the Automatic method.\n", " exact: Optional, the exact values to include in the plot. Should be a 1D\n", " array-like where the values represent exact magnetization.\n", " close: Close the Matplotlib figure before returning.\n", " Returns:\n", " The figure.\n", " \"\"\"\n", " data = pub_result.data\n", "\n", " evs = data.evs\n", " num_qubits = evs.shape[0]\n", " num_params = evs.shape[1]\n", " angles = np.asarray(angles).ravel()\n", " if angles.shape != (num_params,):\n", " raise ValueError(\n", " f\"Incorrect number of angles for input data {angles.size} != {num_params}\"\n", " )\n", "\n", " # Take average magnetization of qubits and its standard error\n", " x_vals = angles / np.pi\n", " y_vals = np.mean(evs, axis=0)\n", " y_errs = np.std(evs, axis=0) / np.sqrt(num_qubits)\n", "\n", " fig, _ = plt.subplots(1, 1)\n", "\n", " # Plot auto method\n", " plt.errorbar(x_vals, y_vals, y_errs, fmt=\"o-\", label=\"ZNE (automatic)\")\n", "\n", " # Plot individual extrapolator results\n", " if plot_extrapolator:\n", " y_vals_extrap = np.mean(data.evs_extrapolated, axis=0)\n", " y_errs_extrap = np.std(data.evs_extrapolated, axis=0) / np.sqrt(\n", " num_qubits\n", " )\n", " for i, extrap in enumerate(plot_extrapolator):\n", " plt.errorbar(\n", " x_vals,\n", " y_vals_extrap[:, i, 0],\n", " y_errs_extrap[:, i, 0],\n", " fmt=\"s-.\",\n", " alpha=0.5,\n", " label=f\"ZNE ({extrap})\",\n", " )\n", "\n", " # Plot raw results\n", " if plot_noise_factors:\n", " y_vals_raw = np.mean(data.evs_noise_factors, axis=0)\n", " y_errs_raw = np.std(data.evs_noise_factors, axis=0) / np.sqrt(\n", " num_qubits\n", " )\n", " for i, nf in enumerate(plot_noise_factors):\n", " plt.errorbar(\n", " x_vals,\n", " y_vals_raw[:, i],\n", " y_errs_raw[:, i],\n", " fmt=\"d:\",\n", " alpha=0.5,\n", " label=f\"Raw (nf={nf:.1f})\",\n", " )\n", "\n", " # Plot exact data\n", " if exact is not None:\n", " plt.plot(x_vals, exact, \"--\", color=\"black\", alpha=0.5, label=\"Exact\")\n", "\n", " plt.ylim(-0.1, 1.2)\n", " plt.xlabel(\"θ/π\")\n", " plt.ylabel(r\"$\\overline{\\langle Z \\rangle}$\")\n", " plt.legend()\n", " plt.title(\n", " f\"Error Mitigated Average Magnetization for Rx(θ) [{num_qubits}-qubit]\"\n", " )\n", " if close:\n", " plt.close(fig)\n", " return fig\n", "\n", "\n", "def plot_qubit_zne_data(\n", " pub_result: PubResult,\n", " angles: Sequence[float],\n", " qubit: int,\n", " noise_factors: Sequence[float],\n", " extrapolator: Sequence[str] | None = None,\n", " extrapolated_noise_factors: Sequence[float] | None = None,\n", " num_cols: int | None = None,\n", " close: bool = True,\n", "):\n", " \"\"\"Plot ZNE extrapolation data for specific virtual qubit\n", " Args:\n", " pub_result: The Estimator PubResult for the PEA experiment.\n", " angles: The Rx theta angles used for the experiment.\n", " qubit: The virtual qubit index to plot.\n", " noise_factors: the raw noise factors.\n", " extrapolator: The extrapolator metadata for multiple extrapolators.\n", " extrapolated_noise_factors: The noise factors used for extrapolation.\n", " num_cols: The number of columns for the generated subplots.\n", " close: Close the Matplotlib figure before returning.\n", " Returns:\n", " The Matplotlib figure.\n", " \"\"\"\n", " data = pub_result.data\n", "\n", " evs_auto = data.evs[qubit]\n", " stds_auto = data.stds[qubit]\n", " evs_extrap = data.evs_extrapolated[qubit]\n", " stds_extrap = data.stds_extrapolated[qubit]\n", " evs_raw = data.evs_noise_factors[qubit]\n", " stds_raw = data.stds_noise_factors[qubit]\n", "\n", " num_params = evs_auto.shape[0]\n", " angles = np.asarray(angles).ravel()\n", " if angles.shape != (num_params,):\n", " raise ValueError(\n", " f\"Incorrect number of angles for input data {angles.size} != {num_params}\"\n", " )\n", "\n", " # Make a square subplot\n", " num_cols = num_cols or int(np.ceil(np.sqrt(num_params)))\n", " num_rows = int(np.ceil(num_params / num_cols))\n", " fig, axes = plt.subplots(\n", " num_rows, num_cols, sharex=True, sharey=True, figsize=(12, 5)\n", " )\n", " fig.suptitle(f\"ZNE data for virtual qubit {qubit}\")\n", "\n", " for pidx, ax in zip(range(num_params), axes.flat):\n", " # Plot auto extrapolated\n", " ax.errorbar(\n", " 0,\n", " evs_auto[pidx],\n", " stds_auto[pidx],\n", " fmt=\"o\",\n", " label=\"PEA (automatic)\",\n", " )\n", "\n", " # Plot extrapolators\n", " if (\n", " extrapolator is not None\n", " and extrapolated_noise_factors is not None\n", " ):\n", " for i, method in enumerate(extrapolator):\n", " ax.errorbar(\n", " extrapolated_noise_factors,\n", " evs_extrap[pidx, i],\n", " stds_extrap[pidx, i],\n", " fmt=\"-\",\n", " alpha=0.5,\n", " label=f\"PEA ({method})\",\n", " )\n", "\n", " # Plot raw\n", " ax.errorbar(\n", " noise_factors, evs_raw[pidx], stds_raw[pidx], fmt=\"d\", label=\"Raw\"\n", " )\n", "\n", " ax.set_yticks([0, 0.5, 1, 1.5, 2])\n", " ax.set_ylim(0, max(1, 1.1 * max(evs_auto)))\n", "\n", " ax.set_xticks([0, *noise_factors])\n", " ax.set_title(f\"θ/π = {angles[pidx]/np.pi:.2f}\")\n", " if pidx == 0:\n", " ax.set_ylabel(r\"$\\langle Z_{\" + str(qubit) + r\"} \\rangle$\")\n", " if pidx == num_params - 1:\n", " ax.set_xlabel(\"Noise Factor\")\n", " ax.legend()\n", " plt.tight_layout()\n", " if close:\n", " plt.close(fig)\n", " return fig" ] }, { "cell_type": "markdown", "id": "431a5bd2-e6ed-471b-ad9e-c4edd27784a8", "metadata": {}, "source": [ "\n", "\n", "## Exemple de simulateur à petite échelle\n", "\n", "Nous allons ignorer cette étape, car la gestion des erreurs d'exécution n'est pas prise en charge sur les simulateurs.\n", "\n", "\n", "\n", "## Exemple de matériel à grande échelle\n", "\n" ] }, { "attachments": {}, "cell_type": "markdown", "id": "988ee237", "metadata": {}, "source": [ "\n", "\n", "### Étape 1 : Mettre en correspondance les entrées classiques avec un problème quantique\n", "\n", "\n", "\n", "#### Créer un circuit de modèle Ising paramétré\n", "\n", "\n", "\n", "##### Mettre en place un backend\n", "\n", "Tout d'abord, choisissez un backend sur lequel vous souhaitez travailler. Cette démonstration fonctionne avec un backend de 127 qubits, mais vous pouvez la modifier pour l'adapter à n'importe quel backend disponible.\n", "\n" ] }, { "cell_type": "code", "execution_count": 2, "id": "a3debf65-06df-4277-933e-14b6f6170756", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "service = QiskitRuntimeService()\n", "backend = service.least_busy(\n", " operational=True, simulator=False, min_num_qubits=127\n", ")\n", "backend" ] }, { "cell_type": "markdown", "id": "c13564d0", "metadata": {}, "source": [ "\n", "\n", "##### Définir les couplages entre couches enchevêtrées\n", "\n", "Pour mettre en œuvre la simulation d'Ising trotterisée, définissez trois couches de couplages de porte à deux qubits pour le dispositif, à répéter à chaque étape de Trotter. Il s'agit des trois couches tourbillonnantes dont il faut connaître le bruit pour mettre en œuvre des mesures d'atténuation.\n", "\n" ] }, { "cell_type": "code", "execution_count": 3, "id": "0211a3f8", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Layer 0:\n", "[(2, 3), (4, 5), (6, 7), (8, 9), (10, 11), (12, 13), (14, 15), (16, 23), (18, 31), (19, 35), (20, 21), (25, 37), (26, 27), (28, 29), (33, 39), (36, 41), (38, 49), (42, 43), (45, 46), (47, 57), (51, 52), (53, 54), (56, 63), (58, 71), (59, 75), (61, 62), (64, 65), (66, 67), (68, 69), (72, 73), (76, 81), (79, 93), (82, 83), (84, 85), (86, 87), (88, 89), (91, 98), (94, 95), (97, 107), (99, 115), (100, 101), (102, 103), (105, 117), (108, 109), (110, 111), (113, 114), (116, 121), (118, 129), (123, 136), (124, 125), (126, 127), (130, 131), (132, 133), (135, 139), (138, 151), (142, 143), (144, 145), (146, 147), (152, 153), (154, 155)]\n", "\n", "Layer 1:\n", "[(0, 1), (3, 16), (5, 6), (7, 8), (11, 18), (13, 14), (17, 27), (21, 22), (23, 24), (25, 26), (29, 38), (30, 31), (32, 33), (34, 35), (39, 53), (41, 42), (43, 56), (44, 45), (47, 48), (49, 50), (51, 58), (54, 55), (57, 67), (60, 61), (62, 63), (65, 66), (69, 78), (70, 71), (73, 79), (74, 75), (77, 85), (80, 81), (83, 84), (87, 97), (89, 90), (91, 92), (93, 94), (96, 103), (101, 116), (104, 105), (106, 107), (109, 118), (111, 112), (113, 119), (114, 115), (117, 125), (121, 122), (123, 124), (127, 137), (128, 129), (131, 138), (133, 134), (136, 143), (139, 155), (140, 141), (145, 146), (147, 148), (149, 150), (151, 152)]\n", "\n", "Layer 2:\n", "[(1, 2), (3, 4), (7, 17), (9, 10), (11, 12), (15, 19), (21, 36), (22, 23), (24, 25), (27, 28), (29, 30), (31, 32), (33, 34), (37, 45), (40, 41), (43, 44), (46, 47), (48, 49), (50, 51), (52, 53), (55, 59), (61, 76), (63, 64), (65, 77), (67, 68), (69, 70), (71, 72), (73, 74), (78, 89), (81, 82), (83, 96), (85, 86), (87, 88), (90, 91), (92, 93), (95, 99), (98, 111), (101, 102), (103, 104), (105, 106), (107, 108), (109, 110), (112, 113), (119, 133), (120, 121), (122, 123), (125, 126), (127, 128), (129, 130), (131, 132), (134, 135), (137, 147), (141, 142), (143, 144), (148, 149), (150, 151), (153, 154)]\n", "\n" ] } ], "source": [ "layer_couplings = construct_layer_couplings(backend)\n", "for i, layer in enumerate(layer_couplings):\n", " print(f\"Layer {i}:\\n{layer}\\n\")" ] }, { "cell_type": "markdown", "id": "d320e933", "metadata": {}, "source": [ "\n", "\n", "##### Supprimer les qubits défectueux\n", "\n", "Regardez la carte des couplages pour le backend et voyez si des qubits se connectent à des couplages avec un taux d'erreur élevé. Retirez ces \"mauvais\" qubits de votre expérience.\n", "\n" ] }, { "cell_type": "code", "execution_count": 4, "id": "fccef708", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "\"Output" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Plot gate error map\n", "# NOTE: These can change over time, so your results may look different\n", "plot_error_map(backend)" ] }, { "cell_type": "code", "execution_count": 5, "id": "5973c90b", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Physical qubits:\n", " [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155]\n" ] } ], "source": [ "bad_qubits = {\n", " 32,\n", " 33,\n", " 71,\n", " 72,\n", " 73,\n", " 102,\n", " 103,\n", "} # qubits removed based on high coupling error (1.00)\n", "good_qubits = list(set(range(backend.num_qubits)).difference(bad_qubits))\n", "print(\"Physical qubits:\\n\", good_qubits)" ] }, { "cell_type": "markdown", "id": "180c4cb5", "metadata": {}, "source": [ "\n", "\n", "##### Génération du circuit principal Trotter\n", "\n" ] }, { "cell_type": "code", "execution_count": 6, "id": "f814ca82", "metadata": {}, "outputs": [], "source": [ "num_steps = 6\n", "theta = Parameter(\"theta\")\n", "circuit = trotter_circuit(\n", " theta, layer_couplings, num_steps, qubits=good_qubits, backend=backend\n", ")" ] }, { "cell_type": "markdown", "id": "7b86b867", "metadata": {}, "source": [ "\n", "\n", "#### Créer une liste des valeurs des paramètres à attribuer ultérieurement\n", "\n" ] }, { "cell_type": "code", "execution_count": 7, "id": "5da6e991", "metadata": {}, "outputs": [], "source": [ "num_params = 12\n", "\n", "# 12 parameter values for Rx between [0, pi/2].\n", "# Reshape to outer product broadcast with observables\n", "parameter_values = np.linspace(0, np.pi / 2, num_params).reshape(\n", " (num_params, 1)\n", ")\n", "num_params = parameter_values.size" ] }, { "cell_type": "markdown", "id": "ac6f36e3", "metadata": {}, "source": [ "\n", "\n", "### Étape 2 : Optimiser le problème pour l'exécution sur du matériel quantique\n", "\n", "\n", "\n", "#### circuit ISA\n", "\n", "Avant d'exécuter le circuit sur le matériel, optimisez-le pour l'exécution matérielle. Ce processus comporte plusieurs étapes :\n", "\n", "* Choisissez une disposition de qubits qui fait correspondre les qubits virtuels de votre circuit aux qubits physiques du matériel.\n", "* Insérez des portes de permutation si nécessaire pour acheminer les interactions entre les qubits qui ne sont pas connectés.\n", "* Traduire les portes de notre circuit en instructions [ISA (Instruction Set Architecture)](/docs/guides/transpile#instruction-set-architecture) qui peuvent être directement exécutées sur le matériel.\n", "* Effectuer des optimisations de circuit pour minimiser la profondeur du circuit et le nombre de portes.\n", "\n", "Bien que le transpondeur intégré à Qiskit puisse réaliser toutes ces étapes, ce tutoriel présente la construction du circuit Trotter à l'échelle de l'entreprise en partant de la base. Sélectionner les bons qubits physiques et définir des couches d'enchevêtrement sur des paires de qubits connectés à partir de ces qubits sélectionnés. Néanmoins, vous devez toujours traduire les portes non-ISA dans le circuit et profiter de l'optimisation du circuit offerte par le transpileur.\n", "\n", "Transpilez votre circuit pour le backend choisi en créant un gestionnaire de passe et en exécutant le gestionnaire de passe sur le circuit. Fixez également la disposition initiale du circuit sur le site déjà sélectionné `good_qubits`. Un moyen simple de créer un gestionnaire de laissez-passer est d'utiliser la fonction [`generate_preset_pass_manager`](/docs/api/qiskit/qiskit.transpiler.generate_preset_pass_manager) fonction. Voir [Transpiler avec les gestionnaires de passe](/docs/guides/transpile-with-pass-managers) pour une explication plus détaillée de la transposition avec les gestionnaires de passe.\n", "\n" ] }, { "cell_type": "code", "execution_count": 8, "id": "1834cb22", "metadata": {}, "outputs": [], "source": [ "pm = generate_preset_pass_manager(\n", " backend=backend,\n", " initial_layout=good_qubits,\n", " layout_method=\"trivial\",\n", " optimization_level=1,\n", ")\n", "\n", "isa_circuit = pm.run(circuit)" ] }, { "cell_type": "markdown", "id": "d395c8cf", "metadata": {}, "source": [ "\n", "\n", "#### Observables ISA\n", "\n", "Ensuite, créez toutes les observables weight-1 $\\langle Z \\rangle$ pour chaque qubit virtuel en ajoutant le nombre nécessaire de termes $\\langle I \\rangle$.\n", "\n" ] }, { "cell_type": "code", "execution_count": 9, "id": "cc5ab1ed", "metadata": {}, "outputs": [], "source": [ "observables = []\n", "num_qubits = len(good_qubits)\n", "for q in range(num_qubits):\n", " observables.append(\n", " SparsePauliOp(\"I\" * (num_qubits - q - 1) + \"Z\" + \"I\" * q)\n", " )" ] }, { "cell_type": "markdown", "id": "030db4ed", "metadata": {}, "source": [ "Le processus de transpilation a mis en correspondance les qubits virtuels de votre circuit avec les qubits physiques du matériel. Les informations relatives à la disposition du qubit sont stockées dans l'attribut `layout` du circuit transposé. Votre observable est également défini en termes de qubits virtuels, vous devez donc appliquer cette disposition à l'observable. Pour ce faire, on utilise la méthode `apply_layout` de `SparsePauliOp`.\n", "\n", "Notez que chaque observable est encapsulé dans une liste dans le bloc de code suivant. Cette opération est effectuée pour *diffuser* les valeurs des paramètres, de sorte que chaque observable de qubit soit mesurée pour chaque valeur de thêta. Vous trouverez les règles de diffusion des primitives dans la [documentation](/docs/guides/primitives) relative aux primitives.\n", "\n" ] }, { "cell_type": "code", "execution_count": 10, "id": "95fd2908", "metadata": {}, "outputs": [], "source": [ "isa_observables = [\n", " [obs.apply_layout(layout=isa_circuit.layout)] for obs in observables\n", "]" ] }, { "attachments": {}, "cell_type": "markdown", "id": "b4d480b3", "metadata": {}, "source": [ "\n", "\n", "### Étape 3 : Exécutez à l'aide d' Qiskit primitives\n", "\n" ] }, { "cell_type": "code", "execution_count": 11, "id": "b22a1b00", "metadata": {}, "outputs": [], "source": [ "pub = (isa_circuit, isa_observables, parameter_values)" ] }, { "cell_type": "markdown", "id": "4ace7773", "metadata": {}, "source": [ "\n", "\n", "#### Configurer les options de l'estimateur\n", "\n", "Configurez ensuite les options `Estimator` nécessaires à l'exécution de l'expérience d'atténuation. Cela inclut des options pour l'apprentissage du bruit des couches enchevêtrées et pour l'extrapolation des ZNE.\n", "\n", "Nous utilisons la configuration suivante :\n", "\n" ] }, { "cell_type": "code", "execution_count": 12, "id": "ad4a4f1c", "metadata": {}, "outputs": [], "source": [ "# Experiment options\n", "num_randomizations = 700\n", "num_randomizations_learning = 40\n", "max_batch_circuits = 3 * num_params\n", "shots_per_randomization = 64\n", "learning_pair_depths = [0, 1, 2, 4, 6, 12, 24]\n", "noise_factors = [1, 1.3, 1.6]\n", "extrapolated_noise_factors = np.linspace(0, max(noise_factors), 20)\n", "\n", "# Base option formatting\n", "options = {\n", " # Builtin resilience settings for ZNE\n", " \"resilience\": {\n", " \"measure_mitigation\": True,\n", " \"zne_mitigation\": True,\n", " # TREX noise learning configuration\n", " \"measure_noise_learning\": {\n", " \"num_randomizations\": num_randomizations_learning,\n", " \"shots_per_randomization\": 1024,\n", " },\n", " # PEA noise model configuration\n", " \"layer_noise_learning\": {\n", " \"max_layers_to_learn\": 3,\n", " \"layer_pair_depths\": learning_pair_depths,\n", " \"shots_per_randomization\": shots_per_randomization,\n", " \"num_randomizations\": num_randomizations_learning,\n", " },\n", " \"zne\": {\n", " \"amplifier\": \"pea\",\n", " \"noise_factors\": noise_factors,\n", " \"extrapolator\": (\"exponential\", \"linear\"),\n", " \"extrapolated_noise_factors\": extrapolated_noise_factors.tolist(),\n", " },\n", " },\n", " # Randomization configuration\n", " \"twirling\": {\n", " \"num_randomizations\": num_randomizations,\n", " \"shots_per_randomization\": shots_per_randomization,\n", " \"strategy\": \"active-circuit\",\n", " },\n", " # Optional Dynamical Decoupling (DD)\n", " \"dynamical_decoupling\": {\"enable\": True, \"sequence_type\": \"XY4\"},\n", " # Job tag\n", " \"environment\": {\"job_tags\": [\"TUT_PEA\"]},\n", "}" ] }, { "cell_type": "markdown", "id": "3f9fd4c4", "metadata": {}, "source": [ "\n", "\n", "##### Explication des options ZNE\n", "\n", "Les paragraphes suivants détaillent les options supplémentaires de la branche expérimentale. Notez que ces options et ces noms ne sont pas définitifs, et que tout ce qui figure ici est susceptible d'être modifié avant la publication officielle.\n", "\n", "* **amplificateur** : méthode à utiliser pour amplifier le bruit jusqu'aux niveaux souhaités.\n", " Les valeurs autorisées sont `\"gate_folding\"`, qui amplifie en répétant des portes de base à deux qubits,\n", " et `\"pea\"`, qui amplifie par échantillonnage probabiliste après apprentissage du modèle de bruit à torsion de Pauli\n", " pour des couches de portes de base à deux qubits avec torsion. D'autres options sont `\"gate_folding_front\"` et `\"gate_folding_back\"`, qui sont décrites dans la [documentation de l'API](/docs/api/qiskit-ibm-runtime/options-zne-options#amplifier).\n", "* **facteurs de bruit extrapolés** : Spécifier une ou plusieurs valeurs de facteur de bruit pour lesquelles évaluer les modèles extrapolés modèles extrapolés. S'il s'agit d'une séquence de valeurs, les résultats renvoyés seront des valeurs de tableau avec le facteur de bruit spécifié évalué pour le modèle d'extrapolation. Une valeur de 0 correspond à une extrapolation sans bruit.\n", "\n", "\n", "\n", "#### Exécution de l'expérimentation\n", "\n" ] }, { "cell_type": "code", "execution_count": 13, "id": "3cf72c8c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Job ID d7fa8oe2cugc739qbb10\n" ] } ], "source": [ "estimator = Estimator(mode=backend, options=options)\n", "job = estimator.run([pub])\n", "print(f\"Job ID {job.job_id()}\")" ] }, { "cell_type": "code", "execution_count": 14, "id": "1eea9c17", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'DONE'" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "job.status()" ] }, { "cell_type": "markdown", "id": "50b94af2", "metadata": {}, "source": [ "\n", "\n", "### Étape 4 : Post-traitement et restitution du résultat dans le format classique souhaité\n", "\n", "Une fois l'expérience terminée, vous pouvez consulter vos résultats. Vous récupérez les valeurs brutes et atténuées des attentes et les comparez aux résultats exacts. Tracez ensuite les valeurs d'espérance, à la fois atténuées (extrapolées) et brutes, moyennées sur tous les qubits pour chaque paramètre. Enfin, tracez les valeurs d'espérance pour votre choix de qubits individuels.\n", "\n" ] }, { "cell_type": "code", "execution_count": 15, "id": "31dc35ea-6554-4ca7-9c3b-0b5394c46e4e", "metadata": {}, "outputs": [], "source": [ "primitive_result = job.result()" ] }, { "cell_type": "markdown", "id": "fbf7ec8d", "metadata": {}, "source": [ "\n", "\n", "#### Formes générales des résultats et métadonnées\n", "\n", "L'objet `PrimitiveResult` contient une structure de type liste nommée `PubResult`. Comme nous ne soumettons qu'un seul PUB à l'estimateur, le `PrimitiveResult` contient un seul objet `PubResult` .\n", "\n", "Les valeurs attendues et les erreurs types du résultat PUB (bloc unifié primitif) sont des valeurs de tableau. Pour les tâches d'estimation avec ZNE, plusieurs champs de données contenant les valeurs attendues et les erreurs types sont disponibles dans le `PubResult`conteneur `DataBin` « s ». Nous aborderons brièvement ici les champs de données relatifs aux valeurs attendues (des champs de données similaires sont également disponibles pour les erreurs types (`stds`)).\n", "\n", "1. `pub_result.data.evs`: Valeurs d'espérance correspondant au bruit zéro (basées sur la meilleure extrapolation heuristique).\n", " * Le premier axe est l'indice du qubit virtuel pour l'observable $\\langle Z_i\\rangle$ ( $124$ virtual-qubits/observables)\n", " * Le deuxième axe indexe la valeur du paramètre pour $\\theta$ (valeurs du paramètre $12$ )\n", "2. `pub_result.data.evs_extrapolated`: Valeurs attendues pour les facteurs de bruit extrapolés pour chaque extrapolateur. Ce tableau comporte deux axes supplémentaires.\n", " * Le troisième axe indexe les méthodes d'extrapolation ( $2$ extrapolateurs, `exponential` et `linear`)\n", " * Le dernier axe indexe les `extrapolated_noise_factors` (points $20$ d'extrapolation spécifiés dans l'option)\n", "3. `pub_result.data.evs_noise_factors`: Valeurs brutes de l'espérance pour chaque facteur de bruit.\n", " * Le troisième axe indexe les facteurs bruts `noise_factors` ( $3$ )\n", "\n" ] }, { "cell_type": "code", "execution_count": 16, "id": "e3aa4fc9", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "pub_result.data.evs.shape=(149, 12)\n", "pub_result.data.evs_extrapolated.shape=(149, 12, 2, 20)\n", "pub_result.data.evs_noise_factors.shape=(149, 12, 3)\n", "\n" ] } ], "source": [ "pub_result = primitive_result[0]\n", "\n", "print(\n", " f\"{pub_result.data.evs.shape=}\\n\"\n", " f\"{pub_result.data.evs_extrapolated.shape=}\\n\"\n", " f\"{pub_result.data.evs_noise_factors.shape=}\\n\"\n", ")" ] }, { "cell_type": "markdown", "id": "4c5cc6ee", "metadata": {}, "source": [ "Plusieurs champs de métadonnées sont également disponibles sur le site `PrimitiveResult`. Les métadonnées incluent notamment :\n", "\n", "* `resilience/zne/noise_factors`: Les facteurs de bruit bruts\n", "* `resilience/zne/extrapolator`: Les extrapolateurs utilisés pour chaque résultat\n", "\n" ] }, { "cell_type": "code", "execution_count": 17, "id": "1c77d83a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{'dynamical_decoupling': {'enable': True,\n", " 'sequence_type': 'XY4',\n", " 'extra_slack_distribution': 'middle',\n", " 'scheduling_method': 'alap'},\n", " 'twirling': {'enable_gates': True,\n", " 'enable_measure': True,\n", " 'num_randomizations': 700,\n", " 'shots_per_randomization': 64,\n", " 'interleave_randomizations': True,\n", " 'strategy': 'active-circuit'},\n", " 'resilience': {'measure_mitigation': True,\n", " 'zne_mitigation': True,\n", " 'pec_mitigation': False,\n", " 'zne': {'noise_factors': [1.0, 1.3, 1.6],\n", " 'extrapolator': ['exponential', 'linear'],\n", " 'extrapolated_noise_factors': [0.0,\n", " 0.08421052631578947,\n", " 0.16842105263157894,\n", " 0.25263157894736843,\n", " 0.3368421052631579,\n", " 0.42105263157894735,\n", " 0.5052631578947369,\n", " 0.5894736842105263,\n", " 0.6736842105263158,\n", " 0.7578947368421053,\n", " 0.8421052631578947,\n", " 0.9263157894736842,\n", " 1.0105263157894737,\n", " 1.0947368421052632,\n", " 1.1789473684210525,\n", " 1.263157894736842,\n", " 1.3473684210526315,\n", " 1.431578947368421,\n", " 1.5157894736842106,\n", " 1.6]},\n", " 'layer_noise_model': [LayerError(circuit=, qubits=[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155], error=PauliLindbladError(generators=['IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...', ...], rates=[0.00155, 0.00144, 0.00637, 0.00023, 0.0, 0.0, 0.00018, 0.00035, 0.0, 0.00014, 5e-05, 0.00041, 0.0, 0.0, 0.0, 0.0001, 0.0001, 0.0, 9e-05, 6e-05, 0.0, 7e-05, 0.0001, 0.00013, 0.00018, 1e-05, 5e-05, 7e-05, 6e-05, 6e-05, 0.00029, 0.00016, 6e-05, 6e-05, 0.00046, 0.00073, 0.00031, 0.00025, 0.00018, 0.00022, 0.0, 8e-05, 0.00012, 0.00015, 0.00012, 0.0, 0.0, 0.00023, 5e-05, 5e-05, 7e-05, 0.00064, 4e-05, 2e-05, 0.00072, 0.00037, 2e-05, 4e-05, 0.00077, 0.0003, 0.00042, 0.00027, 0.00016, 0.0, 8e-05, 5e-05, 0.00019, 0.0, 0.0, 0.00021, 0.00014, 0.00061, 0.0, 0.00016, 3e-05, 0.00053, 0.00013, 0.0, 0.00068, 0.00011, 0.0, 0.00013, 0.00078, 0.01885, 0.00032, 0.00034, 0.00035, 0.00052, 3e-05, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00028, 0.00123, 0.0, 0.0, 0.0, 0.00034, 0.00011, 0.0001, 0.00076, 0.00041, 0.0001, 0.00011, 0.00082, 0.0, 0.00066, 0.0, 0.00055, 7e-05, 0.00018, 0.00011, 0.00024, 3e-05, 0.00015, 0.00014, 0.0, 0.00076, 9e-05, 0.00016, 8e-05, 0.00132, 0.0, 0.00019, 0.00215, 0.00109, 0.00019, 0.0, 0.00201, 0.00021, 0.0006, 0.00032, 0.00046, 0.00027, 0.0, 8e-05, 0.0001, 0.00027, 0.0, 0.00015, 0.00018, 0.0, 0.00026, 0.00024, 5e-05, 0.00031, 0.0, 0.00034, 0.00039, 9e-05, 0.00034, 0.0, 0.00078, 0.00794, 0.00045, 0.00061, 0.00066, 0.0, 0.0, 0.00032, 6e-05, 5e-05, 7e-05, 0.0, 0.0001, 0.00036, 0.0, 0.00037, 0.00013, 0.00016, 3e-05, 8e-05, 0.00067, 0.00024, 8e-05, 3e-05, 0.00074, 0.00224, 0.00029, 0.00026, 0.00031, 0.00076, 5e-05, 0.0, 2e-05, 0.00072, 0.0, 1e-05, 0.00011, 0.00027, 0.0, 0.00017, 0.0, 0.0, 0.00012, 0.0, 0.0, 0.0, 0.0, 0.00067, 0.00063, 0.0, 0.0, 0.0, 0.00102, 0.0, 0.00011, 0.00026, 4e-05, 1e-05, 0.0002, 0.0, 0.00011, 0.0, 0.00021, 0.00015, 0.0005, 0.00011, 0.00013, 0.0, 0.0002, 0.00016, 0.00015, 8e-05, 2e-05, 7e-05, 0.00023, 0.00042, 0.0, 0.00049, 0.00056, 0.00372, 0.00017, 0.00012, 0.0, 0.00026, 0.00021, 0.0, 0.00012, 0.00046, 0.00305, 0.0005, 0.00057, 9e-05, 0.0009, 0.0, 7e-05, 0.00011, 0.00084, 0.0, 0.0, 0.0001, 0.00067, 0.0, 0.0, 0.0, 4e-05, 0.0, 1e-05, 0.00053, 0.0, 9e-05, 0.00021, 0.0, 1e-05, 0.0, 8e-05, 0.0, 0.0, 0.0, 9e-05, 0.00083, 0.00084, 0.00038, 9e-05, 3e-05, 0.00039, 0.02059, 0.0, 0.0, 0.0, 0.01787, 0.00012, 0.00024, 0.0, 0.00401, 0.0, 0.0, 0.0, 4e-05, 0.0, 0.0, 0.00018, 0.0, 0.00031, 0.00018, 0.0, 0.0, 0.0, 0.0, 0.00013, 0.0, 0.00027, 1e-05, 0.0, 0.00021, 0.0, 0.0, 0.00029, 0.00159, 0.0, 0.0, 0.00052, 0.0079, 0.0, 0.0002, 0.00147, 0.00048, 4e-05, 0.00976, 0.00957, 0.0011, 0.0, 0.0, 4e-05, 0.00048, 0.01068, 0.00487, 0.00225, 0.0, 0.0, 0.00026, 0.00052, 0.00033, 0.0, 0.00019, 0.0, 0.0, 0.00038, 0.0, 0.0, 0.0, 0.00154, 0.0, 0.0, 0.0, 0.00046, 0.0, 9e-05, 0.00077, 0.0002, 9e-05, 0.0, 0.00077, 0.00061, 6e-05, 0.00045, 0.00081, 0.00016, 0.0, 0.0, 0.0001, 0.00064, 4e-05, 0.0002, 0.0, 0.00056, 7e-05, 0.0, 0.0, 0.00066, 5e-05, 0.00025, 0.00077, 0.00011, 0.0, 0.0, 0.00065, 0.00025, 5e-05, 0.00082, 6e-05, 0.0, 0.00011, 0.00354, 0.00027, 0.00039, 0.00046, 0.00014, 0.0, 0.00013, 0.00067, 0.00064, 0.0006, 0.00053, 2e-05, 0.00016, 0.00067, 0.0, 0.00013, 0.0, 0.00047, 0.00016, 2e-05, 0.00067, 4e-05, 0.0, 0.00015, 0.00028, 0.00044, 0.00041, 0.00014, 0.00011, 0.0, 0.0, 5e-05, 0.0, 0.00017, 0.00022, 9e-05, 6e-05, 0.0, 0.00021, 0.0007, 3e-05, 0.0, 0.0, 0.0002, 0.00012, 3e-05, 0.0002, 0.0001, 3e-05, 0.00012, 0.00026, 0.00033, 0.00053, 0.00037, 0.00039, 9e-05, 6e-05, 7e-05, 0.00012, 0.00012, 0.0, 0.00022, 0.0, 0.00034, 0.00014, 8e-05, 0.0001, 0.00179, 0.00186, 0.00096, 0.00028, 0.00051, 0.00033, 0.0, 0.0, 0.00015, 0.0004, 0.0, 8e-05, 0.00015, 2e-05, 0.00015, 0.0, 0.00045, 0.0002, 0.0, 0.0, 0.00063, 0.00044, 0.00036, 0.00064, 0.0003, 2e-05, 0.0, 0.00124, 0.0, 0.0, 0.0, 0.00169, 0.00032, 0.00018, 0.0, 0.00147, 0.0, 0.0, 0.00037, 0.00095, 0.0, 0.00051, 0.00182, 0.00088, 0.00051, 0.0, 0.00116, 0.00093, 0.00124, 0.00219, 0.00052, 0.00072, 4e-05, 0.0, 0.0, 4e-05, 0.0, 0.00025, 0.00013, 0.0001, 0.00031, 0.0, 0.00027, 0.00022, 0.0, 0.00016, 0.0, 1e-05, 0.0001, 0.0, 3e-05, 0.0, 0.0, 2e-05, 6e-05, 0.0, 0.00021, 0.00251, 0.0, 0.0, 7e-05, 0.0, 0.0, 0.0, 0.00047, 5e-05, 2e-05, 0.00062, 0.00038, 2e-05, 5e-05, 0.00055, 0.00125, 0.00049, 0.00033, 0.00031, 0.00015, 0.0, 0.00015, 7e-05, 0.00047, 0.0, 1e-05, 3e-05, 1e-05, 0.00014, 0.0, 0.00026, 0.00092, 0.0, 0.0, 0.0, 0.00048, 0.00011, 4e-05, 0.0, 0.00077, 0.00013, 0.00014, 0.00031, 0.00048, 0.0, 0.0001, 0.00066, 6e-05, 2e-05, 0.0, 0.00029, 0.0001, 0.0, 0.00065, 0.0, 0.00013, 3e-05, 0.0, 0.00033, 0.00034, 0.00019, 2e-05, 0.0, 0.00015, 0.00046, 0.0, 2e-05, 1e-05, 0.00046, 8e-05, 6e-05, 0.0, 0.00035, 1e-05, 0.0001, 0.0, 1e-05, 0.0, 0.00012, 8e-05, 7e-05, 5e-05, 0.0, 0.00013, 0.0, 0.0, 0.0, 0.0, 0.00022, 0.0, 0.00013, 0.00028, 0.00014, 0.00013, 0.0, 0.00042, 0.00055, 0.00054, 0.00036, 5e-05, 0.0002, 0.0, 0.0, 0.00014, 1e-05, 0.00019, 2e-05, 6e-05, 0.00026, 0.0001, 0.0, 5e-05, 8e-05, 0.0, 0.00073, 7e-05, 0.0, 0.0, 1e-05, 0.0, 0.0, 6e-05, 4e-05, 0.00018, 0.00046, 0.00016, 0.00018, 4e-05, 0.00053, 0.0002, 0.00057, 0.00055, 0.00042, 0.00077, 6e-05, 0.00025, 5e-05, 0.00062, 0.00026, 0.00012, 4e-05, 0.00033, 8e-05, 0.0, 0.0004, 0.00036, 0.00016, 0.0, 0.0, 4e-05, 0.0, 4e-05, 0.0002, 4e-05, 0.00036, 0.0, 4e-05, 0.00024, 0.0, 0.0002, 0.00044, 0.00017, 0.0002, 0.0, 0.00051, 0.00059, 0.00061, 0.00069, 0.00064, 0.0006, 0.0, 7e-05, 4e-05, 0.00085, 0.0, 4e-05, 0.0, 0.00031, 0.00033, 0.0, 0.0001, 0.00037, 3e-05, 0.0, 0.0, 0.00018, 0.0, 0.00015, 4e-05, 0.00044, 9e-05, 2e-05, 2e-05, 0.00067, 0.00048, 6e-05, 0.0, 0.0, 0.0, 0.00028, 0.0, 1e-05, 0.0, 0.0, 0.00112, 0.0, 0.0, 0.00018, 0.00016, 0.0, 0.00018, 0.00055, 9e-05, 0.00018, 0.0, 0.00028, 0.00254, 0.00064, 0.00025, 0.00045, 0.00072, 7e-05, 6e-05, 0.00114, 0.00026, 0.00013, 0.0, 0.00081, 6e-05, 7e-05, 0.00139, 0.00014, 0.0, 0.00026, 0.00097, 0.00053, 0.00029, 0.00044, 0.0, 6e-05, 0.0, 0.00011, 3e-05, 0.0, 0.0002, 0.00024, 0.0, 5e-05, 5e-05, 5e-05, 0.0, 0.00014, 0.00025, 0.00032, 0.00011, 5e-05, 0.00067, 4e-05, 5e-05, 0.00011, 0.00061, 0.00015, 0.00035, 0.00035, 0.0003, 0.0006, 0.0, 0.00017, 0.0001, 0.0003, 0.00012, 8e-05, 0.00015, 7e-05, 0.0001, 5e-05, 0.00057, 0.0003, 9e-05, 0.00023, 0.0, 0.0001, 0.00015, 0.00073, 0.0, 0.0, 0.00012, 0.00041, 0.00015, 0.0001, 0.00079, 0.0003, 0.00011, 0.0, 0.00042, 0.00088, 0.00066, 0.00062, 0.00051, 0.0, 0.0, 0.00013, 0.00028, 8e-05, 0.00022, 0.0, 0.00044, 0.0, 0.00013, 0.0, 0.0, 0.0002, 0.00014, 0.00062, 0.00022, 0.00014, 0.0002, 0.0005, 4e-05, 0.00064, 0.00058, 0.00046, 0.00055, 0.0, 8e-05, 0.00012, 0.00067, 0.0, 0.0, 0.00014, 0.00095, 0.00025, 0.0, 0.00016, 0.00058, 0.00041, 0.00052, 0.00022, 6e-05, 0.0, 0.00034, 0.00011, 0.0, 0.0, 0.00015, 0.0, 6e-05, 0.00034, 0.0, 0.00016, 4e-05, 0.00126, 0.00041, 0.00037, 0.00015, 0.0, 0.0, 0.0, 0.00011, 0.0, 0.00024, 5e-05, 0.00029, 1e-05, 2e-05, 0.0, 0.00033, 0.00036, 4e-05, 0.00024, 0.001, 0.0, 0.0, 0.0, 0.00046, 0.0, 0.00028, 2e-05, 0.0009, 0.00012, 0.0, 0.00032, 0.00428, 0.00026, 9e-05, 0.0, 0.00372, 0.0, 9e-05, 0.0, 0.00107, 0.00018, 0.0, 0.00047, 0.00025, 0.00031, 0.00024, 0.00068, 0.00063, 0.00052, 4e-05, 0.00011, 0.00011, 0.00044, 7e-05, 4e-05, 4e-05, 5e-05, 0.00011, 0.00011, 0.00034, 0.0, 0.00017, 0.0, 0.00051, 0.00041, 0.00032, 0.00022, 0.0, 0.0, 9e-05, 6e-05, 7e-05, 0.00011, 2e-05, 0.00052, 0.0, 0.0, 0.0, 0.00731, 0.00017, 0.0, 0.0, 0.00026, 0.0, 0.00031, 0.0005, 0.0, 0.00031, 0.0, 0.00063, 0.0, 0.00026, 0.00052, 0.0, 0.0, 4e-05, 0.0, 0.00024, 7e-05, 9e-05, 6e-05, 3e-05, 0.0, 0.0, 0.00025, 0.00029, 0.00025, 0.00012, 4e-05, 5e-05, 0.00014, 4e-05, 0.00091, 9e-05, 0.0, 7e-05, 0.00019, 4e-05, 0.00014, 0.00085, 0.00037, 6e-05, 4e-05, 0.0001, 0.00025, 0.00026, 0.00013, 0.00026, 0.00014, 0.0, 2e-05, 0.00023, 0.0, 0.00021, 0.0, 0.0, 0.00031, 0.00031, 0.0001, 0.00013, 6e-05, 0.00013, 0.00071, 0.00048, 0.00013, 6e-05, 0.00076, 0.00018, 0.00042, 0.00044, 0.00018, 0.00014, 0.0, 0.00013, 9e-05, 0.0003, 0.0, 0.0, 1e-05, 0.0, 0.00019, 0.0, 7e-05, 1e-05, 9e-05, 0.0, 0.00011, 0.0, 7e-05, 0.00041, 0.0, 0.0, 0.00032, 0.0, 7e-05, 0.0, 0.00034, 0.0014, 0.0, 0.0002, 6e-05, 0.00036, 0.00031, 0.00039, 0.00042, 7e-05, 0.0, 0.0, 0.00014, 0.00011, 0.0, 2e-05, 0.00024, 0.0, 9e-05, 0.00036, 0.00023, 0.00012, 0.00011, 0.0, 0.00052, 5e-05, 0.0, 4e-05, 0.00033, 1e-05, 0.0, 9e-05, 0.00064, 0.0, 7e-05, 0.0, 0.00044, 0.00016, 0.0, 0.0, 0.00029, 0.0, 0.0, 0.00012, 0.00021, 0.0, 0.00017, 0.00068, 7e-05, 0.0, 0.00014, 0.00027, 0.00017, 0.0, 0.0006, 9e-05, 1e-05, 0.0, 0.00064, 0.00025, 0.00031, 0.00019, 0.0, 0.0, 0.00013, 0.00056, 0.0, 0.00017, 0.0, 0.00053, 7e-05, 0.0, 6e-05, 0.00029, 0.00018, 6e-05, 3e-05, 0.00027, 0.0, 6e-05, 0.00058, 0.00044, 6e-05, 0.0, 0.00052, 0.0004, 0.00073, 0.00066, 3e-05, 0.0004, 9e-05, 0.0, 0.00021, 0.00048, 0.0, 0.00016, 0.0, 0.00257, 0.0, 0.00021, 0.00024, 0.00012, 0.0, 0.00015, 8e-05, 0.00025, 0.00012, 0.0, 0.0, 0.00025, 0.00028, 0.0, 0.00014, 0.0, 7e-05, 0.00017, 0.00029, 0.0, 0.00017, 7e-05, 0.00024, 0.0, 0.00061, 0.00068, 0.0, 0.00018, 0.0, 7e-05, 1e-05, 0.0, 0.00017, 0.0, 0.0, 0.0003, 0.00013, 1e-05, 0.00024, 0.00098, 0.00071, 0.00142, 9e-05, 0.00011, 0.0, 0.00056, 0.00042, 0.0, 0.00011, 0.00064, 0.00085, 0.00098, 0.00071, 0.00018, 0.00085, 0.00081, 0.00016, 0.0, 0.0, 0.0, 7e-05, 0.0, 0.0, 0.0, 0.0, 0.00036, 0.00012, 0.0, 0.0, 0.00048, 0.00021, 0.00031, 6e-05, 0.00059, 0.00041, 0.00028, 7e-05, 0.00026, 0.0004, 0.00036, 0.00016, 0.00014, 9e-05, 6e-05, 0.00043, 0.0, 8e-05, 7e-05, 0.00036, 6e-05, 9e-05, 0.00055, 6e-05, 0.0, 3e-05, 0.00032, 0.00036, 0.00036, 0.00017, 0.0, 0.0, 1e-05, 0.00038, 0.0, 8e-05, 5e-05, 0.00026, 0.00014, 3e-05, 5e-05, 0.0, 0.0, 0.0, 0.00017, 0.00027, 0.0, 0.00019, 0.00063, 4e-05, 0.00019, 0.0, 0.00077, 0.00116, 0.00051, 0.00048, 0.00036, 8e-05, 0.0, 0.00011, 0.0001, 0.00013, 7e-05, 0.0, 0.0, 0.0, 0.0, 0.00028, 0.00026, 0.00014, 0.0003, 0.00011, 5e-05, 6e-05, 0.00017, 0.0007, 0.0, 0.0, 0.00011, 0.00063, 0.00017, 6e-05, 0.00079, 0.0, 0.0, 5e-05, 9e-05, 0.00029, 0.00021, 0.00048, 0.00072, 0.0, 0.0, 0.0, 0.00034, 9e-05, 4e-05, 0.0, 0.00013, 0.0, 5e-05, 0.00037, 0.0, 0.00011, 0.0, 0.00034, 0.0, 0.0, 7e-05, 0.0, 0.00605, 0.0, 0.00011, 0.00012, 0.00012, 0.00023, 0.0, 0.00026, 0.00016, 0.0, 0.00023, 0.00031, 0.00078, 0.0006, 0.00026, 0.00055, 0.00043, 0.00012, 0.0001, 0.00052, 8e-05, 0.0, 0.0, 0.00033, 0.0001, 0.00012, 0.00051, 5e-05, 0.00012, 0.0, 0.00105, 0.00028, 0.00018, 0.00023, 0.0, 2e-05, 0.0, 0.0, 0.00019, 0.0, 0.00015, 0.00013, 0.00018, 2e-05, 0.0, 7e-05, 0.0001, 0.0002, 0.00014, 0.00029, 0.0, 8e-05, 0.0005, 0.0002, 8e-05, 0.0, 0.00046, 0.0017, 0.00108, 0.00089, 0.00035, 0.0, 0.00016, 1e-05, 9e-05, 0.00024, 0.0, 1e-05, 8e-05, 0.00024, 0.00013, 0.00032, 8e-05, 0.00127, 4e-05, 0.0, 0.0, 0.00095, 0.0, 0.00017, 0.0, 0.00052, 0.00017, 2e-05, 0.00029, 0.00036, 0.00049, 0.00056, 2e-05, 0.00026, 3e-05, 0.00048, 0.0, 3e-05, 0.00014, 0.00024, 3e-05, 0.00026, 0.0006, 2e-05, 0.00015, 5e-05, 0.0, 0.00025, 0.00038, 0.00034, 4e-05, 0.0, 0.00029, 0.00044, 0.00024, 0.0, 0.0, 0.00046, 5e-05, 0.0001, 0.0, 0.00048, 0.0, 4e-05, 0.00028, 0.0, 0.00026, 0.0, 3e-05, 1e-05, 0.0, 0.0, 0.00027, 0.00034, 0.0, 0.00016, 9e-05, 0.00013, 0.00019, 0.0, 0.0, 0.00014, 0.0, 0.0001, 3e-05, 0.00031, 5e-05, 0.00026, 0.00022, 0.0001, 0.00022, 0.0, 5e-05, 0.00012, 0.0, 0.00056, 0.0, 0.0, 0.00023, 0.0, 0.0, 0.00012, 0.00064, 0.00059, 0.0, 2e-05, 0.0, 0.00033, 0.00028, 0.00017, 0.00025, 3e-05, 1e-05, 6e-05, 0.00011, 0.0, 8e-05, 6e-05, 3e-05, 0.00016, 0.00034, 0.0, 0.00011, 0.00015, 0.0, 0.00044, 0.00028, 0.0, 0.00015, 0.00062, 0.00203, 0.00035, 0.00025, 0.00049, 0.00037, 0.0001, 2e-05, 0.0, 0.0003, 7e-05, 8e-05, 0.0, 0.00074, 9e-05, 0.0, 9e-05, 0.00016, 3e-05, 0.00013, 0.00079, 6e-05, 6e-05, 1e-05, 0.0, 0.00013, 3e-05, 0.00076, 0.0, 0.00017, 5e-05, 0.00031, 0.00025, 0.00035, 0.00023, 0.0, 2e-05, 0.0002, 0.00015, 9e-05, 1e-05, 0.00017, 0.0001, 0.00011, 6e-05, 1e-05, 0.00041, 0.0003, 0.00048, 0.0, 0.00017, 4e-05, 0.00025, 0.00063, 0.00018, 0.00025, 4e-05, 0.00065, 0.0019, 0.00043, 0.00028, 0.00033, 0.0, 1e-05, 0.00012, 0.0001, 0.00019, 3e-05, 0.0, 5e-05, 0.00038, 0.00012, 0.0, 0.0, 0.00025, 6e-05, 9e-05, 0.0, 0.00017, 1e-05, 0.0006, 0.00019, 0.0001, 0.00013, 0.0, 1e-05, 0.00017, 0.00068, 0.0, 3e-05, 0.0, 0.00021, 0.00019, 0.00029, 0.00041, 0.00073, 0.00011, 0.0, 0.0, 0.00064, 0.0, 0.00026, 5e-05, 0.00044, 0.0001, 0.0, 0.0002, 0.00037, 6e-05, 0.0, 8e-05, 0.00026, 0.0, 0.00019, 8e-05, 0.00017, 0.0, 0.0, 0.00021, 0.00023, 0.00016, 1e-05, 0.00037, 0.00041, 1e-05, 0.00016, 0.00044, 0.00046, 0.00054, 0.00065, 0.00033, 0.00033, 8e-05, 0.0, 8e-05, 0.00046, 0.0, 0.0001, 0.0, 0.00023, 0.0, 0.00015, 3e-05, 2e-05, 2e-05, 0.00031, 0.00012, 0.00028, 1e-05, 4e-05, 4e-05, 0.00038, 0.00027, 0.0, 0.0, 0.00073, 0.0002, 7e-05, 0.00076, 0.00063, 7e-05, 0.0002, 0.00086, 4e-05, 0.00052, 0.00053, 0.00012, 0.00068, 0.00068, 0.00019, 0.00063, 0.0, 1e-05, 5e-05, 0.00058, 0.0, 0.0, 0.0001, 0.00059, 0.00011, 0.0, 0.0, 0.00024, 0.00012, 0.0, 0.0, 0.00036, 0.0, 2e-05, 1e-05, 0.00021, 0.0, 0.00012, 0.0, 0.00031, 9e-05, 0.0, 0.0, 0.0, 8e-05, 0.00054, 6e-05, 0.0, 0.0, 0.00026, 8e-05, 0.0, 0.00056, 0.00078, 5e-05, 2e-05, 4e-05, 0.00036, 0.0004, 0.00015, 8e-05, 5e-05, 0.00012, 6e-05, 0.00017, 5e-05, 1e-05, 0.0, 0.0, 5e-05, 0.00011, 7e-05, 0.00033, 5e-05, 7e-05, 0.00042, 0.00042, 7e-05, 5e-05, 0.00042, 0.00015, 0.00031, 0.00023, 1e-05, 0.00012, 0.0, 0.0, 0.00013, 0.00022, 2e-05, 0.0, 0.0, 0.00062, 7e-05, 0.0, 0.0, 0.00024, 0.0001, 0.0, 0.0, 1e-05, 6e-05, 0.00046, 0.0, 0.0, 3e-05, 0.00018, 6e-05, 1e-05, 0.00042, 0.00019, 5e-05, 3e-05, 0.0, 0.00026, 0.00024, 0.00016, 0.00029, 5e-05, 0.0, 9e-05, 0.00082, 0.0, 8e-05, 5e-05, 0.00037, 5e-05, 0.00016, 0.0, 0.00147, 0.00017, 5e-05, 0.0, 0.00051, 0.0, 0.0, 4e-05, 0.00646, 0.00045, 0.0, 0.0, 0.00097, 0.0001, 0.00017, 0.00029, 0.00072, 0.00015, 0.00018, 6e-05, 0.0038, 0.00059, 0.00069, 0.00314, 0.00027, 1e-05, 6e-05, 0.0006, 2e-05, 0.0, 0.0, 0.0, 6e-05, 1e-05, 0.00043, 0.0, 0.00027, 8e-05, 0.00024, 0.00048, 0.00037, 0.00034, 0.0, 0.0, 0.00021, 0.00046, 0.0, 0.0, 0.0, 0.00019, 5e-05, 0.00012, 0.0, 0.00017, 0.00025, 0.0, 0.0002, 0.00013, 9e-05, 6e-05, 0.00046, 0.00043, 6e-05, 9e-05, 0.00048, 0.00046, 0.00046, 0.00036, 7e-05, 0.00028, 1e-05, 5e-05, 0.0, 0.00025, 0.0, 0.0, 0.0001, 6e-05, 0.00032, 0.0, 0.0, 0.00036, 4e-05, 7e-05, 7e-05, 1e-05, 0.00012, 0.00053, 0.00044, 0.0, 0.00015, 0.00022, 0.00012, 1e-05, 0.00081, 0.00177, 0.0, 0.0, 0.00021, 0.00035, 0.00034, 0.00039]))),\n", " LayerError(circuit=, qubits=[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155], error=PauliLindbladError(generators=['IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...', ...], rates=[0.00087, 0.00084, 0.00784, 0.0, 0.0, 0.00028, 0.00012, 0.0001, 0.00028, 0.0, 0.00029, 0.0096, 0.00087, 0.00084, 0.0, 0.00054, 0.0, 0.0, 0.0, 0.0, 0.00021, 0.0, 5e-05, 0.00034, 0.0, 0.00019, 0.0, 0.0, 0.00016, 0.0, 9e-05, 0.0, 0.0, 0.0, 0.00018, 0.0, 0.0, 0.0, 6e-05, 0.00017, 0.00011, 0.0, 0.0, 0.00012, 0.0, 0.00014, 0.0, 0.00062, 0.00011, 6e-05, 3e-05, 0.00167, 0.00017, 0.0, 0.0, 0.00174, 0.0, 0.00014, 0.0, 0.00211, 0.0, 0.0, 0.0, 0.00028, 0.00024, 0.00016, 0.0003, 0.0, 0.00016, 0.00024, 0.0001, 3e-05, 0.00184, 0.00188, 0.00039, 0.0, 0.0, 0.0, 0.0004, 0.00065, 0.0, 0.00011, 0.0, 0.005, 0.0, 5e-05, 9e-05, 0.00029, 0.00024, 0.0, 0.00044, 0.00022, 0.0, 0.00024, 0.00043, 0.00068, 0.00102, 0.00088, 0.0005, 0.00055, 0.00015, 0.0, 0.00013, 0.00062, 0.0, 0.0, 7e-05, 0.00038, 0.0, 0.0002, 1e-05, 0.00025, 0.0, 6e-05, 5e-05, 0.00062, 0.0, 0.0, 0.0, 0.00034, 6e-05, 0.0, 3e-05, 0.0, 0.0, 0.00012, 0.00042, 0.00072, 0.00012, 0.0, 3e-05, 0.0005, 7e-05, 0.0, 0.00012, 0.00038, 0.0, 1e-05, 0.0003, 0.00053, 0.00016, 0.0, 0.0, 0.00027, 0.00034, 0.0, 0.0, 0.00011, 0.00012, 7e-05, 7e-05, 0.00021, 0.0, 0.00014, 1e-05, 0.00141, 4e-05, 0.0, 0.00035, 5e-05, 0.00012, 1e-05, 0.00026, 0.0001, 1e-05, 0.00012, 0.00026, 0.00011, 0.00037, 0.00035, 0.00045, 0.00036, 0.0, 5e-05, 5e-05, 0.0005, 4e-05, 7e-05, 5e-05, 0.00014, 0.00017, 4e-05, 0.0001, 0.00014, 0.00015, 1e-05, 0.00027, 0.00023, 1e-05, 0.00015, 0.00035, 0.00086, 0.0005, 0.00032, 0.00036, 0.00082, 0.0, 0.00011, 0.0, 0.0, 0.00064, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 4e-05, 0.00015, 0.00036, 1e-05, 0.00015, 4e-05, 0.00034, 0.00067, 0.001, 0.00089, 0.0009, 0.00042, 0.0, 1e-05, 8e-05, 0.00042, 7e-05, 0.0, 0.0, 0.00025, 9e-05, 0.0, 0.0, 0.0005, 0.00106, 0.00168, 0.00024, 0.0, 0.0, 0.0, 0.0, 5e-05, 7e-05, 0.00015, 0.00053, 0.0001, 0.0, 0.00012, 0.00035, 0.0, 0.0, 0.00061, 0.00064, 0.0, 0.0, 0.00071, 0.00061, 0.00049, 0.00049, 0.00091, 0.0, 0.0, 0.00012, 0.0, 7e-05, 7e-05, 1e-05, 0.00053, 0.0, 0.0, 0.00014, 0.0, 0.0, 0.0, 0.0057, 0.00013, 0.0, 0.0, 0.00019, 0.0, 0.0, 0.00818, 0.0, 4e-05, 0.00844, 0.00635, 4e-05, 0.0, 0.00647, 0.00203, 0.00024, 0.00068, 0.00159, 0.0, 0.0, 0.0, 0.0001, 0.0, 0.00015, 0.0, 0.0, 0.0, 0.00011, 0.00012, 0.0, 0.00051, 0.00033, 0.00025, 0.00051, 5e-05, 0.00025, 0.00033, 0.00038, 0.0001, 0.00032, 0.0004, 0.0, 0.00967, 0.00039, 3e-05, 0.00967, 0.0, 0.0, 0.0, 0.01187, 3e-05, 0.00039, 0.01275, 0.0, 0.0, 0.00042, 0.00994, 0.0012, 0.0002, 0.00248, 0.0, 0.00033, 0.0, 0.00086, 0.0, 0.0, 0.0, 0.00087, 0.0, 0.0, 0.0, 0.00093, 0.0, 0.00045, 0.0, 0.0, 2e-05, 0.00031, 0.00021, 0.0, 0.00021, 9e-05, 0.00014, 0.0, 6e-05, 8e-05, 0.00038, 0.00023, 0.0, 0.0, 0.0, 0.00019, 5e-05, 0.0, 0.0, 0.00021, 0.0, 0.00012, 0.00015, 0.00028, 0.00038, 0.0, 0.00017, 0.00024, 1e-05, 0.00083, 0.00072, 1e-05, 0.00024, 0.0, 1e-05, 0.00024, 0.00098, 0.00278, 0.0, 7e-05, 7e-05, 0.00023, 0.00025, 0.00042, 0.00039, 0.00028, 0.00038, 0.00015, 5e-05, 4e-05, 0.00012, 4e-05, 7e-05, 0.00036, 0.00025, 0.0, 3e-05, 9e-05, 7e-05, 4e-05, 0.00037, 0.00025, 0.00019, 2e-05, 0.0, 0.00039, 0.00028, 6e-05, 0.00035, 7e-05, 0.0, 0.00014, 0.00055, 0.00016, 7e-05, 0.0, 0.0, 0.0, 0.00018, 0.00045, 0.00027, 0.0, 7e-05, 0.0, 0.00014, 0.00018, 7e-05, 0.0, 0.00014, 0.0001, 8e-05, 0.0, 0.00016, 4e-05, 7e-05, 0.00042, 9e-05, 7e-05, 4e-05, 0.00021, 0.0, 0.00053, 0.00053, 5e-05, 0.00074, 0.00073, 0.00078, 0.00033, 0.00048, 0.0002, 0.0, 7e-05, 0.00013, 6e-05, 1e-05, 0.0, 0.00015, 0.00016, 7e-05, 3e-05, 2e-05, 4e-05, 5e-05, 0.0, 0.00071, 0.00014, 0.0, 0.00022, 0.00016, 0.0, 0.00024, 0.0002, 0.0001, 0.0, 0.00066, 0.00088, 0.0, 0.0001, 0.00096, 0.00215, 0.0004, 0.00036, 0.00041, 0.00125, 8e-05, 8e-05, 4e-05, 0.00165, 0.00038, 0.0, 0.0, 0.00243, 0.0, 0.0, 0.00011, 0.00023, 0.0, 0.00016, 0.00029, 0.00013, 0.00031, 0.0, 0.0, 0.00072, 0.00016, 0.0001, 0.0, 0.0, 0.0, 0.00018, 0.0, 0.0, 0.0002, 0.0004, 0.00013, 3e-05, 0.0, 0.00016, 0.0002, 0.0, 0.00059, 0.00123, 2e-05, 0.0, 0.0, 0.00068, 0.00044, 0.00014, 0.0007, 7e-05, 5e-05, 0.0, 0.00069, 0.00018, 0.0, 0.0, 0.0014, 0.0, 0.00021, 0.0, 0.0, 0.0001, 0.00016, 8e-05, 0.0, 0.0, 6e-05, 0.00023, 0.0, 0.0, 0.0, 2e-05, 0.00016, 0.0, 0.00011, 0.00033, 3e-05, 0.00011, 0.0, 0.00033, 0.00049, 0.00062, 0.00072, 0.00067, 0.00086, 1e-05, 6e-05, 0.0, 2e-05, 7e-05, 0.0, 0.00032, 0.0, 7e-05, 0.00043, 3e-05, 0.0, 0.00017, 0.0, 0.00026, 0.0, 0.0, 3e-05, 0.00014, 0.00029, 0.0, 0.00018, 0.00016, 0.00044, 0.00018, 0.00016, 0.00018, 0.00034, 0.0, 0.00101, 0.00102, 0.00052, 0.00022, 0.00011, 0.0, 9e-05, 0.00014, 0.0001, 0.0001, 0.00013, 0.00012, 0.00027, 2e-05, 0.00023, 0.0003, 0.0, 0.00016, 0.0, 0.00036, 0.00022, 0.0, 5e-05, 0.00059, 6e-05, 0.00015, 0.0, 0.0, 2e-05, 0.00016, 0.00108, 0.0, 0.0002, 0.00031, 0.0, 0.00016, 2e-05, 0.00047, 0.00015, 0.0, 0.0, 0.00809, 0.00074, 0.00073, 0.00068, 8e-05, 0.0, 0.0, 8e-05, 0.00022, 0.00019, 2e-05, 0.00012, 0.0001, 9e-05, 0.00023, 5e-05, 0.00028, 6e-05, 0.0, 0.0006, 6e-05, 0.00017, 0.00064, 0.00027, 0.00017, 6e-05, 0.00061, 0.00039, 0.00051, 0.00053, 0.00025, 0.0, 0.0, 0.00029, 0.00032, 0.00019, 0.00029, 0.0, 0.0004, 0.00019, 0.00192, 0.00229, 0.00056, 0.00034, 0.0, 2e-05, 8e-05, 0.00019, 0.00025, 0.00013, 0.00012, 0.00246, 4e-05, 0.0003, 0.00062, 0.00037, 0.0, 0.00012, 0.00037, 0.00032, 0.00012, 0.0, 0.00032, 0.00095, 0.00071, 0.00078, 0.00025, 0.00085, 4e-05, 0.0, 0.0, 0.00045, 0.0, 1e-05, 0.00013, 0.00012, 0.0, 0.00033, 6e-05, 0.00023, 0.0004, 0.00042, 2e-05, 0.0, 0.0, 0.0003, 0.0, 0.0, 0.0, 0.00022, 0.00055, 0.00023, 0.0004, 0.00044, 0.00011, 0.00017, 0.0, 0.0, 0.00028, 0.0, 0.0, 1e-05, 0.0057, 0.0, 0.00032, 0.0, 0.00088, 2e-05, 0.00021, 0.00022, 9e-05, 0.0, 0.00135, 0.00142, 4e-05, 0.0, 0.0, 0.0, 9e-05, 0.00161, 0.00155, 0.00026, 0.0, 9e-05, 0.00028, 0.00029, 0.00021, 0.00054, 0.0, 0.0, 0.00029, 0.00024, 3e-05, 1e-05, 0.0, 0.00018, 0.0, 0.00014, 0.00013, 0.00028, 0.0001, 0.0, 0.0, 0.0, 0.0, 0.00046, 1e-05, 0.00141, 0.0, 0.0, 0.00026, 0.00076, 0.00014, 0.0, 0.00096, 0.0, 0.0, 0.00014, 0.00052, 0.00061, 0.00068, 0.00077, 0.00079, 0.0, 0.00049, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00049, 0.0013, 0.0, 0.00073, 0.0, 0.02919, 0.00044, 0.00069, 0.00012, 0.0, 0.00014, 0.00025, 0.00141, 0.00072, 0.0, 0.0, 0.0008, 0.0, 0.00061, 0.00012, 0.0012, 1e-05, 0.0, 0.0, 0.0, 0.00011, 0.0, 0.00028, 0.0, 0.00043, 0.0, 0.0, 0.00108, 0.00033, 0.0, 0.00014, 0.0006, 0.0, 0.00011, 1e-05, 0.0007, 0.0, 0.0, 0.0, 0.00103, 0.00016, 0.0, 0.0, 0.00032, 0.00031, 0.00036, 0.00034, 5e-05, 0.0, 7e-05, 0.00014, 0.0, 0.00046, 0.00026, 2e-05, 6e-05, 1e-05, 0.0, 0.00014, 0.00035, 0.00093, 0.0, 2e-05, 0.0, 0.00032, 0.00031, 6e-05, 0.00042, 0.0, 0.0, 0.00029, 0.00011, 2e-05, 0.0, 0.00017, 0.00041, 9e-05, 5e-05, 0.0002, 2e-05, 0.00018, 0.0, 0.00025, 0.0, 0.0, 0.00035, 0.0001, 0.00087, 9e-05, 2e-05, 0.00026, 0.0016, 0.0, 0.0001, 0.00173, 0.0013, 0.0001, 0.0, 0.00142, 0.00111, 0.00057, 0.00044, 0.00047, 0.00051, 0.00041, 0.00034, 0.00034, 0.00038, 0.00035, 0.0, 0.0, 0.0, 0.00013, 0.00016, 0.00016, 0.00031, 0.0, 9e-05, 0.00016, 0.0, 0.00016, 0.00016, 0.00035, 0.0, 0.0, 9e-05, 1e-05, 0.00034, 0.00038, 0.00027, 0.0, 0.0, 0.0, 3e-05, 0.00098, 0.00031, 0.00011, 0.0, 0.00973, 0.0, 0.0, 0.00017, 0.0, 0.00024, 0.0, 0.00012, 0.00017, 0.00022, 0.0, 0.0, 0.00021, 5e-05, 4e-05, 4e-05, 0.00013, 7e-05, 0.00018, 0.00029, 0.00018, 0.00018, 7e-05, 0.00026, 0.00033, 0.00023, 0.00095, 0.00018, 0.0002, 9e-05, 2e-05, 0.00045, 1e-05, 0.0, 0.00011, 0.00012, 2e-05, 9e-05, 0.00042, 0.0, 8e-05, 4e-05, 0.00228, 0.00051, 0.00039, 0.00025, 0.00016, 0.0, 0.00015, 0.00021, 0.0001, 0.0, 0.0001, 0.00053, 0.0, 0.0001, 0.0, 0.0006, 0.0, 4e-05, 0.0, 9e-05, 0.0, 0.0001, 0.00011, 0.0, 0.00018, 0.0, 8e-05, 0.00063, 4e-05, 0.0, 0.0, 0.00032, 0.0, 0.00015, 0.0, 0.00043, 7e-05, 2e-05, 0.0, 3e-05, 0.00011, 0.0, 0.0001, 0.00026, 0.0001, 0.0, 3e-05, 0.0, 0.0, 5e-05, 0.00033, 3e-05, 0.00012, 0.0, 1e-05, 0.0, 0.0, 0.00064, 0.0, 0.0, 0.0, 0.0, 0.00012, 0.0001, 0.0001, 0.0, 5e-05, 0.00035, 0.00011, 5e-05, 0.0, 0.00032, 0.00017, 0.00044, 0.00048, 0.00017, 0.0001, 0.00018, 0.0, 0.00012, 0.00021, 0.0, 0.00015, 0.0001, 8e-05, 6e-05, 4e-05, 0.0, 0.00011, 0.00013, 2e-05, 0.00042, 4e-05, 2e-05, 0.00013, 0.00018, 0.00038, 0.00066, 0.00062, 0.00022, 0.00024, 0.0, 0.0, 0.0, 0.0, 0.00014, 0.00021, 0.0001, 0.00014, 0.00018, 0.0, 0.00018, 0.0, 0.0, 0.00155, 0.0, 0.0, 0.0001, 0.00013, 0.0, 0.00012, 0.00036, 0.00011, 0.00013, 0.0005, 0.00034, 0.00013, 0.00011, 0.00046, 0.00041, 0.00059, 0.00061, 0.00026, 0.00065, 1e-05, 1e-05, 8e-05, 0.00045, 0.0, 2e-05, 0.00013, 0.0004, 0.00013, 0.0001, 7e-05, 0.00027, 0.0, 1e-05, 5e-05, 0.00069, 0.0, 0.00015, 0.0, 0.00115, 0.0, 0.00033, 0.0, 0.00021, 0.0, 0.00013, 0.0003, 0.00019, 0.00013, 0.0, 0.0003, 9e-05, 0.00048, 0.00041, 5e-05, 0.00019, 0.0, 3e-05, 0.00012, 0.0004, 0.00014, 8e-05, 0.0, 0.00063, 0.00012, 4e-05, 0.00022, 0.00023, 0.0, 0.00013, 0.0, 0.00024, 4e-05, 0.0, 0.0, 0.00052, 6e-05, 0.0, 1e-05, 0.002, 0.00128, 0.00096, 0.0004, 0.0, 0.0, 5e-05, 0.00034, 0.0, 3e-05, 0.00013, 0.00066, 0.0, 4e-05, 0.0, 0.0005, 0.00037, 0.00029, 0.00018, 2e-05, 3e-05, 0.00055, 0.00034, 3e-05, 2e-05, 0.00068, 0.00077, 0.0005, 0.00037, 0.00018, 0.00033, 0.0, 0.0, 0.00013, 0.0003, 7e-05, 5e-05, 0.0, 0.00021, 9e-05, 8e-05, 0.0, 0.0002, 0.0, 0.00012, 2e-05, 0.0, 3e-05, 0.00038, 0.00021, 6e-05, 0.0, 2e-05, 3e-05, 0.0, 0.00042, 0.00076, 3e-05, 0.0, 5e-05, 0.00046, 0.00042, 0.0002, 0.00054, 0.0, 1e-05, 0.0, 0.00071, 4e-05, 5e-05, 0.0, 0.00032, 0.0, 7e-05, 2e-05, 0.00034, 4e-05, 0.0, 4e-05, 0.00019, 5e-05, 7e-05, 0.0, 0.00125, 3e-05, 0.0, 8e-05, 0.00026, 0.0, 0.00014, 0.0, 0.00048, 0.0, 0.0, 3e-05, 0.00026, 6e-05, 0.0, 0.00021, 5e-05, 0.00016, 0.0, 0.00024, 5e-05, 0.0, 6e-05, 0.00023, 1e-05, 7e-05, 0.0, 0.00011, 0.0, 0.0, 0.0004, 6e-05, 0.0, 0.00023, 8e-05, 0.0, 0.00021, 0.00011, 0.0, 0.00013, 0.00025, 0.00022, 0.00013, 0.0, 0.00029, 0.0007, 0.00056, 0.00042, 0.00045, 0.00021, 8e-05, 0.0, 0.0, 0.0001, 3e-05, 7e-05, 0.0001, 0.00176, 3e-05, 0.0, 0.0, 0.0, 0.0, 3e-05, 0.00029, 0.00023, 0.0001, 0.0, 0.0, 0.00036, 0.00018, 9e-05, 0.00011, 0.00038, 4e-05, 4e-05, 0.0, 8e-05, 9e-05, 0.00045, 0.00046, 0.00012, 2e-05, 0.0, 9e-05, 8e-05, 0.0006, 0.00023, 0.0, 0.0, 0.00018, 0.00029, 0.00034, 0.00038, 0.0, 6e-05, 4e-05, 0.00035, 4e-05, 4e-05, 6e-05, 0.00029, 0.0, 0.00045, 0.00051, 0.00014, 0.00017, 3e-05, 0.00011, 3e-05, 0.00033, 0.0, 0.0001, 2e-05, 0.00137, 0.00017, 0.0, 0.00037, 0.00031, 8e-05, 0.0, 0.00037, 0.0, 0.0, 8e-05, 0.0003, 0.0, 0.00048, 0.00045, 0.00034, 0.0003, 0.00013, 7e-05, 0.00052, 0.00049, 7e-05, 0.00013, 0.00054, 0.00061, 0.00058, 0.00042, 0.00012, 0.0005, 0.00029, 0.00037, 0.0, 0.00012, 0.00012, 0.00012, 0.0, 0.00021, 3e-05, 9e-05, 6e-05, 0.0001, 0.00014, 4e-05, 0.0, 0.00016, 0.00122, 0.00018, 3e-05, 0.00016, 4e-05, 5e-05, 0.00019, 5e-05, 7e-05, 0.00013, 0.00047, 0.00031, 0.00013, 7e-05, 0.00034, 0.00044, 0.0006, 0.0006, 0.00055, 0.00034, 8e-05, 2e-05, 5e-05, 6e-05, 0.00019, 0.0, 0.00027, 0.00031, 0.00015, 1e-05, 0.0003, 0.00016, 0.00014, 3e-05, 0.00037, 0.00035, 3e-05, 0.00014, 0.00041, 0.0, 0.00071, 0.00077, 0.00011, 0.00036, 5e-05, 9e-05, 0.00067, 0.00018, 0.0, 0.0, 0.00016, 9e-05, 5e-05, 0.00072, 0.0, 6e-05, 0.00023, 0.00597, 0.00035, 0.00044, 0.00102, 3e-05, 0.0, 0.00052, 0.00043, 4e-05, 7e-05, 0.0, 0.00044, 9e-05, 0.0, 0.0, 0.0, 0.0, 0.0002, 0.00035, 0.0, 0.00017, 5e-05, 0.0, 0.0, 0.0, 1e-05, 0.00025, 0.00048, 0.0, 5e-05, 0.00012, 0.00035, 0.0001, 0.0, 0.0, 4e-05, 0.00012, 9e-05, 5e-05, 6e-05, 3e-05, 0.00022, 0.00017, 0.00013, 0.0, 8e-05, 0.00013, 5e-05, 3e-05, 0.00051, 0.0002, 2e-05, 0.0002, 0.0002, 3e-05, 5e-05, 0.00064, 0.0, 1e-05, 9e-05, 0.00018, 0.00046, 0.00031, 0.00025, 0.00063, 0.0, 0.0, 0.0, 0.0006, 6e-05, 2e-05, 3e-05, 0.00051, 0.00011, 0.0, 0.00016, 0.0, 0.0, 0.0, 0.00031, 0.00028, 0.00011, 0.0, 0.0, 0.0006, 5e-05, 1e-05, 0.0, 0.00022, 0.0, 0.00013, 9e-05, 0.00063, 0.0, 0.0, 2e-05, 0.0, 0.00026, 0.0, 0.0, 0.00028, 0.0, 2e-05, 7e-05, 0.0, 0.0, 0.00017, 0.00022, 5e-05, 4e-05, 4e-05, 0.0, 0.0, 0.00015, 9e-05, 0.00017, 0.0, 0.00012, 0.0001, 1e-05, 0.00013, 0.00035, 0.0, 8e-05, 0.00045, 0.00014, 8e-05, 0.0, 0.0004, 1e-05, 0.00054, 0.00049, 0.00031, 0.00078, 0.0, 6e-05, 0.00015, 0.00054, 0.0, 0.0002, 0.00019, 0.0, 0.0001, 0.0, 0.00022, 0.00016, 6e-05, 0.0, 0.00018, 7e-05, 0.00013, 0.00012, 0.0, 0.0003, 3e-05, 0.00013, 0.00019, 0.00016, 9e-05, 0.0, 0.00037, 0.00018, 0.0, 9e-05, 0.00025, 0.00054, 0.00047, 0.00052, 0.00025, 0.00026, 0.0, 4e-05, 0.00055, 0.00017, 4e-05, 0.0, 0.00049, 0.0001, 0.00048, 0.00055, 3e-05, 0.00039, 3e-05, 0.00027, 0.0, 0.00041, 0.0, 0.00015, 0.0, 0.00042, 0.00018, 0.0, 0.00024, 0.00036, 0.00031, 0.00026, 0.00039, 5e-05, 0.0, 0.00053, 0.00038, 0.0, 5e-05, 0.0005, 0.00051, 0.00036, 0.00031, 4e-05, 0.00058, 0.0, 0.0, 1e-05, 0.00024, 0.0, 9e-05, 0.0, 0.00027, 0.00013, 3e-05, 4e-05, 0.00023, 0.00018, 0.0, 0.00044, 1e-05, 5e-05, 4e-05, 0.00026, 0.0, 0.00018, 0.0005, 0.0, 5e-05, 0.0, 0.00049, 0.0004, 0.00033, 0.00018, 2e-05, 1e-05, 0.0, 0.00051, 9e-05, 4e-05, 0.0, 0.00016, 2e-05, 6e-05, 6e-05, 0.00029, 0.0, 9e-05, 0.00011, 0.00027, 2e-05, 6e-05, 0.0, 0.00028, 4e-05, 0.0, 9e-05, 0.00013, 0.0, 0.0, 0.00015, 8e-05, 1e-05, 6e-05, 0.00022, 8e-05, 6e-05, 1e-05, 0.00021, 0.00047, 0.00034, 0.00041, 0.00019, 0.00029, 6e-05, 5e-05, 0.0001, 7e-05, 0.0, 0.0, 0.00024, 3e-05, 3e-05, 8e-05, 0.0, 2e-05, 0.00013, 0.00032, 0.00013, 0.0, 0.0, 6e-05, 0.00011, 0.0, 0.00033, 0.0002, 7e-05, 0.00071, 0.00044, 7e-05, 0.0002, 0.00066, 0.00058, 0.00056, 0.00053, 0.00019, 0.00117, 0.0, 0.00022, 0.00042, 0.00183, 0.00029, 0.0, 0.00029, 0.00916, 8e-05, 0.0, 0.0, 0.00012, 0.00026, 0.00038, 0.00064, 0.0003, 0.00038, 0.00026, 0.00097, 0.00262, 0.00181, 0.00241, 0.00299, 0.0, 2e-05, 0.00022, 0.00054, 0.00028, 0.0, 0.0, 0.0, 0.0001, 0.0, 0.00038, 0.0, 0.00042, 2e-05, 0.0, 0.00018, 0.0001, 0.00018, 0.00023, 0.00025, 0.0, 0.00025, 5e-05, 0.00016, 0.00042, 9e-05, 0.00016, 5e-05, 0.00034, 0.00049, 0.00102, 0.00086, 0.00073, 0.0005, 0.0, 0.00024, 0.0, 0.0004, 6e-05, 0.0, 0.0001, 0.00049, 0.00011, 0.0, 0.0002, 0.00049, 3e-05, 0.0, 0.0, 0.00037, 5e-05, 0.0001, 0.0, 0.00037, 0.0, 0.0, 0.00015, 0.00036, 0.0, 0.00017, 0.00048, 0.0, 0.00011, 0.0, 0.0004, 0.00017, 0.0, 0.00049, 6e-05, 0.0, 3e-05, 0.00124, 0.00069, 0.00056, 0.00014, 1e-05, 0.0, 0.0]))),\n", " LayerError(circuit=, qubits=[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155], error=PauliLindbladError(generators=['IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...', ...], rates=[0.00135, 0.001, 0.00567, 0.0004, 0.0, 7e-05, 0.0, 9e-05, 0.0, 7e-05, 0.00013, 0.00241, 5e-05, 0.0, 0.0, 0.00014, 0.00013, 3e-05, 0.00036, 2e-05, 3e-05, 0.00013, 0.00029, 0.0, 0.00051, 0.00034, 0.0001, 0.00019, 6e-05, 0.00018, 0.0, 0.00018, 9e-05, 9e-05, 8e-05, 0.00214, 7e-05, 0.0, 0.00027, 0.0, 0.0, 7e-05, 0.0002, 0.0, 7e-05, 0.0, 0.00017, 0.0, 0.00043, 0.00044, 0.00016, 0.0011, 0.00014, 0.00012, 0.00012, 0.00111, 7e-05, 0.00014, 0.00018, 0.00109, 0.00013, 0.0, 0.00027, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00054, 0.0, 0.0, 0.0, 0.0005, 0.0, 0.0, 0.0, 0.00089, 0.0, 0.0, 0.0, 0.0, 0.00028, 0.00028, 7e-05, 0.0, 0.00028, 0.00028, 0.00016, 0.0, 0.00054, 0.0005, 0.00042, 0.00096, 0.0, 5e-05, 6e-05, 0.00077, 0.0002, 0.0, 0.0, 0.00072, 0.0, 0.00014, 0.0, 0.0003, 0.00014, 0.0, 0.00048, 0.00023, 0.0, 0.00014, 0.00044, 0.00054, 0.00135, 0.00142, 0.00023, 0.00031, 1e-05, 7e-05, 0.00011, 0.00047, 0.00018, 0.0, 0.0, 0.00011, 0.0, 0.00014, 3e-05, 0.00029, 0.0, 4e-05, 0.0, 0.00014, 6e-05, 8e-05, 9e-05, 0.00014, 0.00011, 0.00016, 2e-05, 0.00029, 0.0, 0.0, 0.00017, 0.00024, 9e-05, 3e-05, 0.0, 0.00036, 5e-05, 1e-05, 0.0, 0.00025, 0.0, 0.0, 0.0, 0.0002, 0.0, 0.0, 0.0, 0.00058, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.37843, 0.0, 0.0, 0.53164, 0.5365, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00028, 9e-05, 9e-05, 4e-05, 7e-05, 0.0, 0.0, 0.00025, 0.00011, 0.0, 0.00012, 7e-05, 4e-05, 0.00035, 0.00015, 4e-05, 7e-05, 0.00029, 0.0, 0.00047, 0.00036, 9e-05, 0.00164, 0.00232, 0.0028, 0.00131, 0.0, 0.0, 0.0, 0.00148, 0.0, 0.0, 0.0, 0.00084, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00521, 0.00527, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.40338, 0.0, 0.0, 0.0, 0.30521, 0.09093, 0.09126, 0.14967, 0.0, 0.0, 0.0, 0.0, 0.0, 0.25536, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 2.70904, 0.0, 0.0, 0.0, 0.0, 0.44482, 0.05059, 1.98941, 2.66137, 1.82174, 1.98941, 0.0, 1.82174, 2.66137, 0.0, 0.0, 0.10991, 0.02851, 1.35927, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00581, 0.0, 0.0, 0.0, 0.00042, 0.00025, 0.00021, 0.00026, 0.0, 0.0, 0.00084, 0.00058, 0.00021, 0.00019, 0.00022, 0.0, 0.0, 0.00072, 0.0, 9e-05, 0.00016, 0.00029, 0.0, 0.0, 0.0005, 0.00067, 0.00059, 0.00051, 0.00058, 0.00013, 0.0, 0.00015, 2e-05, 0.0, 1e-05, 0.00032, 3e-05, 0.00015, 0.0002, 0.0, 0.00011, 0.0, 0.00022, 7e-05, 0.0, 0.00015, 0.0, 0.0, 7e-05, 0.00035, 0.0, 0.0, 0.00077, 0.00017, 0.0, 0.0, 0.00066, 0.00234, 0.00131, 0.00148, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00214, 0.0, 0.0, 0.0, 0.00178, 0.0, 0.0, 0.0, 0.00307, 0.0, 0.0, 0.0, 0.00178, 0.00165, 0.00056, 0.00035, 0.00033, 0.00061, 0.0, 0.00028, 4e-05, 9e-05, 0.0, 0.0, 0.00052, 0.0, 8e-05, 0.00017, 0.0002, 0.0, 0.0, 0.00038, 0.00022, 6e-05, 0.00029, 0.0, 0.00035, 0.00033, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1e-05, 0.0, 0.00043, 0.00147, 0.00019, 0.0, 0.0001, 0.01096, 0.0, 0.00027, 4e-05, 0.01189, 0.0, 0.00048, 0.0, 0.0, 0.00088, 0.0, 0.0, 0.00084, 0.00106, 0.00067, 0.00119, 0.00069, 0.00067, 0.00106, 0.00117, 0.0048, 0.0117, 0.0124, 0.00417, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00051, 0.0, 0.0, 0.0, 0.00035, 0.00048, 0.00099, 5e-05, 0.0, 0.0, 0.00043, 0.0, 0.0, 0.0, 0.00067, 0.00087, 0.0, 0.0, 0.00021, 0.00031, 0.00016, 0.00031, 0.00044, 0.00017, 0.00031, 0.00016, 0.00047, 1e-05, 0.00073, 0.00086, 0.00056, 0.00019, 0.0, 0.0, 0.0, 0.00016, 0.0, 0.0, 0.0, 0.00108, 4e-05, 0.00021, 0.00028, 0.0, 0.00023, 0.00044, 0.00039, 0.0, 0.0, 0.00012, 0.0, 0.00042, 0.00034, 0.00032, 0.0, 0.0, 0.00017, 0.0, 0.00069, 0.00049, 0.00032, 0.00019, 0.00016, 0.0, 0.00032, 0.0, 0.0, 0.0, 0.00035, 0.0, 0.0, 0.0, 0.00013, 0.0, 0.0, 0.0, 0.00013, 0.0, 5e-05, 0.00056, 0.00032, 5e-05, 0.0, 0.00059, 0.00053, 0.00032, 0.00035, 9e-05, 0.00029, 0.0, 7e-05, 0.0001, 0.00019, 1e-05, 0.0, 0.00015, 0.0002, 0.0003, 0.0, 0.0, 0.0, 8e-05, 0.0, 0.00023, 0.0, 8e-05, 0.00067, 0.00015, 0.0, 9e-05, 1e-05, 8e-05, 0.0, 0.00048, 0.00075, 0.0, 1e-05, 0.0, 0.00045, 0.00035, 0.00013, 0.00063, 2e-05, 9e-05, 3e-05, 0.00059, 0.0, 8e-05, 0.00012, 0.00045, 0.00035, 5e-05, 0.0, 0.00013, 5e-05, 0.0, 0.00028, 0.00025, 3e-05, 0.00018, 0.0, 0.00042, 0.0, 1e-05, 9e-05, 0.0, 0.0, 2e-05, 0.001, 0.0, 0.00043, 1e-05, 0.0, 0.0, 0.0, 0.0, 7e-05, 0.00027, 6e-05, 0.0, 0.0, 0.00098, 1e-05, 8e-05, 0.0, 0.00539, 2e-05, 0.0, 0.0, 0.00051, 0.0, 0.00015, 0.0, 0.00053, 0.0, 0.0, 9e-05, 0.00072, 0.00012, 5e-05, 0.0, 6e-05, 0.0001, 9e-05, 0.00036, 0.00021, 9e-05, 0.0001, 0.00035, 0.00017, 0.00047, 0.00047, 0.00014, 0.00044, 0.00029, 0.00075, 0.0, 0.0, 1e-05, 0.0, 0.0, 8e-05, 0.0, 0.00013, 0.0007, 9e-05, 0.0, 6e-05, 0.00074, 0.00022, 9e-05, 0.0003, 0.0, 0.0, 0.0, 0.0, 0.00177, 0.00024, 0.00027, 0.0002, 0.00866, 0.0, 0.0002, 0.0, 8e-05, 1e-05, 0.0, 0.00901, 0.0, 0.00042, 0.00042, 0.0, 0.00057, 0.0, 0.00748, 0.0, 0.0, 0.00116, 6e-05, 0.0, 0.00055, 0.0, 0.00082, 0.00104, 0.00061, 0.00124, 0.00104, 0.00082, 0.00129, 0.00317, 0.00896, 0.01041, 0.00599, 0.00052, 0.0, 0.0, 0.0, 0.00039, 5e-05, 0.0, 8e-05, 0.00468, 0.00064, 0.0, 0.0, 0.0009, 0.0, 0.00013, 0.00028, 0.00097, 0.00033, 5e-05, 0.0, 0.0004, 0.00021, 0.00017, 0.00014, 0.0, 0.0, 0.0, 0.00036, 7e-05, 0.0, 0.00014, 0.0, 0.0, 0.0, 0.00026, 0.0, 6e-05, 3e-05, 0.00043, 0.0, 0.0, 0.00038, 0.00027, 0.00016, 5e-05, 0.00031, 7e-05, 0.0, 0.00045, 0.00028, 0.0, 7e-05, 0.0004, 0.00059, 0.00054, 0.0003, 0.00045, 0.00064, 0.0, 0.0, 0.0, 0.00026, 4e-05, 0.0, 0.00034, 0.0007, 0.00011, 0.00012, 0.0, 0.00056, 0.0, 0.0002, 0.00057, 0.00065, 0.0002, 0.0, 0.00066, 0.00067, 0.00121, 0.00123, 0.00025, 0.00043, 0.00044, 0.0005, 0.00075, 0.0, 0.00014, 0.00022, 0.0, 6e-05, 7e-05, 0.00083, 0.00028, 0.0, 0.0, 0.00013, 0.0, 0.0, 0.00099, 2e-05, 0.0, 0.0, 2e-05, 0.0, 2e-05, 0.00024, 0.0001, 4e-05, 0.00038, 0.00026, 4e-05, 0.0001, 0.00031, 0.00026, 0.00045, 0.00054, 0.0004, 0.00023, 0.00026, 0.0002, 0.00047, 0.0, 0.0002, 0.00026, 0.0003, 0.00087, 0.00106, 0.00088, 0.00097, 0.00151, 0.0, 6e-05, 0.00023, 0.00137, 0.00015, 0.0, 0.0, 0.00016, 0.00042, 0.00053, 0.00013, 0.00075, 0.00043, 0.00018, 0.00075, 0.00062, 0.00051, 0.0, 0.00015, 0.0, 0.0, 3e-05, 0.00012, 0.0, 0.0, 0.0, 5e-05, 0.00015, 0.0, 6e-05, 0.00021, 0.0, 0.0, 0.0, 8e-05, 2e-05, 0.0, 0.00015, 0.00011, 7e-05, 9e-05, 0.00039, 0.00028, 9e-05, 7e-05, 0.00057, 0.00552, 0.00028, 0.00045, 0.00041, 0.0, 0.0, 0.00029, 0.0, 0.0, 0.00018, 0.0, 0.0, 0.0, 0.0001, 0.0, 0.00036, 0.00033, 0.0, 0.00011, 0.0, 0.00015, 0.00013, 0.0, 0.0, 0.00036, 0.0, 0.00012, 5e-05, 0.00022, 0.0, 0.00018, 7e-05, 5e-05, 7e-05, 0.0, 0.00032, 8e-05, 5e-05, 0.0, 4e-05, 1e-05, 8e-05, 0.00027, 0.00016, 7e-05, 0.00018, 0.0, 3e-05, 0.00027, 0.00034, 3e-05, 7e-05, 0.00048, 0.00045, 7e-05, 3e-05, 0.00053, 0.00018, 0.00058, 0.00057, 8e-05, 0.0, 8e-05, 0.0, 0.00016, 0.0, 0.0, 7e-05, 0.00014, 0.0, 6e-05, 1e-05, 0.0, 0.00022, 0.00011, 0.0, 0.00022, 0.00026, 0.0, 0.00011, 0.00035, 0.00033, 0.00045, 0.00032, 0.00016, 0.0005, 0.00027, 3e-05, 0.0008, 0.0, 0.0, 0.0, 0.0003, 3e-05, 0.00027, 0.00083, 0.0, 0.0, 0.0, 2e-05, 0.00181, 0.00152, 0.00038, 0.0, 9e-05, 0.0, 0.0, 0.00012, 0.00011, 7e-05, 7e-05, 4e-05, 0.00014, 0.00012, 0.0, 0.00014, 0.00029, 0.00012, 0.00039, 0.0, 0.00032, 0.00066, 0.00032, 0.00032, 0.0, 0.0009, 0.00201, 0.00021, 0.00041, 0.00014, 6e-05, 3e-05, 0.00021, 0.0, 0.0002, 0.0, 0.0, 0.00011, 0.00028, 2e-05, 0.0, 0.0, 9e-05, 4e-05, 9e-05, 9e-05, 0.0, 0.0001, 0.0005, 0.0002, 0.0, 0.0, 0.0, 0.0001, 0.0, 0.00039, 0.00028, 0.0, 0.0, 6e-05, 0.0003, 0.00031, 0.0001, 0.00092, 0.0, 0.00012, 4e-05, 0.00098, 4e-05, 7e-05, 4e-05, 0.00062, 0.00015, 0.0, 0.0, 0.00049, 5e-05, 0.0, 0.0, 0.00029, 6e-05, 0.0, 8e-05, 0.00102, 0.0, 0.0, 0.0001, 0.00037, 1e-05, 0.00021, 0.00038, 6e-05, 0.00021, 1e-05, 7e-05, 0.00062, 0.00026, 0.00036, 0.0003, 0.00045, 1e-05, 0.0, 0.0, 0.00047, 0.0, 3e-05, 9e-05, 0.00057, 0.00022, 8e-05, 6e-05, 0.0, 2e-05, 0.00036, 0.0, 0.00021, 0.0, 0.0, 0.0001, 0.0005, 0.00019, 1e-05, 0.0, 4e-05, 8e-05, 3e-05, 0.00028, 0.00013, 3e-05, 8e-05, 0.00021, 0.0, 0.00054, 0.00044, 0.0002, 0.00148, 0.00101, 0.00116, 0.00033, 0.00012, 0.0, 0.0, 0.00034, 0.0, 7e-05, 0.0001, 0.00066, 2e-05, 0.0, 0.0, 0.00079, 0.00061, 9e-05, 0.00011, 0.0, 0.0, 0.00012, 0.0001, 3e-05, 0.0, 7e-05, 0.00019, 3e-05, 3e-05, 0.0, 0.00027, 0.0001, 0.0, 0.00037, 0.00012, 0.0, 0.0001, 0.0003, 0.0002, 0.00043, 0.00033, 0.00018, 0.00033, 0.0, 3e-05, 0.0001, 0.0, 0.0, 4e-05, 0.00025, 0.0, 0.0, 0.0, 0.0, 4e-05, 0.0, 0.00028, 6e-05, 5e-05, 0.0, 0.0001, 0.00014, 0.0, 0.00033, 0.0, 3e-05, 0.00042, 0.00025, 3e-05, 0.0, 0.0003, 0.00054, 0.00049, 0.0003, 0.00081, 0.00041, 0.0, 0.0, 0.0, 0.00022, 0.0, 0.0, 0.0, 0.00184, 9e-05, 5e-05, 0.0, 3e-05, 6e-05, 0.0001, 0.00032, 7e-05, 0.0001, 6e-05, 0.0002, 0.00062, 0.00045, 0.00037, 0.00015, 0.00043, 0.0, 0.0001, 0.00073, 0.0, 0.0, 7e-05, 0.00029, 0.0001, 0.0, 0.00076, 0.00015, 0.0, 0.00015, 0.0, 0.00028, 0.00036, 0.00014, 0.00014, 0.00013, 0.0, 7e-05, 0.0, 1e-05, 9e-05, 4e-05, 2e-05, 0.0001, 0.0002, 0.0002, 0.00021, 4e-05, 2e-05, 0.00041, 0.0001, 0.00016, 0.00083, 0.00013, 0.00016, 0.0001, 0.00051, 0.00138, 0.00017, 0.00036, 0.00048, 0.0005, 0.0, 7e-05, 0.0, 0.00032, 0.0, 0.0, 0.00015, 0.00028, 6e-05, 8e-05, 0.00035, 0.00059, 5e-05, 0.0, 0.0002, 0.0, 0.0, 0.0, 0.00051, 0.0, 8e-05, 8e-05, 1e-05, 0.0, 0.00011, 0.00027, 0.00019, 1e-05, 6e-05, 6e-05, 0.0001, 0.0, 0.0003, 7e-05, 0.0, 0.00011, 0.00023, 0.00016, 2e-05, 0.0, 0.00016, 0.0, 0.00012, 7e-05, 0.00038, 0.0, 0.0, 7e-05, 0.00058, 7e-05, 0.0, 0.0, 0.00119, 0.00013, 0.00013, 0.0, 0.00019, 3e-05, 1e-05, 3e-05, 0.00045, 0.0, 5e-05, 0.00012, 0.00067, 1e-05, 7e-05, 0.0, 0.00038, 0.00019, 0.0, 0.0, 0.00026, 0.00015, 1e-05, 0.0, 0.00041, 0.0, 0.00021, 0.00053, 0.00021, 0.00027, 0.00033, 7e-05, 0.00014, 0.0, 0.00013, 1e-05, 5e-05, 0.00061, 0.0, 0.0, 2e-05, 0.00016, 5e-05, 1e-05, 0.00039, 0.0, 0.0, 5e-05, 5e-05, 0.00021, 0.00027, 9e-05, 0.0003, 0.0001, 4e-05, 0.0, 0.00027, 2e-05, 0.0, 8e-05, 0.00019, 0.00014, 0.00026, 0.00019, 0.00023, 6e-05, 1e-05, 0.00068, 0.00018, 1e-05, 6e-05, 0.00057, 0.00117, 0.00044, 0.00037, 0.00034, 0.00046, 0.0, 2e-05, 0.0, 0.00028, 6e-05, 0.0, 0.00011, 0.00014, 9e-05, 0.00017, 9e-05, 0.00021, 3e-05, 4e-05, 8e-05, 9e-05, 0.0, 0.0, 0.00037, 0.0, 0.0, 1e-05, 0.0, 4e-05, 6e-05, 0.00054, 0.00021, 0.0, 0.0, 3e-05, 8e-05, 3e-05, 0.00012, 0.00015, 1e-05, 0.00033, 8e-05, 1e-05, 0.00015, 0.00027, 0.0, 0.00046, 0.00049, 0.00027, 0.0, 0.00012, 0.0, 0.00023, 3e-05, 9e-05, 0.00012, 0.0, 0.0, 0.0, 8e-05, 4e-05, 0.00019, 0.00015, 0.00011, 0.00025, 9e-05, 0.00011, 0.00015, 0.00037, 0.00042, 0.00061, 0.00043, 0.00033, 0.0, 0.0, 0.0, 0.00023, 0.0, 0.00015, 0.00014, 0.0, 5e-05, 0.00012, 3e-05, 3e-05, 0.00013, 0.0, 0.0, 4e-05, 0.0, 0.00034, 4e-05, 0.0, 0.00011, 0.00028, 4e-05, 0.00011, 0.00039, 0.00032, 0.00011, 4e-05, 0.00032, 0.00012, 0.00044, 0.00038, 0.0003, 0.0, 0.0, 0.0, 0.00026, 0.00032, 0.00011, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0002, 6e-05, 1e-05, 7e-05, 0.00024, 6e-05, 7e-05, 1e-05, 0.00039, 0.00021, 0.00032, 0.00049, 0.0003, 0.00028, 0.00017, 7e-05, 0.00064, 0.00018, 0.0, 0.0, 0.0, 7e-05, 0.00017, 0.00078, 0.0, 0.00021, 0.00021, 0.00043, 0.00059, 0.00045, 0.00036, 0.0, 0.00011, 2e-05, 0.0002, 0.00017, 0.0, 0.0, 8e-05, 0.0, 7e-05, 0.00024, 0.00041, 0.0, 0.00032, 5e-05, 0.00042, 4e-05, 6e-05, 0.00049, 0.0, 6e-05, 4e-05, 0.0002, 0.001, 0.00037, 0.0004, 0.00021, 0.0005, 0.0, 0.0, 0.0, 0.00027, 9e-05, 1e-05, 0.00011, 0.00032, 0.00021, 0.00019, 7e-05, 0.0, 8e-05, 0.00013, 0.00012, 0.00019, 2e-05, 0.0, 7e-05, 0.0, 0.00015, 7e-05, 0.00014, 0.00051, 0.00016, 3e-05, 0.0, 0.00078, 0.0, 0.0, 7e-05, 0.00041, 0.0, 0.0, 0.00014, 0.00253, 4e-05, 0.0001, 0.0, 0.00224, 0.0, 0.0, 4e-05, 8e-05, 0.0, 0.00019, 0.00018, 0.00057, 0.00048, 0.0003, 0.00032, 8e-05, 1e-05, 3e-05, 0.00036, 0.0, 2e-05, 0.0, 0.00048, 0.0, 0.0, 9e-05, 0.00035, 3e-05, 3e-05, 0.00042, 0.00031, 3e-05, 3e-05, 0.00032, 0.00024, 0.00044, 0.00039, 0.00018, 0.00032, 1e-05, 0.0, 0.00014, 0.0, 0.0, 0.0, 0.00043, 5e-05, 0.0, 0.0, 4e-05, 1e-05, 0.0, 0.00069, 0.0, 6e-05, 8e-05, 3e-05, 0.0, 4e-05, 0.00019, 6e-05, 2e-05, 0.00028, 0.00013, 2e-05, 6e-05, 0.00021, 0.0, 0.00047, 0.00053, 6e-05, 0.00036, 5e-05, 0.0, 0.00024, 0.00063, 0.0, 5e-05, 6e-05, 0.00032, 4e-05, 3e-05, 0.0, 0.00022, 0.0, 0.0, 0.0, 0.00033, 0.0, 0.0, 3e-05, 0.00033, 0.00011, 6e-05, 7e-05, 0.00046, 8e-05, 7e-05, 0.00067, 0.0, 0.0, 7e-05, 0.00036, 7e-05, 8e-05, 0.00066, 0.0, 3e-05, 4e-05, 0.0, 0.00032, 0.00028, 5e-05, 6e-05, 0.0, 0.0, 0.00033, 0.0, 0.0, 0.00012, 0.00039, 0.0, 5e-05, 5e-05, 0.00099, 0.00013, 0.00017, 9e-05, 0.00052, 0.0, 0.00024, 0.00095, 0.00046, 0.00024, 0.0, 0.00118, 0.01194, 0.00045, 0.0005, 0.0, 0.0, 0.0, 1e-05, 0.00057, 0.00038, 0.0, 0.00022, 0.0, 0.00398, 0.00042, 0.00049, 0.0016, 0.0, 6e-05, 0.0, 0.0001, 4e-05, 0.0, 0.00031, 0.00013, 0.0, 0.0001, 0.0, 0.0, 4e-05, 0.00044, 0.0, 0.0, 6e-05, 8e-05, 0.0003, 0.00077, 0.00031, 0.00038, 2e-05, 0.0, 0.0, 0.00029, 0.0, 7e-05, 0.0, 0.00034, 0.00018, 0.00012, 2e-05, 0.00028, 0.00011, 0.0, 0.0, 0.0003, 5e-05, 0.0, 4e-05, 0.00045, 0.0, 4e-05, 0.0, 0.00031, 0.00012, 0.00011, 0.00031, 7e-05, 0.00011, 0.00012, 0.00028, 0.0003, 0.00039, 0.00039, 0.00017, 0.00096, 0.0, 1e-05, 0.0, 0.0, 2e-05, 9e-05, 0.00075, 0.0, 5e-05, 0.0001, 0.0, 5e-05, 2e-05, 0.00012, 9e-05, 9e-05, 9e-05, 0.0, 0.00015, 0.0])))]},\n", " 'version': 2}" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "primitive_result.metadata" ] }, { "cell_type": "markdown", "id": "69f5426e", "metadata": {}, "source": [ "L'objet `PubResult` contient des métadonnées de résilience supplémentaires sur les modèles de bruit appris utilisés pour l'atténuation.\n", "\n" ] }, { "cell_type": "code", "execution_count": 18, "id": "52482e42", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "noise_overhead: 9.2584227461744e+229\n", "total_mitigated_layers: 18\n", "unique_mitigated_layers: 3\n", "unique_mitigated_layers_noise_overhead: [2.0713004613510885e+36, 10.600275591731494, 9.687147432958504]\n" ] } ], "source": [ "# Print learned layer noise metadata\n", "for field, value in pub_result.metadata[\"resilience\"][\"layer_noise\"].items():\n", " print(f\"{field}: {value}\")" ] }, { "cell_type": "code", "execution_count": null, "id": "2b96bdd2", "metadata": {}, "outputs": [], "source": [ "# Exact data computed using the methods described in the original reference\n", "# Y. Kim et al. \"Evidence for the utility of quantum computing before fault tolerance\" (Nature 618,\n", "# 500–505 (2023)) Directly used here for brevity\n", "exact_data = np.array(\n", " [\n", " 1,\n", " 0.9899,\n", " 0.9531,\n", " 0.8809,\n", " 0.7536,\n", " 0.5677,\n", " 0.3545,\n", " 0.1607,\n", " 0.0539,\n", " 0.0103,\n", " 0.0012,\n", " 0.0,\n", " ]\n", ")" ] }, { "cell_type": "markdown", "id": "f6dfbb9a", "metadata": {}, "source": [ "\n", "\n", "### Résultats de la simulation Plot Trotter\n", "\n", "Le code suivant crée un graphique pour comparer les résultats bruts et atténués de l'expérience avec la solution exacte.\n", "\n" ] }, { "cell_type": "code", "execution_count": 20, "id": "e466736a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "\"Output" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "zne_metadata = primitive_result.metadata[\"resilience\"][\"zne\"]\n", "# Plot Trotter simulation results\n", "fig = plot_trotter_results(\n", " pub_result,\n", " parameter_values,\n", " plot_extrapolator=zne_metadata[\"extrapolator\"],\n", " plot_noise_factors=zne_metadata[\"noise_factors\"],\n", " exact=exact_data,\n", ")\n", "display(fig)" ] }, { "cell_type": "markdown", "id": "1cd46c88", "metadata": {}, "source": [ "Alors que les valeurs bruitées (facteur de bruit `nf=1.0`) présentent un écart important par rapport aux valeurs exactes, les valeurs atténuées sont proches des valeurs exactes, ce qui démontre l'utilité de la technique d'atténuation basée sur la PEA.\n", "\n", "\n", "\n", "### Résultats de l'extrapolation de la courbe pour chaque qubit individuel\n", "\n", "Enfin, le code suivant crée un graphique montrant les courbes d'extrapolation pour différentes valeurs de thêta sur un qubit spécifique.\n", "\n" ] }, { "cell_type": "code", "execution_count": 21, "id": "bea9695a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "\"Output" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "virtual_qubit = 1\n", "plot_qubit_zne_data(\n", " pub_result=pub_result,\n", " angles=parameter_values,\n", " qubit=virtual_qubit,\n", " noise_factors=zne_metadata[\"noise_factors\"],\n", " extrapolator=zne_metadata[\"extrapolator\"],\n", " extrapolated_noise_factors=zne_metadata[\"extrapolated_noise_factors\"],\n", ")" ] }, { "cell_type": "markdown", "id": "75f48e6a-c7e4-46f3-9d39-a7a877427a04", "metadata": {}, "source": [ "\n", "\n", "## Etapes suivantes\n", "\n", "\n", " Si ce travail vous a paru intéressant, les ressources suivantes pourraient vous intéresser :\n", "\n", " * Un [tutoriel](/docs/tutorials/combine-error-mitigation-techniques) consacré à la combinaison de techniques d'atténuation des erreurs.\n", " * [Documentation](/docs/guides/error-mitigation-and-suppression-techniques) détaillée sur les techniques d'atténuation des erreurs disponibles dans Qiskit.\n", " * Cours supplémentaires consacrés aux expériences à l'échelle industrielle : [Utility II](/learning/courses/utility-scale-quantum-computing/utility-ii) et [Utility III](/learning/courses/utility-scale-quantum-computing/utility-iii).\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "id": "a1b8767d", "source": "© IBM Corp., 2017-2026" } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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" }, "hours": 1.5, "qpuSeconds": 840 }, "nbformat": 4, "nbformat_minor": 5 }