{ "cells": [ { "cell_type": "markdown", "id": "d2c31ae8", "metadata": {}, "source": [ "---\n", "title: \"Mitigación de errores a gran escala con amplificación probabilística de errores\"\n", "description: \"Realizar un experimento de mitigación de errores a escala industrial con extrapolación de ruido cero y amplificación probabilística de errores.\"\n", "---\n", "\n", "{/* cspell:ignore mapsto multigraph inds extrap sharex sharey pidx */}\n", "\n", "\n", "\n", "# Mitigación de errores a gran escala con amplificación probabilística de errores\n", "\n", "*Tiempo estimado de ejecución: 14 minutos en un procesador Heron r3 (NOTA: Se trata solo de una estimación). (El tiempo de ejecución puede variar.)*\n", "\n" ] }, { "cell_type": "markdown", "id": "8bf80006", "metadata": {}, "source": [ "\n", "\n", "## Resultados del aprendizaje\n", "\n", "Una vez completado este tutorial, los usuarios deberían comprender:\n", "\n", "* La teoría en la que se basa *la extrapolación sin ruido* (ZNE), los distintos métodos para amplificar el ruido y por qué se prefiere *la amplificación probabilística del error* (PEA) para los experimentos a escala industrial.\n", "* Cómo implementar ZNE con PEA en la práctica utilizando Qiskit.\n", "\n", "\n", "\n", "## Requisitos previos\n", "\n", "Recomendamos a los usuarios que se familiaricen con los siguientes temas antes de seguir este tutorial:\n", "\n", "* [La lección](/learning/courses/utility-scale-quantum-computing/error-mitigation) sobre mitigación de errores del curso *de computación cuántica a escala industrial,* destinada a adquirir conocimientos básicos sobre el uso de la mitigación de errores en Qiskit.\n", "* [La lección «Utility-I»](/learning/courses/utility-scale-quantum-computing/utility-i) del curso *sobre computación cuántica a escala industrial,* para obtener más información sobre el experimento a escala industrial que se utiliza como ejemplo en este tutorial.\n", "\n" ] }, { "cell_type": "markdown", "id": "a929ccce", "metadata": {}, "source": [ "\n", "\n", "## En segundo plano\n", "\n", "Este tutorial muestra cómo llevar a cabo un experimento de mitigación de errores a escala industrial con « Qiskit Runtime », utilizando una versión experimental de *la extrapolación sin ruido* (ZNE) con *amplificación probabilística de errores* (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", "**Referencia**\n", ": Y. Kim et al. *Pruebas de la utilidad de la computación cuántica antes de la tolerancia a fallos.* [Nature 618.7965 (2023)](https://www.nature.com/articles/s41586-023-06096-3)\n", "\n" ] }, { "cell_type": "markdown", "id": "a89ed8dd", "metadata": {}, "source": [ "\n", "\n", "### Extrapolación sin ruido (ZNE)\n", "\n", "La extrapolación de ruido cero (ZNE) es una técnica de mitigación de errores que elimina los efectos de un ruido *desconocido* durante la ejecución de un circuito que puede escalarse de forma *conocida*.\n", "\n", "Supone que los valores de las expectativas se escalan con el ruido mediante una función conocida\n", "\n", "$$\n", "\\langle A(\\lambda) \\rangle = \\langle A(0) \\rangle + \\sum_{k=0}^{m} a_k \\lambda^k + R\n", "$$\n", "\n", "donde $\\lambda$ parametriza la intensidad del ruido y puede amplificarse.\n", "\n", "Podemos implantar la ZNE con los siguientes pasos:\n", "\n", "1. Amplificar el ruido del circuito para varios factores de ruido $\\lambda_1, \\lambda_2, ... $\n", "2. Ejecuta cada circuito amplificado por ruido para medir $\\langle A(\\lambda_1)\\rangle, ...$\n", "3. Extrapolar al límite de ruido cero $\\langle A(0)\\rangle$\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", "#### Amplificar el ruido para ZNE\n", "\n", "El principal reto para aplicar con éxito la ZNE es disponer de un modelo preciso del ruido en el valor de expectativa y amplificar el ruido de forma conocida.\n", "\n", "Hay tres formas habituales de aplicar la amplificación de errores para la ZNE.\n", "\n", "| **Estiramiento del pulso** | **Puerta abatible** | **Amplificación probabilística de errores** |\n", "| -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ |\n", "| Escala la duración del pulso mediante calibración | Repetir puertas en ciclos de identidad $U\\mapsto U(U^{-1}U)^{\\lambda-1}/2$ | Añadir ruido mediante el muestreo de canales 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. Naturaleza (2019) | Shultz et al. PRA (2022) | Li & Benjamin PRX (2017) |\n", "\n" ] }, { "cell_type": "markdown", "id": "c23e43ee", "metadata": {}, "source": [ "Para los experimentos a escala de servicios públicos, la *amplificación probabilística de errores* (PEA) es la más atractiva.\n", "\n", "* El estiramiento de pulsos asume que el ruido de puerta es proporcional a la duración, lo que no suele ser cierto. La calibración también es costosa.\n", "* El plegado de compuertas requiere grandes factores de estiramiento que limitan enormemente la profundidad de los circuitos que se pueden ejecutar.\n", "* PEA puede aplicarse a cualquier circuito que pueda funcionar con factor de ruido nativo ( $\\lambda=1$ ) pero requiere aprender el modelo de ruido.\n", "\n", "\n", "\n", "### Aprenda el modelo de ruido para PEA\n", "\n", "PEA asume el mismo modelo de ruido basado en capas que *la cancelación probabilística de errores* (PEC); sin embargo, evita la sobrecarga de muestreo que escala exponencialmente con el ruido del circuito.\n", "\n", "| **Paso 1** | **Paso 2** | **Paso 3** |\n", "| ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ | --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |\n", "| Capas Pauli twirl de puertas de dos qubits | Repite los pares de capas de identidad y aprende el ruido | Derivar una fidelidad (error para cada canal de ruido) |\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", "**Referencia** : E. van den Berg, Z. Minev, A. Kandala y K. Temme, *Cancelación probabilística de errores con modelos Pauli-Lindblad dispersos en procesadores cuánticos ruidosos* [arXiv:2201.09866](https://arxiv.org/abs/2201.09866)\n", "\n" ] }, { "cell_type": "markdown", "id": "55b94021", "metadata": {}, "source": [ "\n", "\n", "## Requisitos\n", "\n", "Antes de empezar este tutorial, asegúrate de tener instalado lo siguiente:\n", "\n", "* Qiskit SDK v2.0 o posterior, con soporte [para visualización](/docs/api/qiskit/visualization)\n", "* Qiskit Runtime v0.22 o posterior (`pip install qiskit-ibm-runtime`)\n", "\n" ] }, { "attachments": {}, "cell_type": "markdown", "id": "7db2e559", "metadata": {}, "source": [ "\n", "\n", "## Configuración\n", "\n", "En la celda siguiente, importamos los paquetes pertinentes y creamos algunas funciones auxiliares para construir los circuitos de la evolución temporal trotterizada de un modelo de Ising bidimensional con campo transversal que se ajusta a la topología del 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", "## Ejemplo de simulador a pequeña escala\n", "\n", "Omitiremos este paso, ya que la mitigación de errores en tiempo de ejecución no es compatible con los simuladores.\n", "\n", "\n", "\n", "## Ejemplo de hardware a gran escala\n", "\n" ] }, { "attachments": {}, "cell_type": "markdown", "id": "988ee237", "metadata": {}, "source": [ "\n", "\n", "### Paso 1: Asignar entradas clásicas a un problema cuántico\n", "\n", "\n", "\n", "#### Crear un circuito modelo Ising parametrizado\n", "\n", "\n", "\n", "##### Configurar un backend\n", "\n", "En primer lugar, elija un backend para ejecutar. Esta demostración se ejecuta en un backend de 127 qubits, pero puedes modificarlo a cualquier backend que tengas 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", "##### Definir acoplamientos de capas entrelazadas\n", "\n", "Para implementar la simulación Trotterized Ising, defina tres capas de acoplamientos de puerta de dos qubits para el dispositivo, que se repetirán en cada uno de los pasos Trotter. Éstas definen las tres capas giradas de las que hay que aprender el ruido para aplicar la mitigación.\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", "##### Eliminar los qubits defectuosos\n", "\n", "Mira el mapa de acoplamientos para el backend y comprueba si algún qubits se conecta a acoplamientos con alto error. Elimina estos qubits \"malos\" de tu experimento.\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", "##### Generación del circuito 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", "#### Crear una lista de valores de parámetros que se asignarán más adelante\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", "### Paso 2: Optimizar el problema para la ejecución en hardware cuántico\n", "\n", "\n", "\n", "#### Circuito ISA\n", "\n", "Antes de ejecutar el circuito en hardware, optimízalo para su ejecución en hardware. Este proceso consta de varios pasos:\n", "\n", "* Elige una disposición de qubits que asigne los qubits virtuales de tu circuito a qubits físicos en el hardware.\n", "* Inserta puertas de intercambio según sea necesario para dirigir las interacciones entre qubits que no estén conectados.\n", "* Traducir las puertas de nuestro circuito a instrucciones [ISA (Instruction Set Architecture](/docs/guides/transpile#instruction-set-architecture) ) que puedan ejecutarse directamente en el hardware.\n", "* Optimiza los circuitos para minimizar su profundidad y el número de puertas.\n", "\n", "Aunque el transpilador integrado en Qiskit puede llevar a cabo todos estos pasos, este tutorial muestra cómo construir el circuito Trotter a escala de servicio público desde cero. Seleccionar los qubits físicos buenos y definir capas de enredo en pares de qubits conectados a partir de esos qubits seleccionados. No obstante, aún es necesario traducir las puertas noISA del circuito y aprovechar cualquier optimización del circuito que ofrezca el transpilador.\n", "\n", "Transpila tu circuito para el backend elegido creando un gestor de pases y ejecutando el gestor de pases en el circuito. Además, fija el trazado inicial del circuito al ya seleccionado `good_qubits`. Una forma sencilla de crear un gestor de pases es utilizar la función [`generate_preset_pass_manager`](/docs/api/qiskit/qiskit.transpiler.generate_preset_pass_manager) función Consulte [Transpilar](/docs/guides/transpile-with-pass-managers) con gestores de pases para obtener una explicación más detallada de la transpilación con gestores de pases.\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", "A continuación, cree todos los observables weight-1 $\\langle Z \\rangle$ para cada qubit virtual rellenando el número necesario de términos $\\langle I \\rangle$.\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": [ "El proceso de transpilación ha mapeado los qubits virtuales de tu circuito a qubits físicos en el hardware. La información sobre la disposición de los qubits se almacena en el atributo `layout` del circuito transpilado. Su observable también se define en términos de los qubits virtuales, por lo que necesita aplicar esta disposición al observable. Para ello se utiliza el método `apply_layout` de `SparsePauliOp`.\n", "\n", "Fíjate en que, en el siguiente bloque de código, cada observable está envuelto en una lista. Esto se hace para *realizar una transmisión* con valores de parámetros, de modo que se mida cada observable de qubit para cada valor de theta. Consulta las reglas de difusión de los primitivos en la [documentación sobre primitivos](/docs/guides/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", "### Paso 3: Ejecutar utilizando 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", "#### Configurar las opciones del Estimador\n", "\n", "A continuación, configure las opciones de `Estimator` necesarias para ejecutar el experimento de mitigación. Esto incluye opciones para el aprendizaje del ruido de las capas de enredo y para la extrapolación ZNE.\n", "\n", "Utilizamos la siguiente configuración:\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", "##### Explicación de las opciones ZNE\n", "\n", "A continuación se detallan las opciones adicionales de la rama experimental. Tenga en cuenta que estas opciones y nombres no son definitivos, y que todo lo aquí expuesto está sujeto a cambios antes de su publicación oficial.\n", "\n", "* **amplificador** : Método que se utiliza para amplificar el ruido hasta los niveles deseados.\n", " Los valores permitidos son `\"gate_folding\"`, que amplifica mediante la repetición de puertas de base de dos qubits,\n", " y `\"pea\"`, que amplifica mediante muestreo probabilístico tras aprender el modelo de ruido con giro de Pauli\n", " para capas de puertas de base de dos qubits con giro. Otras opciones son `\"gate_folding_front\"` y `\"gate_folding_back\"`, que se explican en la [documentación de la API](/docs/api/qiskit-ibm-runtime/options-zne-options#amplifier).\n", "* **factores\\_de\\_ruido\\_extrapolados** : Especifique uno o más valores del factor de ruido con los que evaluar los modelos extrapolados. Si se trata de una secuencia de valores, los resultados devueltos serán valores de matriz con el factor de ruido especificado evaluado para el modelo de extrapolación. Un valor 0 corresponde a una extrapolación sin ruido.\n", "\n", "\n", "\n", "#### Ejecute el experimento\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", "### Paso 4: Procesamiento posterior y devolución del resultado en el formato clásico deseado\n", "\n", "Una vez finalizado el experimento, puedes ver los resultados. Se obtienen los valores de las expectativas brutas y atenuadas y se comparan con los resultados exactos. A continuación, traza los valores de las expectativas, tanto mitigadas (extrapoladas) como brutas, promediadas sobre todos los qubits para cada parámetro. Por último, trace los valores de las expectativas para su elección de qubits individuales.\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", "#### Formas generales de resultados y metadatos\n", "\n", "El objeto `PrimitiveResult` contiene una estructura en forma de lista denominada `PubResult`. Como sólo enviamos un PUB al estimador, el `PrimitiveResult` contiene un único objeto `PubResult` .\n", "\n", "Los valores esperados y los errores estándar del resultado PUB (bloque unificado primitivo) son valores de matriz. Para los trabajos de estimación con ZNE, hay varios campos de datos de valores esperados y errores estándar disponibles en el `PubResult`contenedor `DataBin` 's. Aquí analizaremos brevemente los campos de datos para los valores esperados (también hay campos de datos similares disponibles para los errores estándar (`stds`)).\n", "\n", "1. `pub_result.data.evs`: Valores esperados correspondientes al ruido cero (basados en la mejor extrapolación heurística).\n", " * El primer eje es el índice de qubits virtuales para el observable $\\langle Z_i\\rangle$ ( $124$ virtual-qubits/observables)\n", " * El segundo eje indexa el valor del parámetro para $\\theta$ ( $12$ valores del parámetro)\n", "2. `pub_result.data.evs_extrapolated`: Valores esperados de los factores de ruido extrapolados para cada extrapolador. Esta matriz tiene dos ejes adicionales.\n", " * El tercer eje indexa los métodos de extrapolación ( $2$ extrapoladores, `exponential` y `linear`)\n", " * El último eje indexa los `extrapolated_noise_factors` (puntos $20$ de extrapolación especificados en la opción)\n", "3. `pub_result.data.evs_noise_factors`: Valores esperados brutos para cada factor de ruido.\n", " * El tercer eje indexa los `noise_factors` brutos ( $3$ factores)\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": [ "También hay disponibles varios campos de metadatos en `PrimitiveResult`. Los metadatos incluyen:\n", "\n", "* `resilience/zne/noise_factors`: Los factores de ruido bruto\n", "* `resilience/zne/extrapolator`: Los extrapoladores utilizados para cada resultado\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": [ "El objeto `PubResult` tiene metadatos de resiliencia adicionales sobre los modelos de ruido aprendidos utilizados en la mitigación.\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", "### Resultados de la simulación Plot Trotter\n", "\n", "El siguiente código crea un gráfico para comparar los resultados brutos y atenuados del experimento con la solución exacta.\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": [ "Mientras que los valores ruidosos (factor de ruido `nf=1.0`) muestran una gran desviación con respecto a los valores exactos, los valores mitigados se aproximan a los valores exactos, lo que demuestra la utilidad de la técnica de mitigación basada en PEA.\n", "\n", "\n", "\n", "### Resultados de la extrapolación de la trama para qubits individuales\n", "\n", "Finalmente, el siguiente código crea un gráfico para mostrar las curvas de extrapolación para diferentes valores de theta en un qubit específico.\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", "## Próximos pasos\n", "\n", "\n", " Si te ha parecido interesante este trabajo, quizá te interese el siguiente material:\n", "\n", " * Un [tutorial](/docs/tutorials/combine-error-mitigation-techniques) centrado en la combinación de técnicas de mitigación de errores.\n", " * [Documentación](/docs/guides/error-mitigation-and-suppression-techniques) detallada sobre las técnicas de mitigación de errores disponibles en Qiskit.\n", " * Lecciones adicionales sobre experimentos a escala industrial: [«Utility II»](/learning/courses/utility-scale-quantum-computing/utility-ii) y «[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 }