{ "cells": [ { "cell_type": "markdown", "id": "d2c31ae8", "metadata": {}, "source": [ "---\n", "title: \"Mitigação de erro em escala de utilidade com amplificação probabilística de erro\"\n", "description: \"Execute um experimento de mitigação de erros em escala utilitária com extrapolação de ruído zero e amplificação probabilística de erros.\"\n", "---\n", "\n", "{/* cspell:ignore mapsto multigraph inds extrap sharex sharey pidx */}\n", "\n", "\n", "\n", "# Mitigação de erro em escala de utilidade com amplificação probabilística de erro\n", "\n", "*Estimativa de tempo de execução: 14 minutos em um processador Heron r3 (NOTA: Trata-se apenas de uma estimativa. (O tempo de execução pode variar.)*\n", "\n" ] }, { "cell_type": "markdown", "id": "8bf80006", "metadata": {}, "source": [ "\n", "\n", "## Resultados do aprendizado\n", "\n", "Após concluir este tutorial, os usuários deverão compreender:\n", "\n", "* A teoria por trás *da extrapolação de ruído zero* (ZNE), os diferentes métodos para amplificar o ruído e por que *a amplificação probabilística de erros* (PEA) é a preferida para experimentos em escala industrial.\n", "* Como implementar a ZNE com PEA na prática usando o Qiskit.\n", "\n", "\n", "\n", "## Pré-requisitos\n", "\n", "Recomendamos que os usuários estejam familiarizados com os seguintes tópicos antes de seguir com este tutorial:\n", "\n", "* [A aula](/learning/courses/utility-scale-quantum-computing/error-mitigation) sobre mitigação de erros do curso *de computação quântica em escala industrial,* voltada para o conhecimento básico sobre o uso da mitigação de erros no Qiskit.\n", "* [A aula “Utility-I”](/learning/courses/utility-scale-quantum-computing/utility-i) do curso *sobre computação quântica em escala de serviços* públicos, para obter mais informações sobre o experimento em escala de serviços públicos usado como exemplo neste tutorial.\n", "\n" ] }, { "cell_type": "markdown", "id": "a929ccce", "metadata": {}, "source": [ "\n", "\n", "## Segundo plano\n", "\n", "Este tutorial demonstra como executar um experimento de mitigação de erros em escala de rede elétrica com o Serviço de Computação d IBM Quantum, utilizando uma versão experimental da *extrapolação sem ruído* (ZNE) com *amplificação probabilística de erros* (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", "**Referência**\n", ": Y. Kim et al. *Evidências da utilidade da computação quântica antes da tolerância a falhas.* [Nature 618.7965 (2023)](https://www.nature.com/articles/s41586-023-06096-3)\n", "\n" ] }, { "cell_type": "markdown", "id": "a89ed8dd", "metadata": {}, "source": [ "\n", "\n", "### Extrapolação sem ruído (ZNE)\n", "\n", "A extrapolação de ruído zero (ZNE) é uma técnica de atenuação de erros que remove os efeitos de um ruído *desconhecido* durante a execução do circuito que pode ser dimensionado de forma *conhecida*.\n", "\n", "Ele pressupõe que os valores de expectativa são escalonados com ruído por uma função conhecida\n", "\n", "$$\n", "\\langle A(\\lambda) \\rangle = \\langle A(0) \\rangle + \\sum_{k=0}^{m} a_k \\lambda^k + R\n", "$$\n", "\n", "onde $\\lambda$ parametriza a intensidade do ruído e pode ser amplificado.\n", "\n", "Podemos implementar a ZNE com as seguintes etapas:\n", "\n", "1. Amplificar o ruído do circuito para vários fatores de ruído $\\lambda_1, \\lambda_2, ... $\n", "2. Execute todos os circuitos amplificados por ruído para medir $\\langle A(\\lambda_1)\\rangle, ...$\n", "3. Extrapolar de volta para o limite de ruído zero $\\langle A(0)\\rangle$\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 ruído para ZNE\n", "\n", "O principal desafio na implementação bem-sucedida do ZNE é ter um modelo preciso para o ruído no valor esperado e amplificar o ruído de uma forma conhecida.\n", "\n", "Há três maneiras comuns de implementar a amplificação de erros para o ZNE.\n", "\n", "| **Alongamento de pulso** | **Portão dobrável** | **Amplificação de erros probabilísticos** |\n", "| -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ |\n", "| Dimensionar a duração do pulso por meio de calibração | Repetir portas em ciclos de identidade $U\\mapsto U(U^{-1}U)^{\\lambda-1}/2$ | Adicionar ruído por meio da amostragem de canais Pauli |\n", "| ![zne\\_pulse\\_stretching.png](https://eu-de.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://eu-de.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://eu-de.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. Natureza (2019) | Shultz et al. PRA (2022) | Li & Benjamin PRX (2017) |\n", "\n" ] }, { "cell_type": "markdown", "id": "c23e43ee", "metadata": {}, "source": [ "Para experimentos em escala de serviços públicos, a *amplificação probabilística de erros* (PEA) é a mais atraente.\n", "\n", "* O alongamento de pulso pressupõe que o ruído da porta é proporcional à duração, o que normalmente não é verdade. A calibração também é cara.\n", "* A dobragem de portas requer grandes fatores de extensão que limitam muito a profundidade dos circuitos que podem ser executados.\n", "* A PEA pode ser aplicada a qualquer circuito que possa ser executado com fator de ruído nativo ( $\\lambda=1$ ), mas requer o aprendizado do modelo de ruído.\n", "\n", "\n", "\n", "### Aprenda o modelo de ruído para PEA\n", "\n", "A PEA pressupõe o mesmo modelo de ruído baseado em camadas que o *cancelamento de erro probabilístico* (PEC); no entanto, ela evita a sobrecarga de amostragem que aumenta exponencialmente com o ruído do circuito.\n", "\n", "| **Etapa 1** | **Etapa 2** | **Etapa 3** |\n", "| ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ | --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |\n", "| Camadas de giro Pauli de portas de dois qubits | Repita a identidade dos pares de camadas e aprenda o ruído | Derivar uma fidelidade (erro para cada canal de ruído) |\n", "| ![pec\\_pauli\\_twirling.png](https://eu-de.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://eu-de.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://eu-de.quantum.cloud.ibm.com/docs/images/tutorials/utility-scale-error-mitigation-with-probabilistic-error-amplification/c51bd42d-2463-4c78-807b-d284ca79296f.avif) |\n", "\n", "**Referência** : E. van den Berg, Z. Minev, A. Kandala e K. Temme, *Cancelamento de erro probabilístico com modelos Pauli-Lindblad esparsos em processadores quânticos com ruído* [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 iniciar este tutorial, certifique-se de que os seguintes itens estejam instalados:\n", "\n", "* Qiskit SDK v2.0 ou posterior, com suporte [à visualização](/docs/api/qiskit/visualization)\n", "* Qiskit Runtime v0.22 ou mais tarde (`pip install qiskit-ibm-runtime`)\n", "\n" ] }, { "attachments": {}, "cell_type": "markdown", "id": "7db2e559", "metadata": {}, "source": [ "\n", "\n", "## Instalação\n", "\n", "Na célula abaixo, importamos os pacotes relevantes e criamos algumas funções auxiliares para construir os circuitos da evolução temporal de Trotter de um modelo de Ising bidimensional de campo transversal que se adapta à topologia do 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", "## Exemplo de simulador em pequena escala\n", "\n", "Vamos pular esta etapa, uma vez que a mitigação de erros em tempo de execução não é compatível com simuladores.\n", "\n", "\n", "\n", "## Exemplo de hardware em grande escala\n", "\n" ] }, { "attachments": {}, "cell_type": "markdown", "id": "988ee237", "metadata": {}, "source": [ "\n", "\n", "### Passo 1: Mapear entradas clássicas para um problema quântico\n", "\n", "\n", "\n", "#### Crie um circuito de modelo Ising parametrizado\n", "\n", "\n", "\n", "##### Implementar um backend\n", "\n", "Primeiro, escolha um backend para ser executado. Esta demonstração é executada em um backend de 127 qubit, mas você pode modificá-la para qualquer backend disponível.\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 acoplamentos de camadas entrelaçadas\n", "\n", "Para implementar a simulação de Ising Trotterizada, defina três camadas de acoplamentos de porta de dois qubits para o dispositivo, a serem repetidas em cada uma das etapas de Trotter. Elas definem as três camadas giratórias para as quais você precisa conhecer o ruído para implementar a atenuação.\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", "##### Remova os qubits defeituosos\n", "\n", "Observe o mapa de acoplamento do backend e veja se algum qubits se conecta a acoplamentos com alto erro. Remova esses qubits \"ruins\" do seu 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", "##### Geração do 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", "#### Crie uma lista de valores de parâmetros a serem atribuídos posteriormente\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", "### Etapa 2: Otimizar o problema para execução em hardware quântico\n", "\n", "\n", "\n", "#### circuito ISA\n", "\n", "Antes de executar o circuito no hardware, otimize-o para a execução no hardware. Esse processo envolve algumas etapas:\n", "\n", "* Escolha um layout de qubit que mapeie os qubits virtuais de seu circuito para qubits físicos no hardware.\n", "* Insira portas de troca conforme necessário para rotear interações entre qubits que não estão conectados.\n", "* Traduzir as portas em nosso circuito para instruções [de arquitetura de conjunto de instruções (ISA)](/docs/guides/transpile#instruction-set-architecture) que podem ser executadas diretamente no hardware.\n", "* Realizar otimizações de circuito para minimizar a profundidade do circuito e a contagem de portas.\n", "\n", "Embora o transpilador incorporado ao Qiskit possa executar todas essas etapas, este tutorial demonstra a construção do circuito Trotter em escala de utilidade pública de maneira básica. Selecione os bons qubits físicos e defina camadas de entrelaçamento em pares de qubits conectados a partir desses qubits selecionados. No entanto, você ainda precisa traduzir as portas não ISA no circuito e aproveitar qualquer otimização de circuito oferecida pelo transpilador.\n", "\n", "Transpile seu circuito para o backend escolhido criando um gerenciador de passes e, em seguida, executando o gerenciador de passes no circuito. Além disso, fixe o layout inicial do circuito no site já selecionado `good_qubits`. Uma maneira fácil de criar um gerenciador de passes é usar a função [`generate_preset_pass_manager`](/docs/api/qiskit/qiskit.transpiler.generate_preset_pass_manager) função. Consulte [Transpilar com gerenciadores](/docs/guides/transpile-with-pass-managers) de passagens para obter uma explicação mais detalhada da transpilação com gerenciadores de passagens.\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", "#### Observáveis ISA\n", "\n", "Em seguida, crie todos os observáveis weight-1 $\\langle Z \\rangle$ para cada qubit virtual preenchendo o número necessário de termos $\\langle I \\rangle$.\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": [ "O processo de transpilação mapeou os qubits virtuais de seu circuito para qubits físicos no hardware. As informações sobre o layout do qubit são armazenadas no atributo `layout` do circuito transpilado. Seu observável também é definido em termos de qubits virtuais, portanto, você precisa aplicar esse layout ao observável. Isso é feito usando o método `apply_layout` de `SparsePauliOp`.\n", "\n", "Observe que cada observável está contido em uma lista no bloco de código a seguir. Isso é feito para *realizar a transmissão* com valores de parâmetros, de modo que cada observável do qubit seja medido para cada valor de theta. Consulte as regras de transmissão para primitivas na [documentação](/docs/guides/primitives) sobre primitivas.\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", "### Passo 3: Execute usando 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 opções do Estimador\n", "\n", "Em seguida, configure as opções do site `Estimator` necessárias para executar o experimento de mitigação. Isso inclui opções para o aprendizado de ruído das camadas de entrelaçamento e para a extrapolação de ZNE.\n", "\n", "Usamos a seguinte configuração:\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", "##### Explicação das opções ZNE\n", "\n", "A seguir, são apresentados detalhes sobre as opções adicionais na ramificação experimental. Observe que essas opções e nomes não estão finalizados, e tudo aqui está sujeito a alterações antes de um lançamento oficial.\n", "\n", "* **amplificador** : O método a ser utilizado para amplificar o ruído até os níveis desejados.\n", " Os valores permitidos são `\"gate_folding\"`, que amplifica por meio da repetição de portas de base de dois qubits,\n", " e `\"pea\"`, que amplifica por meio de amostragem probabilística após o aprendizado do modelo de ruído com torção de Pauli\n", " para camadas de portas de base de dois qubits com torção. Outras opções são `\"gate_folding_front\"` e `\"gate_folding_back\"`, que são explicadas na [documentação](/docs/api/qiskit-ibm-runtime/options-zne-options#amplifier) da API.\n", "* **extrapolated\\_noise\\_factors** : Especifique um ou mais valores de fator de ruído para avaliar os modelos extrapolados. Se for uma sequência de valores, os resultados retornados serão valorados por matriz com o fator de ruído especificado avaliado para o modelo de extrapolação. Um valor de 0 corresponde à extrapolação de ruído zero.\n", "\n", "\n", "\n", "#### Executar o 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", "### Etapa 4: Pós-processamento e retorno do resultado no formato clássico desejado\n", "\n", "Quando o experimento for concluído, você poderá visualizar os resultados. Você obtém os valores de expectativa brutos e atenuados e os compara com os resultados exatos. Em seguida, faça um gráfico dos valores de expectativa, tanto atenuados (extrapolados) quanto brutos, com média de todos os qubits para cada parâmetro. Por fim, trace valores de expectativa para sua escolha de qubits individuais.\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", "#### Formatos gerais de resultados e metadados\n", "\n", "O objeto `PrimitiveResult` contém uma estrutura em forma de lista denominada `PubResult`. Como enviamos apenas um PUB para o estimador, o `PrimitiveResult` contém um único objeto `PubResult` .\n", "\n", "Os valores esperados e os erros padrão do resultado PUB (bloco unificado primitivo) são valores de matriz. Para trabalhos de estimativa com ZNE, existem vários campos de dados de valores esperados e erros padrão disponíveis no contêiner `DataBin` `PubResult`'s. Discutiremos brevemente os campos de dados para valores esperados aqui (campos de dados semelhantes também estão disponíveis para erros padrão (`stds`)).\n", "\n", "1. `pub_result.data.evs`: Valores de expectativa correspondentes ao ruído zero (com base na melhor extrapolação heurística).\n", " * O primeiro eixo é o índice do qubit virtual para o observável $\\langle Z_i\\rangle$ ( $124$ virtual-qubits/observables)\n", " * O segundo eixo indexa o valor do parâmetro para $\\theta$ (valores do parâmetro $12$ )\n", "2. `pub_result.data.evs_extrapolated`: Valores de expectativa para fatores de ruído extrapolados para cada extrapolador. Essa matriz tem dois eixos adicionais.\n", " * O terceiro eixo indexa os métodos de extrapolação ( $2$ extrapolators, `exponential` e `linear`)\n", " * O último eixo indexa os pontos `extrapolated_noise_factors` de $20$ extrapolação especificados na opção\n", "3. `pub_result.data.evs_noise_factors`: Valores brutos de expectativa para cada fator de ruído.\n", " * O terceiro eixo indexa o `noise_factors` bruto (fatores $3$ )\n", "\n" ] }, { "cell_type": "code", "execution_count": 16, "id": "e3aa4fc9", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "pub_result.data.evs.shape=(149, 12)\n", "pub_result.data.evs_extrapolated.shape=(149, 12, 2, 20)\n", "pub_result.data.evs_noise_factors.shape=(149, 12, 3)\n", "\n" ] } ], "source": [ "pub_result = primitive_result[0]\n", "\n", "print(\n", " f\"{pub_result.data.evs.shape=}\\n\"\n", " f\"{pub_result.data.evs_extrapolated.shape=}\\n\"\n", " f\"{pub_result.data.evs_noise_factors.shape=}\\n\"\n", ")" ] }, { "cell_type": "markdown", "id": "4c5cc6ee", "metadata": {}, "source": [ "Vários campos de metadados também estão disponíveis no site `PrimitiveResult`. Os metadados incluem\n", "\n", "* `resilience/zne/noise_factors`: Os fatores de ruído brutos\n", "* `resilience/zne/extrapolator`: Os extrapoladores usados 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, 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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, 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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, 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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": [ "O objeto `PubResult` tem metadados de resiliência adicionais sobre os modelos de ruído aprendidos usados na atenuação.\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 da simulação do Plot Trotter\n", "\n", "O código a seguir cria um gráfico para comparar os resultados brutos e atenuados do experimento com a solução exata.\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": [ "Embora os valores ruidosos (fator de ruído `nf=1.0`) apresentem um alto desvio dos valores exatos, os valores atenuados estão próximos dos valores exatos, demonstrando a utilidade da técnica de atenuação baseada em PEA.\n", "\n", "\n", "\n", "### Resultados da extrapolação do gráfico para qubits individuais\n", "\n", "Por fim, o código a seguir cria um gráfico para mostrar as curvas de extrapolação para diferentes valores de theta em um 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", "## Próximas etapas\n", "\n", "\n", " Se você achou este trabalho interessante, talvez se interesse pelo seguinte material:\n", "\n", " * Um [tutorial](/docs/tutorials/combine-error-mitigation-techniques) voltado para a combinação de técnicas de mitigação de erros.\n", " * [Documentação](/docs/guides/error-mitigation-and-suppression-techniques) detalhada sobre as técnicas de mitigação de erros disponíveis no Qiskit.\n", " * Aulas adicionais sobre experimentos em escala industrial: [Utilidade II](/learning/courses/utility-scale-quantum-computing/utility-ii) e [Utilidade 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 }