{ "cells": [ { "cell_type": "markdown", "id": "d2c31ae8", "metadata": {}, "source": [ "---\n", "title: \"확률적 오류 증폭을 활용한 유틸리티 규모의 오류 완화\"\n", "description: \"잡음 외삽 없이 확률적 오류 증폭을 적용한 유틸리티 규모의 오류 완화 실험을 수행한다.\"\n", "---\n", "\n", "{/* cspell:ignore mapsto multigraph inds extrap sharex sharey pidx */}\n", "\n", "\n", "\n", "# 확률적 오류 증폭을 활용한 유틸리티 규모의 오류 완화\n", "\n", "*예상 소요 시간: Heron r3 프로세서 기준 14분 (참고: 이는 예상치에 불과합니다.) (실행 시간은 다를 수 있습니다.)*\n", "\n" ] }, { "cell_type": "markdown", "id": "8bf80006", "metadata": {}, "source": [ "\n", "\n", "## 학습 성과\n", "\n", "* *제로 노이즈 외삽법* (ZNE)의 이론적 배경, 노이즈 증폭을 위한 다양한 방법, 그리고 유틸리티 규모 실험에서 *확률적 오차 증폭법* (PEA)이 선호되는 이유.\n", "* Qiskit을 사용하여 PEA와 함께 ZNE를 실제로 구현하는 방법.\n", "\n", "\n", "\n", "## 전제조건\n", "\n", "* Qiskit에서 [오류 완화](/learning/courses/utility-scale-quantum-computing/error-mitigation) 기술을 활용하는 데 필요한 기초 지식을 다루는 *‘유틸리티급 양자 컴퓨팅’* 과정의 오류 완화 강의입니다.\n", "* 이 튜토리얼에서 예시로 사용된 유틸리티 *규모* 실험에 대한 자세한 배경 지식을 얻으려면 ‘유틸리티 규모 양자 컴퓨팅’ 과정의 [‘유틸리티-I’ 강의를](/learning/courses/utility-scale-quantum-computing/utility-i) 참고하세요.\n", "\n" ] }, { "cell_type": "markdown", "id": "a929ccce", "metadata": {}, "source": [ "\n", "\n", "## 배경\n", "\n", "이 튜토리얼에서는 *확률적 오차 증폭* (PEA)이 적용된 *제로 노이즈 외삽법* (ZNE)의 실험용 버전을 사용하여, IBM Quantum 컴퓨트 서비스를 통해 유틸리티급 오차 완화 실험을 수행하는 방법을 보여줍니다.\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", "**참조**\n", ": Y. Kim 등 *오류 허용 기능이 도입되기 전 양자 컴퓨팅의 유용성을 입증하는 증거.* [《네이처》 618.7965 (2023)](https://www.nature.com/articles/s41586-023-06096-3)\n", "\n" ] }, { "cell_type": "markdown", "id": "a89ed8dd", "metadata": {}, "source": [ "\n", "\n", "### 무잡음 외삽법 (ZNE)\n", "\n", "제로 노이즈 외삽법(ZNE)은 *알려진* 방식으로 확장할 수 있는 회로 실행 중 *알* 수 없는 노이즈의 영향을 제거하는 오류 완화 기법입니다.\n", "\n", "기대값은 알려진 함수에 따라 노이즈에 따라 조정된다고 가정합니다\n", "\n", "$$\n", "\\langle A(\\lambda) \\rangle = \\langle A(0) \\rangle + \\sum_{k=0}^{m} a_k \\lambda^k + R\n", "$$\n", "\n", "여기서 $\\lambda$ 은 노이즈 강도를 매개변수화하여 증폭할 수 있습니다.\n", "\n", "다음 단계를 통해 ZNE를 구현할 수 있습니다:\n", "\n", "1. 여러 노이즈 요인에 대한 회로 노이즈 증폭 $\\lambda_1, \\lambda_2, ... $\n", "2. 모든 노이즈 증폭 회로를 실행하여 다음을 측정합니다 $\\langle A(\\lambda_1)\\rangle, ...$\n", "3. 제로 노이즈 한계로 다시 추정하기 $\\langle A(0)\\rangle$\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", "#### ZNE를 위한 소음 증폭\n", "\n", "ZNE를 성공적으로 구현하기 위한 주요 과제는 기대값의 노이즈에 대한 정확한 모델을 확보하고 알려진 방식으로 노이즈를 증폭하는 것입니다.\n", "\n", "ZNE에 오류 증폭을 구현하는 일반적인 방법은 세 가지가 있습니다.\n", "\n", "| **맥박 스트레칭** | **게이트 폴딩** | **확률적 오류 증폭** |\n", "| -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ |\n", "| 보정을 통한 펄스 지속 시간 조정 | ID 주기에서 게이트 반복 $U\\mapsto U(U^{-1}U)^{\\lambda-1}/2$ | 폴리 채널 샘플링을 통한 노이즈 추가 |\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", "| 칸달라 외 네이처 (2019) | Shultz et al. PRA (2022) | 리 & 벤자민 PRX (2017) |\n", "\n" ] }, { "cell_type": "markdown", "id": "c23e43ee", "metadata": {}, "source": [ "유틸리티 규모 실험의 경우, *확률적 오류 증폭* (PEA)이 가장 매력적입니다.\n", "\n", "* 펄스 스트레칭은 게이트 노이즈가 지속 시간에 비례한다고 가정하지만, 일반적으로 그렇지 않습니다. 보정에는 비용도 많이 듭니다.\n", "* 게이트 폴딩에는 큰 스트레치 계수가 필요하므로 실행할 수 있는 회로의 깊이가 크게 제한됩니다.\n", "* PEA는 기본 노이즈 계수( $\\lambda=1$ )로 실행할 수 있는 모든 회로에 적용할 수 있지만 노이즈 모델을 학습해야 합니다.\n", "\n", "\n", "\n", "### PEA의 잡음 모델을 학습하십시오\n", "\n", "PEA는 *확률적 오류 제거* (PEC)와 동일한 계층 기반 잡음 모델을 가정하지만, 회로 잡음에 따라 기하급수적으로 증가하는 샘플링 오버헤드를 피할 수 있습니다.\n", "\n", "| **1단계** | **2단계** | **3단계** |\n", "| ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ | --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |\n", "| 2큐비트 게이트의 폴리 트위클 레이어 | 레이어의 아이덴티티 쌍을 반복하고 노이즈 학습하기 | 충실도(각 노이즈 채널별 오차) 도출 |\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", "**참조** : E. 반 덴 베르그, Z. 미네브, A. 칸달라, 그리고 K. Temme, *잡음이 많은 양자 프로세서에서 희소 폴리-린드블라드 모델을 사용한 확률론적 오류 제거* [arXiv:2201.09866](https://arxiv.org/abs/2201.09866)\n", "\n" ] }, { "cell_type": "markdown", "id": "55b94021", "metadata": {}, "source": [ "\n", "\n", "## 요구사항\n", "\n", "이 튜토리얼을 시작하기 전에 다음 항목이 설치되어 있는지 확인하십시오:\n", "\n", "* Qiskit SDK v2.0 또는 그 이후 버전, [시각화](/docs/api/qiskit/visualization) 기능 지원\n", "* Qiskit Runtime v0.22 또는 이후 (`pip install qiskit-ibm-runtime`)\n", "\n" ] }, { "attachments": {}, "cell_type": "markdown", "id": "7db2e559", "metadata": {}, "source": [ "\n", "\n", "## 설정\n", "\n", "아래 셀에서는 관련 패키지를 불러오고, 백엔드의 위상 구조를 따르는 2차원 횡자장 이징 모델의 트로터화 시간 진화 회로를 구성하기 위한 몇 가지 보조 함수를 정의합니다.\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", "## 소규모 시뮬레이터 예시\n", "\n", "시뮬레이터에서는 런타임 오류 완화 기능이 지원되지 않으므로 이 단계는 생략하겠습니다.\n", "\n", "\n", "\n", "## 대규모 하드웨어 예시\n", "\n" ] }, { "attachments": {}, "cell_type": "markdown", "id": "988ee237", "metadata": {}, "source": [ "\n", "\n", "### 1단계: 고전적 입력을 양자 문제에 매핑하기\n", "\n", "\n", "\n", "#### 매개변수화된 이징 모델 회로 생성\n", "\n", "\n", "\n", "##### 백엔드 구축\n", "\n", "먼저 실행할 백엔드를 선택합니다. 이 데모는 127큐비트 백엔드에서 실행되지만, 사용 가능한 모든 백엔드로 수정할 수 있습니다.\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", "##### 얽힘 계층 결합 정의\n", "\n", "트로터화 아이싱 시뮬레이션을 구현하려면 각 트로터 단계에서 반복할 장치에 대한 두 큐비트 게이트 커플링의 세 레이어를 정의합니다. 이는 완화를 구현하기 위해 노이즈를 학습하는 데 필요한 세 개의 꼬인 레이어를 정의합니다.\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", "##### 불량 큐비트 제거\n", "\n", "백엔드의 커플링 맵을 살펴보고 오류가 많은 커플링에 연결되는 큐비트가 있는지 확인하세요. 실험에서 이러한 '불량' 큐비트를 제거하세요.\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", "##### 메인 트로터 회로 생성\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", "#### 나중에 할당할 매개변수 값 목록을 생성하십시오\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", "### 2단계: 양자 하드웨어 실행을 위한 문제 최적화\n", "\n", "\n", "\n", "#### ISA 회로\n", "\n", "하드웨어에서 회로를 실행하기 전에 하드웨어 실행에 맞게 최적화하세요. 이 과정에는 몇 가지 단계가 포함됩니다:\n", "\n", "* 회로의 가상 큐비트를 하드웨어의 물리적 큐비트에 매핑하는 큐비트 레이아웃을 선택합니다.\n", "* 필요에 따라 스왑 게이트를 삽입하여 연결되지 않은 큐비트 간의 상호 작용을 라우팅합니다.\n", "* 회로의 게이트를 하드웨어에서 직접 실행할 수 있는 명령어 [집합 아키텍처(ISA)](/docs/guides/transpile#instruction-set-architecture) 명령어로 변환합니다.\n", "* 회로 최적화를 수행하여 회로 깊이와 게이트 수를 최소화합니다.\n", "\n", "키스킷에 내장된 트랜스파일러로 이 모든 단계를 수행할 수 있지만, 이 튜토리얼에서는 유틸리티 규모의 트로터 회로를 처음부터 직접 구축하는 방법을 보여드립니다. 양호한 물리적 큐비트를 선택하고 선택한 큐비트에서 연결된 큐비트 쌍에 얽힘 레이어를 정의합니다. 그럼에도 불구하고 여전히 회로에서 비 ISA 게이트를 변환하고 트랜스파일러가 제공하는 회로 최적화를 활용해야 합니다.\n", "\n", "패스 매니저를 생성한 다음 회로에서 패스 매니저를 실행하여 선택한 백엔드에 대한 서킷을 트랜스파일합니다. 또한 회로의 초기 레이아웃을 이미 선택한 `good_qubits` 으로 수정합니다. 패스 관리자를 만드는 쉬운 방법은 [`generate_preset_pass_manager`](/docs/api/qiskit/qiskit.transpiler.generate_preset_pass_manager) 함수를 사용하는 것입니다. 패스 관리자를 사용한 [트랜스파일링에](/docs/guides/transpile-with-pass-managers) 대한 자세한 설명은 패스 관리자를 사용한 트랜스파일링을 참조하세요.\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", "#### ISA 관측량\n", "\n", "다음으로, 각 가상 큐비트에 대해 필요한 수의 $\\langle I \\rangle$ 용어를 채워서 weight-1 $\\langle Z \\rangle$ 관측값을 모두 생성합니다.\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": [ "트랜스필레이션 프로세스는 회로의 가상 큐비트를 하드웨어의 물리적 큐비트에 매핑했습니다. 큐비트 레이아웃에 대한 정보는 트랜스파일된 회로의 `layout` 어트리뷰트에 저장됩니다. 옵저버블은 가상 큐비트 측면에서도 정의되므로 이 레이아웃을 옵저버블에 적용해야 합니다. `SparsePauliOp` 의 `apply_layout` 방법을 사용하여 수행됩니다.\n", "\n", "다음 코드 블록에서 각 관측 가능한 변수가 리스트로 감싸져 있음을 확인할 수 있습니다. 이는 매 썬타 값에 대해 각 큐비트 관측량을 측정할 수 있도록 매개변수 값을 *지정* 하여 실행하기 위함입니다. 프리미티브에 대한 방송 규칙은 [프리미티브 문서](/docs/guides/primitives) 에서 확인할 수 있습니다.\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", "### 3단계: `Qiskit primitives` 명령어로 실행합니다\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", "#### 추정기 옵션 구성\n", "\n", "다음으로 완화 실험을 실행하는 데 필요한 `Estimator` 옵션을 구성합니다. 여기에는 얽힘 레이어의 노이즈 학습과 ZNE 외삽 옵션이 포함됩니다.\n", "\n", "저희는 다음 구성을 사용합니다:\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", "##### ZNE 옵션 설명\n", "\n", "다음은 실험 브랜치의 추가 옵션에 대한 자세한 설명입니다. 이러한 옵션과 이름은 확정된 것이 아니며, 여기에 나와 있는 모든 내용은 공식 출시 전에 변경될 수 있습니다.\n", "\n", "* **증폭기** : 노이즈를 목표 노이즈 계수까지 증폭할 때 사용하는 방법.\n", " `\"pea\"``\"gate_folding\"`허용되는 값은 두 큐비트 기저 게이트를 반복하여 증폭하는\n", " 와, 회전된 두 큐비트 기저 게이트 레이어에 대한 파울리 회전 잡음 모델을 학습한 후\n", " 확률적 샘플링을 통해 증폭하는 입니다. `\"gate_folding_back\"`그 밖의 옵션으로는 와 가 있으며 `\"gate_folding_front\"` , 이에 대한 설명은 [API 문서](/docs/api/qiskit-ibm-runtime/options-zne-options#amplifier) 에서 확인할 수 있습니다.\n", "* **extrapolated\\_noise\\_factors** : 추정된 모델을 평가할 노이즈 계수 값을 하나 이상 지정합니다 노이즈 계수 값을 지정합니다. 값의 시퀀스인 경우, 반환된 결과는 외삽 모델에 대해 평가된 지정된 노이즈 계수를 사용하여 배열 값으로 변환됩니다. 값 값이 0이면 무노이즈 외삽에 해당합니다.\n", "\n", "\n", "\n", "#### 실험 실행\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", "### 4단계: 후처리 수행 및 원하는 클래식 형식으로 결과 반환\n", "\n", "실험이 완료되면 결과를 확인할 수 있습니다. 원시값과 완화한 기대값을 가져와 정확한 결과와 비교합니다. 그런 다음 각 매개변수에 대한 모든 큐비트에 대해 평균화된(외삽된) 기대값과 원시값을 모두 플롯합니다. 마지막으로 선택한 개별 큐비트에 대한 기대값을 플롯합니다.\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", "#### 일반 결과 형상 및 메타데이터\n", "\n", "`PrimitiveResult` 객체에는 `PubResult` 이라는 목록과 같은 구조가 포함되어 있습니다. 견적서에 PUB 하나만 제출하므로 `PrimitiveResult` 에는 `PubResult` 객체 하나가 포함됩니다.\n", "\n", "(원시 통합 PUB 블록) 결과 기대값과 표준 오차는 배열 값이다. ZNE를 사용한 추정기 작업의 경우, 's' `DataBin``PubResult` 컨테이너에서 기대값과 표준 오차에 대한 여러 데이터 필드를 사용할 수 있습니다. 여기서 기대값에 대한 데이터 필드를 간략히 논의하겠습니다(표준 오차(`stds`)에 대해서도 유사한 데이터 필드를 사용할 수 있습니다).\n", "\n", "1. `pub_result.data.evs`: 제로 노이즈에 해당하는 기대값(휴리스틱적으로 최선의 추정 기준)입니다.\n", " * 첫 번째 축은 관측 가능한 가상 큐비트 인덱스 $\\langle Z_i\\rangle$ ( $124$ virtual-qubits/observables)입니다\n", " * 두 번째 축은 $\\theta$ ( $12$ 매개 변수 값)의 매개 변수 값을 인덱싱합니다\n", "2. `pub_result.data.evs_extrapolated`: 모든 외삽기에 대한 외삽된 노이즈 인자에 대한 기대값입니다. 이 배열에는 두 개의 축이 추가로 있습니다.\n", " * 세 번째 축은 외삽 방법( $2$ 외삽기, `exponential` 및 `linear`)을 색인화합니다\n", " * 마지막 축은 (옵션에 $20$ 지정된 `extrapolated_noise_factors` 외삽점)을 인덱싱합니다\n", "3. `pub_result.data.evs_noise_factors`: 각 노이즈 인자에 대한 원시 기대값입니다.\n", " * 세 번째 축은 원시 `noise_factors` ( $3$ 요인)을 인덱싱합니다\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": [ "`PrimitiveResult` 에서도 여러 메타데이터 필드를 사용할 수 있습니다. 메타데이터에 포함되는 항목은 다음과 같습니다.\n", "\n", "* `resilience/zne/noise_factors`: 원시 노이즈 요인\n", "* `resilience/zne/extrapolator`: 각 결과에 사용된 외삽기\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, 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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, 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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", " 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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": [ "`PubResult` 개체에는 완화에 사용된 학습된 노이즈 모델에 대한 추가 복원력 메타데이터가 있습니다.\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", "### 플롯 트로터 시뮬레이션 결과\n", "\n", "다음 코드는 원시 및 완화 실험 결과를 정확한 솔루션과 비교하기 위한 플롯을 생성합니다.\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": [ "노이즈(노이즈 계수 `nf=1.0`) 값은 정확한 값과 큰 편차를 보이지만, 완화한 값은 정확한 값에 근접하여 PEA 기반 완화 기법의 유용성을 보여줍니다.\n", "\n", "\n", "\n", "### 개별 큐비트에 대한 플롯 외삽 결과\n", "\n", "마지막으로, 다음 코드는 특정 큐비트에서 다양한 세타 값에 대한 외삽 곡선을 보여주는 플롯을 생성합니다.\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", "## 다음 단계\n", "\n", "\n", " 이 글이 흥미로웠다면, 다음 자료도 참고해 보시기 바랍니다:\n", "\n", " * 오류 완화 기법을 결합하는 방법에 중점을 둔 [튜토리얼입니다](/docs/tutorials/combine-error-mitigation-techniques).\n", " * Qiskit에서 사용할 수 있는 오류 완화 기법에 대한 자세한 [설명](/docs/guides/error-mitigation-and-suppression-techniques).\n", " * 대규모 실험을 다루는 추가 강의: [Utility II](/learning/courses/utility-scale-quantum-computing/utility-ii) 및 [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 }