量子态层析测量设置的启发式优化、综合与优先级排序

中文摘要 AI 辅助

量子计算应用（如量子模拟和量子态层析（QST））中的一项关键任务是将任意算子集划分为相互对易的子集，以实现高效测量。然而，随着算子数量和维度的增长，蛮力法很快变得难以处理。本文将算子划分重新表述为图着色（GC）问题，并开发了一个平衡精度与效率的高效计算框架来求解该问题。该框架可利用一系列GC算法，本文对这些算法在算子划分中的性能进行了基准测试。随后，本文展示了这些算法在优化QST实验中的实用性，其中确定QST的非重叠数据采集设置是一项重大挑战，且对这些设置进行优先级排序（即选择能提供最多信息的实验）同样重要。本文进一步展示了如何通过综合Clifford电路来执行这些实验，以对多量子比特系统中的对易Pauli算子进行联合测量。本文在多量子比特（最多5个量子比特）、多量子utrit（最多3个量子utrit）以及混合量子比特-量子utrit系统上对该框架进行了验证。结果表明，启发式GC方法大幅减少了QST所需的测量设置数量，并支持基于优先级的调度，以最大化每项实验的信息增益。该优化在学生级笔记本电脑上数分钟内即可收敛，即使对于这些相对较小的量子系统，其速度也比蛮力法快几个数量级。这证明了GC启发式算法作为噪声中等规模量子设备表征的可扩展且实用工具的潜力。本文已将用于优化和调度QST实验的GC框架的Python实现公开提供在此httpsURL。

英文摘要

A key task in many quantum-computing applications, e.g., quantum simulation and quantum state tomography (QST), is to partition an arbitrary set of operators into mutually commuting subsets for efficient measurements. However, brute-force approaches to this task quickly become intractable as the number and dimensionality of operators grow. Here, we reformulate operator partitioning as a graph-coloring (GC) problem and develop an efficient computational framework to solve it, balancing accuracy and efficiency. Our framework enables leveraging a range of GC algorithms, which we benchmark for operator partitioning. Then, we demonstrate their utility in optimizing QST experiments, where determining non-overlapping data acquisition settings for QST is a major challenge, and prioritizing among these settings, i.e., selecting the experiments that provide the most information. We further show how to perform these experiments by synthesizing Clifford circuits for joint measurement of commuting Pauli operators in multi-qubit systems. We validate our framework across multi-qubit (up to five qubits), multi-qutrit (up to three qutrits), and hybrid qubit-qutrit systems. Our results show that heuristic GC methods substantially reduce the number of required measurement settings for QST and enable priority-based scheduling that maximizes the information gain per experiment. The optimization converges within minutes on a student-grade laptop, providing speedups of several orders of magnitude over brute-force methods already for these relatively small quantum systems. This demonstrates the potential of GC heuristics as a scalable and practical tool for characterization of noisy intermediate-scale quantum devices. We have made the Python implementation of our GC framework to optimize and schedule QST experiments publicly available at https://github.com/ssm8015/QST_GT.git.

发表机构

• Chalmers University of Technology（查尔姆斯理工大学）

机构由 AI 辅助整理，请以论文原文为准。