基于平均误差分析的优化随机哈密顿模拟
Optimized Randomized Hamiltonian Simulation via Average-Error Analysis
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中文总结 AI 辅助
本文提出一种基于平均误差分析的随机哈密顿模拟优化框架，通过最小化 Haar 平均误差界来优化采样概率，显著降低误差界，并在 FeMoco 模型中实现约 5.65 倍的改进。
中文摘要 AI 辅助
哈密顿模拟是量子计算的核心应用。随机哈密顿模拟通过采样量子电路来近似目标动力学，并且通常允许更简单的电路实现。我们开发了一个随机哈密顿模拟框架，其中哈密顿项以任意概率被采样，相应的短时演化按顺序实现。相对于理想时间演化的主要通道误差由采样生成器的方差控制。最小化基于方差的 worst-case 误差上界可以恢复 qDRIFT，这是一种领先的随机哈密顿模拟算法，它按照项的算子范数比例进行采样。然而，对于典型的输入态，这种采样分布不一定是最优的。最小化 Haar 平均误差界反而产生与项的 Hilbert-Schmidt 范数成比例的采样概率。这种选择可以提供比传统 qDRIFT 更小的平均误差界。对于表示为 Pauli 字符串之和的哈密顿量，我们将此框架与交换 Pauli 分组相结合，在固定的 $R_z$ 深度下获得比传统 qDRIFT 更小的误差界。Sachdev-Ye-Kitaev 模型的数值基准显示误差界改进因子与量子比特数呈线性缩放一致。对于 108 量子比特的 FeMoco 哈密顿量，误差界减少了约 5.65 倍。这些结果确立了平均误差优化作为随机哈密顿模拟的实用设计原则。
英文摘要
Hamiltonian simulation is a central application of quantum computing. Randomized Hamiltonian simulation approximates the target dynamics by sampling quantum circuits and often allows simpler circuit implementations. We develop a framework for randomized Hamiltonian simulation in which Hamiltonian terms are sampled with arbitrary probabilities and the corresponding short-time evolutions are implemented sequentially. The leading channel error relative to ideal time evolution is governed by the variance of the sampled generators. Minimizing the variance-based upper bound on the worst-case error recovers qDRIFT, a leading randomized Hamiltonian simulation algorithm that samples terms in proportion to their operator norms. For typical input states, however, this sampling distribution need not be optimal. Minimizing Haar-averaged error bounds instead yields sampling probabilities proportional to the Hilbert-Schmidt norms of the terms. This choice can provide smaller average-error bounds than conventional qDRIFT. For Hamiltonians expressed as sums of Pauli strings, we combine this framework with commuting Pauli grouping to obtain smaller error bounds than conventional qDRIFT at fixed $R_z$ depth. Numerical benchmarks for the Sachdev-Ye-Kitaev model show error-bound improvement factors consistent with linear scaling in the number of qubits. For the 108-qubit FeMoco Hamiltonian, the error bounds are reduced by a factor of about 5.65. These results establish average-error optimization as a practical design principle for randomized Hamiltonian simulation.
发表机构
- Graduate School of Engineering Science, The University of Osaka（大阪大学工学研究科）
- Graduate School of Informatics, Kyoto University（京都大学情报学研究科）
- Center for Quantum Information and Quantum Biology, The University of Osaka（大阪大学量子信息与量子生物学中心）
- RIKEN Center for Quantum Computing (RQC)（理化学研究所量子计算中心）
机构由 AI 辅助整理，请以论文原文为准。
