AI 中文总结
针对量子吉布斯采样器收敛性诊断问题，提出利用其弱测量的与哈密顿量无关的低成本收敛监测准则，通过统计与数值分析验证其性能。
AI 中文摘要
近期全量子马尔可夫链蒙特卡洛方法的进展使量子计算机上的高效吉布斯态采样成为可能[Chen等人，《自然》646，561（2025）]。尽管对于经典上难以处理的系统，混合时间的严格最坏情况界限大多仍无法获得，但经典蒙特卡洛的经验表明，相关可观测量的收敛可能仍然很快。这提出了一个实际问题：如何以至多多项式开销高效诊断收敛。我们提出一种低成本的收敛监测准则，该准则利用了量子吉布斯采样器及其量子比特高效变体[Ding等人，arXiv:2508.05703（2025）]中固有的弱测量。我们的方法基于这样一种观察：在热平衡时，系统与环境之间的净能量流消失，能量交换统计满足平衡条件。该条件出现在从弱测量记录中提取的（准）频率分布中，我们利用它构造了一种仅基于采样器已生成数据的与哈密顿量无关的停止准则。我们提供了统计分析，以及数值和解析研究以理解其性能、假设和局限性。
英文摘要
Recent progress in fully quantum Markov chain Monte Carlo methods enables efficient Gibbs-state sampling on quantum computers [Chen et al., Nature 646, 561 (2025)]. Although rigorous worst-case bounds on mixing times remain largely inaccessible for classically intractable systems, experience from classical Monte Carlo suggests that convergence of relevant observables may nevertheless be rapid. This raises the practical question of how to diagnose convergence efficiently, i.e., with at most polynomial overhead. We propose a low-cost criterion for convergence monitoring that exploits the weak measurements inherent in quantum Gibbs samplers and their qubit-efficient variants [Ding et al., arXiv:2508.05703 (2025)]. Our approach is based on the observation that, at thermal equilibrium, the net energy flow between system and environment vanishes and energy-exchange statistics satisfy a balance condition. This condition appears in the distribution of (quasi-)frequencies extracted from the weak-measurement record and we use it to construct a Hamiltonian-agnostic stopping criterion based solely on data already generated by the sampler. We provide a statistical analysis, along with numerical and analytical studies to understand its performance, assumptions, and limitations.
Comments12+19 pages, 7 figures
