In this article, we propose a novel method for sampling potential functions based on noisy observation data of a finite number of observables in quantum canonical ensembles, which leads to the accurate sampling of a wide class of test observables. The method is based on the Bayesian inversion framework, which provides a platform for analyzing the posterior distribution and naturally leads to an efficient numerical sampling algorithm. We highlight that, the stability estimate is obtained by treating the potential functions as intermediate variables in the following way: the discrepancy between two sets of observation data of training observables can bound the distance between corresponding posterior distributions of potential functions, while the latter naturally leads to a bound of the discrepancies between corresponding thermal averages of test observables. Besides, the training observables can be more flexible than finite samples of the local density function, which are mostly used in previous researches. The method also applies to the multi-level quantum systems in the non-adiabatic regime. In addition, we provide extensive numerical tests to verify the accuracy and efficiency of the proposed algorithm.

在本文中，我们提出了一种新颖的方法，该方法基于量子规范合奏中有限数量的可观察对象的嘈杂观测数据对潜在函数进行采样，从而可以对多种测试可观察对象进行精确采样。该方法基于贝叶斯反演框架，该框架提供了一个分析后验分布的平台，自然而然地产生了一种有效的数值采样算法。我们强调，通过将潜在函数作为中间变量按以下方式获得来获得稳定性估计：训练可观察物的两组观测数据之间的差异可以限制潜在函数的相应后验分布之间的距离，而后者自然会导致测试可观察物的相应热平均值之间存在差异。此外，训练可观测值比局部密度函数的有限样本更灵活，后者在以前的研究中大多使用。该方法也适用于非绝热状态下的多能级量子系统。此外，我们提供了广泛的数值测试，以验证所提出算法的准确性和效率。