The Bayesian inversion problem for thermal average sampling of quantum systems

JOURNAL OF COMPUTATIONAL PHYSICS

卷:413

Article

Chen, Ziheng¹  Zhou, Zhennan² 

[1] Univ Texas Austin, Dept Math, Austin, TX 78705 USA

[2] Peking Univ, Beijing Int Ctr Math Res, Beijing 100871, Peoples R China

关键词: Bayesian inversion;    Thermal average;    Quantum canonical ensemble;    Path integral molecular dynamics;   

DOI  :  10.1016/j.jcp.2020.109448

来源: Elsevier

【 摘 要 】

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. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free