Gibbs states (i.e., thermal states) can be used for several applications such as quantum simulation, quantum machine learning, quantum optimization, and the study of open quantum systems. Moreover, semi-definite programming, combinatorial optimization problems, and training quantum Boltzmann machines can all be addressed by sampling from well-prepared Gibbs states. With that, however, comes the fact that preparing and sampling from Gibbs states on a quantum computer are notoriously difficult tasks. Such tasks can require large overhead in resources and/or calibration even in the simplest of cases, as well as the fact that the implementation might be limited to only a specific set of systems. We propose a method based on sampling from a quasi-distribution consisting of tensor products of mixed states on local clusters, i.e., expanding the full Gibbs state into a sum of products of local “Gibbs-cumulant” type states easier to implement and sample from on quantum hardware. We begin with presenting results for 4-spin linear chains with XY spin interactions, for which we obtain the ZZ dynamical spin-spin correlation functions and dynamical structure factor. We also present the results of measuring the specific heat of the 8-spin chain Gibbs state ρ₈.

吉布斯态（即热态）可用于多种应用，例如量子模拟、量子机器学习、量子优化和开放量子系统的研究。此外，半定规划、组合优化问题和训练量子玻尔兹曼机都可以通过从准备好的吉布斯状态中采样来解决。然而，随之而来的是，在量子计算机上准备和采样吉布斯态是众所周知的困难任务。即使在最简单的情况下，此类任务也可能需要大量的资源开销和/或校准，并且实施可能仅限于一组特定的系统。我们提出了一种基于从局部集群上混合状态的张量积组成的准分布中采样的方法，即将完整的吉布斯状态扩展为局部“吉布斯累积量”类型状态的乘积之和，这些状态更容易在量子硬件上实现和采样。我们首先展示了具有 XY 自旋相互作用的 4 自旋线性链的结果，为此我们获得了 ZZ 动态自旋-自旋相关函数和动力学结构因子。我们还提出了测量 8 自旋链吉布斯态 ρ₈ 的比热的结果。