Fast Algorithms for Stoquastic Spin Systems

2026-08-19

AI Summary

本文提出了一种基于快速混合马尔可夫链和亚临界渗流过程的框架，用于解决高温下stoquastic自旋系统中的快速采样与计数问题。

Abstract

We establish a general framework for developing fast sampling and counting algorithms for stoquastic spin systems at high temperature. Our framework is based on a rapidly mixing Markov chain for polymer models and a subcritical percolation process for sampling individual polymers. We apply our framework to obtain fast algorithms for approximating the partition function and sampling from the thermal distribution of (1) general stoquastic spin systems, (2) ferromagnetic Heisenberg models, and (3) antiferromagnetic Heisenberg models on bipartite graphs. For the Heisenberg models, we obtain an improved bound on the inverse temperature by using their respective cycle and loop representations.

Problem

• stoquastic spin systems
• fast algorithms
• high temperature

Innovation

• fast sampling and counting algorithms
• stoquastic spin systems
• rapidly mixing Markov chain
• subcritical percolation process
• Heisenberg models