随机自旋系统的快速算法
Fast Algorithms for Stoquastic Spin Systems
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中文总结 AI 辅助
该研究建立通用框架，结合聚合物模型的马尔可夫链与次临界渗流过程，开发高温下随机自旋系统的快速采样与计数算法，还改进了海森堡模型的逆温度界。
中文摘要 AI 辅助
我们建立了一个通用框架，用于开发高温下随机自旋系统的快速采样与计数算法。该框架基于聚合物模型的快速混合马尔可夫链，以及用于采样单个聚合物的次临界渗流过程。我们将此框架应用于三类场景以获取快速算法：一是近似一般随机自旋系统的配分函数，二是从二分图上铁磁海森堡模型的热分布中采样，三是从二分图上反铁磁海森堡模型的热分布中采样。对于海森堡模型，我们利用其各自的循环与环表示，得到了逆温度的改进界。
英文摘要
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.
