Efficient Algorithms for Weakly-Interacting Quantum Spin Systems

TL;DR

This paper introduces efficient algorithms for simulating weakly-interacting quantum spin systems at any temperature, including a fully polynomial-time approximation scheme for the partition function and a sampling method for thermal distributions.

Contribution

It presents the first fully polynomial-time approximation scheme for the partition function and sampling in weakly-interacting quantum spin systems using cluster expansion techniques.

Findings

Successfully approximates the partition function efficiently

Provides an effective sampling scheme for thermal distributions

Demonstrates the applicability of cluster expansion methods

Abstract

We establish efficient algorithms for weakly-interacting quantum spin systems at arbitrary temperature. In particular, we obtain a fully polynomial-time approximation scheme for the partition function and an efficient approximate sampling scheme for the thermal distribution over a classical spin space. Our approach is based on the cluster expansion method and a standard reduction from approximate sampling to approximate counting.