Belief propagation algorithm for computing correlation functions in finite-temperature quantum many-body systems on loopy graphs

TL;DR

This paper evaluates the effectiveness of loopy quantum belief propagation in approximating correlation functions in finite-temperature quantum many-body systems, especially on graphs with large loops, for applications like quantum spin glasses and error correction.

Contribution

It benchmarks loopy quantum belief propagation's performance in quantum many-body physics, demonstrating its reliability for high-temperature correlation estimates on graphs with large loops.

Findings

QBP provides reliable high-temperature correlation estimates on large-loop graphs.

Effective for studying quantum spin glasses on Bethe lattices.

Useful in decoding sparse quantum error correction codes.

Abstract

Belief propagation -- a powerful heuristic method to solve inference problems involving a large number of random variables -- was recently generalized to quantum theory. Like its classical counterpart, this algorithm is exact on trees when the appropriate independence conditions are met and is expected to provide reliable approximations when operated on loopy graphs. In this paper, we benchmark the performances of loopy quantum belief propagation (QBP) in the context of finite-tempereture quantum many-body physics. Our results indicate that QBP provides reliable estimates of the high-temperature correlation function when the typical loop size in the graph is large. As such, it is suitable e.g. for the study of quantum spin glasses on Bethe lattices and the decoding of sparse quantum error correction codes.