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

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.

5 pages, 4 figures

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• Perturbative analysis of topological entanglement entropy from conditional independence
• Gauging tensor networks with belief propagation
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• Griffiths-McCoy singularities, Lee-Yang zeros and the cavity method in a solvable diluted ferromagnet
• Investigation of commuting Hamiltonian in quantum Markov network
• Quantum Cluster Variational Method and Message Passing Algorithms Revisited
• Gibbs state sampling via cluster expansions