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

Poulin, David and Bilgin, Ersen (2008) Belief propagation algorithm for computing correlation functions in finite-temperature quantum many-body systems on loopy graphs. Physical Review A, 77 (5). Art. No. 052318. ISSN 1050-2947. https://resolver.caltech.edu/CaltechAUTHORS:POUpra08

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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-temperature 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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevA.77.052318DOIUNSPECIFIED
Additional Information:©2008 The American Physical Society. (Received 23 October 2007; published 16 May 2008) We thank Matt Leifer for stimulating discussions on graphical models and QBP. D.P. was supported in part by the Gordon and Betty Moore Foundation, by the NSF under Grant No. PHY-0456720, and by NSERC.
Subject Keywords:decoding; error correction codes; graph theory; many-body problems; quantum theory
Issue or Number:5
Record Number:CaltechAUTHORS:POUpra08
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:POUpra08
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:10556
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:17 May 2008
Last Modified:03 Oct 2019 00:10

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