One-step replica symmetry breaking in the language of tensor networks

We develop an exact mapping between the one-step replica symmetry breaking cavity method and tensor networks. The two schemes come with complementary mathematical and numerical toolboxes that could be leveraged to improve the respective states of the art. As an example, we construct a tensor-network...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2023-06
Main Authors: Pancotti, Nicola, Gray, Johnnie
Format: Article
Language:English
Subjects:
Algorithms
Broken symmetry
Mathematical analysis
Networks
Solvers
Tensors
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We develop an exact mapping between the one-step replica symmetry breaking cavity method and tensor networks. The two schemes come with complementary mathematical and numerical toolboxes that could be leveraged to improve the respective states of the art. As an example, we construct a tensor-network representation of Survey Propagation, one of the best deterministic k-SAT solvers. The resulting algorithm outperforms any existent tensor-network solver by several orders of magnitude. We comment on the generality of these ideas, and we show how to extend them to the context of quantum tensor networks.
ISSN:2331-8422