One-step replica symmetry breaking in the language of tensor networks
Abstract
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- June 2023
- DOI:
- 10.48550/arXiv.2306.15004
- arXiv:
- arXiv:2306.15004
- Bibcode:
- 2023arXiv230615004P
- Keywords:
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- Quantum Physics;
- Condensed Matter - Disordered Systems and Neural Networks;
- Condensed Matter - Statistical Mechanics;
- Computer Science - Computational Complexity;
- Physics - Computational Physics