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Journal Club for Condensed Matter Physics

Classical and quantum glasses based on expanders

MPI-PKS Dresden, Roderich Moessner

Published Aug 31, 2025• 0 citations
Publisher

Abstract

1. Topological Quantum Spin Glass Order and its realization in qLDPC codes Authors: Benedikt Placke, Tibor Rakovszky, Nikolas P. Breuckmann, and Vedika Khemani arxiv:2412.13248, DOI: 10.48550/arXiv.2412.13248 2. Expansion creates spin-glass order in finite-connectivity models: a rigorous and intuitive approach from the theory of LDPC codes Authors: Benedikt Placke, Grace M. Sommers, Nikolas P. Breuckmann, Tibor […]

DOI
10.36471/jccm_august_2025_01

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  1. Topological Quantum Spin Glass Order and its realization in qLDPC codes Authors: Benedikt Placke, Tibor Rakovszky, Nikolas P. Breuckmann, and Vedika Khemani arxiv:2412.13248, DOI: 10.48550/arXiv.2412.13248 2. Expansion creates spin-glass order in finite-connectivity models: a rigorous and intuitive approach from the theory of LDPC codes Authors: Benedikt Placke, Grace M. Sommers, Nikolas P. Breuckmann, Tibor […]
Ordered phases of matter have close connections to computation. Two prominent examples are spin glass order, with wide-ranging applications in machine learning and optimization, and topological order, closely related to quantum error correction. Here, we introduce the concept of topological quantum spin glass (TQSG) order which marries these two notions, exhibiting both the complex energy landscapes of spin glasses, and the quantum memory and long-range entanglement characteristic of topologically ordered systems. Using techniques from coding theory and a quantum generalization of Gibbs state decompositions, we show that TQSG order is the low-temperature phase of various quantum LDPC codes on expander graphs, including hypergraph and balanced product codes. Our work introduces a topological analog of spin glasses that preserves quantum information, opening new avenues for both statistical mechanics and quantum computer science.