Stable valleys in the glassy landscape of a low-density parity-check (LDPC) code

@misc{sommers2026stable,
  title = {{Stable valleys in the glassy landscape of a low-density parity-check (LDPC) code}},
  author = {Grace M. Sommers and David A. Huse},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2607.20421},
  eprint = {2607.20421},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.20421},
}

TY  - UNPB
TI  - Stable valleys in the glassy landscape of a low-density parity-check (LDPC) code
AU  - Grace M. Sommers
AU  - David A. Huse
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2607.20421
UR  - https://arxiv.org/abs/2607.20421
AB  - Classical low-density parity-check (cLDPC) codes defined on expander graphs are a fundamental ingredient in the construction of good quantum LDPC codes, a recent milestone in quantum error correction. They also define interesting statistical mechanics models in their own right, as they include examples of spin glass order without quenched randomness or frustration. We investigate this via a case study of a cLDPC code on a locally tree-like expander graph. Recursive techniques on trees, made possible by the locally tree-like property, probe a menagerie of stable, incongruent valleys induced by imposing different boundary conditions at low temperature. Analysis of stable and unstable fixed points within the cavity method, complemented by a numerical study of the valleys on closed finite graphs, reveals the inequivalence of the microcanonical and canonical ensemble for certain valleys.
ER  -