Approximate maximum-likelihood decoding via truncated free energies
Yuanqi Liu, Weilei Zeng, Junjie Wu, Lingling Lao · 2026 · arXiv
| 编号 QE278 | 主题 译码算法 | 链接 arXiv:2609.03928 |
摘要
摘要保留原文（英文）
摘要取自 arXiv / 出版方元数据，未作翻译，以保证与原文一致。
Maximum-likelihood decoding (MLD) achieves the minimum logical error rate of stabilizer codes under known i.i.d. Pauli noise, but its exact evaluation is #P-hard. Practical pipelines therefore approximate MLD by minimum-weight decoding (MWD), retaining only the lowest-weight recovery per syndrome and discarding the coset degeneracy. The minimum-weight search is in turn implemented by stochastic solvers. We introduce approximate maximum-likelihood decoding (AMLD), a black-box framework that recycles the candidate samples discarded by stochastic inner decoders into a per-class truncated free-energy estimator. For every logical class represented in the candidate pool, the estimator is provably bounded below by the exact free energy and above by the empirical minimum weight. AMLD returns the logical class minimizing the estimated free energy with linear classical overhead. In SA-based Ising-decoder benchmarks, AMLD closes up to of the MWD—MLD threshold gap across the toric and color codes under bit-flip and depolarizing noise. The largest threshold improvement, from to , occurs on the color code under depolarizing noise. We further demonstrate AMLD on the bivariate-bicycle code, whose bit-flip decoding problem has a hypergraph structure. This application requires neither matching-based enumeration nor code-specific tensor-network contraction. At , AMLD reduces the logical error rate by relative to MWD evaluated on the same BP-OSD candidate pool.
本站词条在引用该文献时，会以 wikilink（sources/QE278）链接到本页；右侧「反向链接」面板自动列出所有引用它的词条。