用大模型发现新型量子纠错码，突破传统设计限制
Large-Language-Model Discovery of Quantum LDPC Codes through Structured Concept Evolution
- 结合大模型与代数变异语法，分层演化代码构造概念
- 发现多类高性能量子低密度奇偶校验码，含非阿贝尔构造
- 仅用轻量级模型即可探索复杂编码结构，适合量子算法研究者
量子计算机要在关键问题上超越经典机器，必须能规模化纠正量子硬件中的错误。量子低密度奇偶校验（qLDPC）码通过稀疏奇偶校验、有限编码率和增长距离，为这一目标提供了有前景的路径，但其构造仍是困难的离散设计问题。本文提出结构化概念演化（SCE），将大语言模型与结构化的代数变异语法规则结合，用于发现提升积码族——一类CSS型qLDPC码。SCE不直接要求大模型从头设计代码，而是通过层级变异演化由代数规范与可执行程序组成的结构化概念，修改群代数、原型图几何或基空间。运行SCE后，我们发现了多样且性能优异的码族，涵盖阿贝尔构造及超出标准设计（如双变量自行车码）的非阿贝尔群构造，并在码容量去极化噪声下以BP+OSD解码进行表征。所有结果均基于轻量级模型（GPT-5.4-mini 和 GPT-5.4-nano）完成。
原文摘要 · Abstract (English)
Quantum computers could outperform classical machines on important problems, but only if the errors that pervade quantum hardware can be corrected at scale. Quantum low-density parity-check (qLDPC) codes offer a promising route to this goal by combining sparse parity checks with finite encoding rate and growing distance, but their construction remains a challenging discrete design problem. Here we introduce structured concept evolution (SCE), a search framework that pairs a large language model with a structured algebraic mutation grammar to discover lifted-product code families, a class of CSS qLDPC codes. Instead of asking the LLM to design codes from first principles, SCE evolves structured concepts consisting of algebraic specifications paired with executable programs that realize them, using hierarchical mutations that modify the group algebra, protograph geometry, or base space. Running SCE, we discover a diverse set of competitive code families, ranging from abelian constructions to families over non-abelian groups beyond those underlying standard designs such as bivariate-bicycle codes, and characterize them under code-capacity depolarizing noise with BP+OSD decoding. These results are obtained with lightweight models (GPT-5.4-mini and GPT-5.4-nano).
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。