Large-Language-Model Discovery of Quantum LDPC Codes through Structured Concept Evolution

The paper presents a novel search framework called structured concept evolution (SCE) that utilizes large language models (LLMs) to discover quantum low-density parity-check (qLDPC) codes, specifically lifted-product code families. By employing a structured algebraic mutation grammar, SCE evolves algebraic specifications and executable programs, leading to the identification of competitive code families, including those over non-abelian groups, characterized under code-capacity depolarizing noise using BP+OSD decoding. This approach highlights the potential of LLMs in tackling complex design problems in quantum error correction, offering practitioners new methodologies for code development in quantum computing.