Large-Language-Model Discovery of Quantum LDPC Codes through Structured Concept Evolution
2026-06-23 • Artificial Intelligence
Artificial Intelligence
AI summaryⓘ
The authors developed a new method called structured concept evolution (SCE) that uses a large language model combined with algebraic rules to find better quantum error-correcting codes called quantum low-density parity-check (qLDPC) codes. Instead of creating codes from scratch, their approach evolves algebraic structures and programs that define the codes. Using this method, they discovered various competitive code families, including ones based on different mathematical groups, and tested how well these codes handle noise. Their work demonstrates a novel way to design complex quantum codes with relatively small AI models.
quantum error correctionqLDPC codesCSS codeslarge language modelstructured concept evolutionalgebraic mutation grammarlifted-product codesbivariate-bicycle codesdepolarizing noiseBP+OSD decoding
Authors
Zidu Liu, Florian Marquardt
Abstract
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).