Title: LLM-Driven Evolutionary Search Uncovers Novel Bivariate Bicycle Quantum Codes

Discovering quantum Low-Density Parity-Check (LDPC) codes involves navigating vast algebraic design spaces while rigorously verifying the parameters and equivalence classes of potential candidates. To address this challenge, we present an evolutionary framework guided by Large Language Models (LLMs). In this workflow, language models act as agents that mutate Python scripts designed to generate ansätze for both bivariate-bicycle codes and their perturbed variants.

The system underwent five distinct search campaigns, executing approximately 1,650 evolutionary iterations. During this process, it evaluated roughly $2 \times 10^5$ candidate codes, consuming approximately 140 hours of computational time and incurring about US$400 in LLM inference costs. To ensure reliability, candidates underwent a multi-stage validation pipeline. This rigorous assessment included calculating ranks over $\mathrm{GF}(2)$, estimating and certifying code distance, employing mixed-integer linear programming (MILP), deduplicating Tanner graphs using BLISS, analyzing decomposability, and checking for local-Clifford equivalence.

For block lengths of $n \leq 360$, the workflow successfully identified 465 unique candidate codes. These comprised 97 CSS bivariate-bicycle codes and 368 non-CSS perturbed variants. The search within the CSS category not only recovered previously known high-performing codes but also uncovered new finite-length representatives. Notable findings include an indecomposable [[288,16,12]] code and codes with higher weights, achieving up to $k = 50$ at a distance of $d = 8$.

Simultaneously, the non-CSS search yielded perturbed codes that matched the gross-code figure of merit for [[144,12,12]]. It also produced additional high-distance candidates, with their status reported as either certified values or upper bounds based on MILP outcomes. Collectively, these findings demonstrate that LLM-guided program evolution, when coupled with independent evaluation methods, serves as a viable and practical approach for the structured discovery of quantum codes.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC