Evolutionary Discovery of Bivariate Bicycle Codes with LLM-Guided Search

• URL: http://arxiv.org/abs/2606.02418v1
• Date: Mon, 01 Jun 2026 15:58:52 GMT
• Title: Evolutionary Discovery of Bivariate Bicycle Codes with LLM-Guided Search
• Abstract summary: Quantum LDPC code discovery requires searching large algebraic design spaces while reliably certifying the parameters and equivalence classes of any candidates found.<n>We introduce an LLM-guided evolutionary workflow in which language models mutate Python programs.<n>Across five campaigns, the system performed approximately 1,650 evolutionary iterations, screened about $2 times 105$ candidate codes, and required $sim140$ hours of computation and $sim$US$400 in LLM inference cost.
• Score: 1.1038052779321077
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum LDPC code discovery requires searching large algebraic design spaces while reliably certifying the parameters and equivalence classes of any candidates found. We introduce an LLM-guided evolutionary workflow in which language models mutate Python programs that generate bivariate-bicycle and perturbed bivariate-bicycle code ansätze. Across five campaigns, the system performed approximately 1{,}650 evolutionary iterations, screened about $2 \times 10^5$ candidate codes, and required ${\sim}140$ hours of computation and ${\sim}$US\$400 in LLM inference cost. Candidate codes are evaluated through a staged validation pipeline combining $\mathrm{GF}(2)$ rank computation, distance estimation and certification, mixed-integer linear programming, BLISS Tanner-graph deduplication, decomposability analysis, and local-Clifford equivalence checks. At block length $n \leq 360$, the workflow identifies 465 distinct candidate codes: 97 CSS bivariate-bicycle codes and 368 non-CSS perturbed variants. The CSS search recovers known high-performing codes and finds new finite-length representatives, including an indecomposable [[288,16,12]] code and higher-weight codes with up to $k = 50$ at distance $d = 8$. The non-CSS search produces perturbed codes matching the gross-code figure of merit at [[144,12,12]], along with additional high-distance candidates reported as certified values or upper bounds according to MILP status. Overall, these results show that LLM-guided program evolution can serve as a practical tool for structured quantum-code discovery when paired with independent evaluation.

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