Evolutionary Discovery of Bivariate Bicycle Codes with LLM-Guided Search

2026-06-01

AI Summary

This work addresses the challenge of efficiently discovering high-performance quantum low-density parity-check (LDPC) codes within vast algebraic spaces by introducing a novel approach that integrates large language model–guided program evolution with rigorous mathematical verification. The method evolves Python programs generating bivariate bicycle codes and their perturbed variants, coupled with a multi-stage validation pipeline incorporating GF(2) rank computation, distance certification, mixed-integer linear programming, Tanner graph deduplication, and local Clifford equivalence detection to enable automated discovery of structured quantum codes. Within block lengths up to 360, the framework identifies 465 new codes, including 97 indecomposable CSS codes—such as [[288,16,12]]—and 368 high-performance non-CSS perturbed codes like [[144,12,12]], several of which represent novel high-dimension, high-distance constructions.

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.

Problem

• quantum LDPC codes
• bivariate bicycle codes
• code discovery
• equivalence classes
• parameter certification

Innovation

• LLM-guided evolution
• quantum LDPC codes
• bivariate bicycle codes
• code discovery
• program mutation