---
aliases:
  - '/publication/2026-bivariatebicyclecodesllm/'
title: "Evolutionary Discovery of Bivariate Bicycle Codes with LLM-Guided Search"
date: 2026-06-01
authors:
  - "Juan Cruz-Benito"
  - "Andrew W. Cross"
  - "David Kremer"
  - "Ismael Faro"
abstract: "Quantum LDPC code discovery requires searching large algebraic design spaces while reliably certifying the parameters and equivalence classes of any candidates found. We present a workflow that uses large language models to mutate Python programs generating quantum LDPC code designs—specifically bivariate-bicycle and perturbed bivariate-bicycle code ansätze—coupled with a rigorous independent validation pipeline (GF(2) rank computation, distance estimation, MILP, BLISS Tanner-graph deduplication, decomposability analysis, and local-Clifford equivalence checks). Across five campaigns running roughly 1,650 evolutionary iterations and screening approximately 2 × 10^5 candidate codes—requiring around 140 hours of computation and ~US$400 in LLM inference costs—the system identified 465 distinct candidate codes at block length n ≤ 360 (97 CSS bivariate-bicycle codes and 368 non-CSS perturbed variants). Notable finds include an indecomposable [[288,16,12]] code and higher-weight codes reaching k = 50 at distance d = 8, while non-CSS results included perturbed codes matching the gross-code benchmark at [[144,12,12]]. These results suggest that LLM-guided program evolution, combined with rigorous independent evaluation, can be a practical approach for structured quantum-code discovery."
publication_types:
  - "article"
selected: true
publication: "*arXiv preprint arXiv:2606.02418*"
tags:
  - "Quantum Computing"
  - "Quantum Error Correction"
  - "Quantum LDPC Codes"
  - "Bivariate Bicycle Codes"
  - "Large Language Models"
  - "Evolutionary Search"
  - "Artificial Intelligence"
links:
- type: pdf
  url: "https://arxiv.org/pdf/2606.02418"
- type: source
  url: "https://arxiv.org/abs/2606.02418"
hugoblox:
  ids:
    doi: "10.48550/arXiv.2606.02418"
---