+++
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"]
publication_types = ["3"]
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."
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"]
url_source = "https://arxiv.org/abs/2606.02418"
url_pdf = "https://arxiv.org/pdf/2606.02418"
doi = "10.48550/arXiv.2606.02418"
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