---
title: "Large Language Model-Guided Discovery of Weight-Five Bivariate Bicycle Codes"
date: 2026-10-05
authors:
  - "Juan Cruz-Benito"
abstract: "Building on our earlier program-evolution workflow guided by large language models (LLMs), we study weight-five bivariate bicycle (BB) and perturbed bivariate bicycle (PBB) codes. The resulting catalogue contains 1,142 distinct code proposals, including 1,081 nonbaseline proposals attributable to LLM-generated programs. Across the catalogue, we certify connected Calderbank–Shor–Steane (CSS) realizations [[96,4,10]], [[140,6,10]], and [[180,4,14]]. A post-search comparison certifies seven imported Lin–Pryadko archive constructions. For leading parameter triples also represented in that archive, we provide exact distance evidence, explicit bivariate presentations, and verified component reductions. A basis-independent connectivity analysis identifies 409 of the 1,142 catalogue entries as disconnected and shows that 73.1% of the classes with exact distance certificates contain repeated connected components. Algebraic analysis organizes the connected CSS classes into order-3, order-7, and order-15 cyclotomic-kernel strata. The strongest exact connected PBB parameter point is [[216,4,10]], attained by two distinct component classes. Among the 936 distinct CSS proposals from the LLM-guided campaign with a recorded positive distance, 816 (87.18%) are certified at d ≥ 5. For comparison, three random-search controls each sample 6,444 CSS code proposals uniformly without replacement, using the same per-lattice and encoded-dimension sample counts as the LLM-guided campaign. In these controls, 4,672–4,785 proposals (72.50–74.26%) meet the same criterion. The LLM-guided campaign has the higher certified yield, while the random controls cover more connected classes. Together, these results extend LLM-guided discovery to a more constrained code family and provide a reproducible structural and exact-distance account of its strongest candidates."
publication_types:
  - "article"
selected: true
publication: "*arXiv preprint arXiv:2610.06623*"
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/2610.06623"
- type: source
  url: "https://arxiv.org/abs/2610.06623"
hugoblox:
  ids:
    doi: "10.48550/arXiv.2610.06623"
---