# Large Language Model-Guided Discovery of Weight-Five Bivariate Bicycle Codes

arXiv: https://arxiv.org/abs/2610.06623 · HTML: https://mlsanity.com/paper/2610.06623/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 54 references that are in the map.
- First posted on arXiv 5 Oct 2026.

## Builds on (most cited first, 5 of 5)

- [Evolutionary Discovery of Bivariate Bicycle Codes with LLM-Guided Search](https://mlsanity.com/paper/2606.02418/) (2026)
- [Discovering highly efficient low-weight quantum error-correcting codes with reinforcement learning](https://mlsanity.com/paper/2502.14372/) (2025)
- [Large-Language-Model Discovery of Quantum LDPC Codes through Structured Concept Evolution](https://mlsanity.com/paper/2606.24808/) (2026)
- [OmniQEC: discovering practical quantum error-correcting codes by an AI scientist](https://mlsanity.com/paper/2607.25865/) (2026)
- [Multi-agent discovery of practical quantum LDPC codes](https://mlsanity.com/paper/2608.08996/) (2026)

## Abstract (arXiv)

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.