# Evolutionary Discovery of Bivariate Bicycle Codes with LLM-Guided Search

arXiv: https://arxiv.org/abs/2606.02418 · HTML: https://mlsanity.com/paper/2606.02418/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 134 references that are in the map.
- First posted on arXiv 1 Jun 2026.

## Builds on (most cited first, 2 of 2)

- [Optimizing Quantum Error Correction Codes with Reinforcement Learning](https://mlsanity.com/paper/1812.08451/) (2018)
- [Discovery of Optimal Quantum Error Correcting Codes via Reinforcement Learning](https://mlsanity.com/paper/2305.06378/) (2023)

## Built on by (most cited first, 7 of 7)

- [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)
- [Dictionaries, Not Darwin: Set-Level Selection Beats LLM Evolution in Scientific Equation Discovery](https://mlsanity.com/paper/2607.04108/) (2026)
- [Symmetry and AI-assisted discovery of magic-state factories](https://mlsanity.com/paper/2610.06535/) (2026)
- [Large Language Model-Guided Discovery of Weight-Five Bivariate Bicycle Codes](https://mlsanity.com/paper/2610.06623/) (2026)
- [Distance Prediction for Quantum Codes](https://mlsanity.com/paper/2610.18130/) (2026)

## Abstract (arXiv)

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 ans"atze. Across five campaigns, the system performed approximately 1,650 evolutionary iterations, screened about 2 × 105 candidate codes, and required ~140 hours of computation and ~US400 in LLM inference cost. Candidate codes are evaluated through a staged validation pipeline combining 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 ≤ 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.