# Large-Language-Model Discovery of Quantum LDPC Codes through Structured Concept Evolution

arXiv: https://arxiv.org/abs/2606.24808 · HTML: https://mlsanity.com/paper/2606.24808/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 59 references that are in the map.
- First posted on arXiv 23 Jun 2026.

## Builds on (most cited first, 10 of 10)

- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Illuminating search spaces by mapping elites](https://mlsanity.com/paper/1504.04909/) (2015)
- [Quantum advantage in learning from experiments](https://mlsanity.com/paper/2112.00778/) (2021)
- [Provably efficient machine learning for quantum many-body problems](https://mlsanity.com/paper/2106.12627/) (2021)
- [Optimizing Quantum Error Correction Codes with Reinforcement Learning](https://mlsanity.com/paper/1812.08451/) (2018)
- [Meta-Designing Quantum Experiments with Language Models](https://mlsanity.com/paper/2406.02470/) (2024)
- [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)
- [Co-Designing Quantum Codes with Transversal Diagonal Gates via Multi-Agent Systems](https://mlsanity.com/paper/2510.20728/) (2025)

## Built on by (most cited first, 4 of 4)

- [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)
- [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)

## Abstract (arXiv)

Quantum computers could outperform classical machines on important problems, but only if the errors that pervade quantum hardware can be corrected at scale. Quantum low-density parity-check (qLDPC) codes offer a promising route to this goal by combining sparse parity checks with finite encoding rate and growing distance, but their construction remains a challenging discrete design problem. Here we introduce structured concept evolution (SCE), a search framework that pairs a large language model with a structured algebraic mutation grammar to discover lifted-product code families, a class of CSS qLDPC codes. Instead of asking the LLM to design codes from first principles, SCE evolves structured concepts consisting of algebraic specifications paired with executable programs that realize them, using hierarchical mutations that modify the group algebra, protograph geometry, or base space. Running SCE, we discover a diverse set of competitive code families, ranging from abelian constructions to families over non-abelian groups beyond those underlying standard designs such as bivariate-bicycle codes, and characterize them under code-capacity depolarizing noise with BP+OSD decoding. These results are obtained with lightweight models (GPT-5.4-mini and GPT-5.4-nano).