Large-Language-Model Discovery of Quantum LDPC Codes through Structured Concept Evolution
Abstract
Quantum low-density parity-check codes promise low-overhead error correction, but high-performing constructions remain hard to find. Here we introduce structured concept evolution, in which a large language model (LLM) evolves construction programs and their internal search strategies by modifying the finite group, protograph shapes or entry-assignment rule. We search for codes with fewer than $600$ data qubits and check weight at most $12$, optimizing kd2/n or the circuit-level logical error rate. Our method improves on published lifted-product benchmarks in selected parameter regimes, with exactly certified distances for the leading results. Circuit-level optimization typically yields lower logical error rates than kd2/n optimization, often despite smaller code distances. With the same evolution framework and step budget, the best LLM outperforms all random-mutation and hill-climbing runs on both objectives. Our results point to LLM-driven program search as an approach to designing general quantum LDPC codes.
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BibTeX
@misc{liu2026largelanguagemodel,
title = {{Large-Language-Model Discovery of Quantum LDPC Codes through Structured Concept Evolution}},
author = {Zidu Liu and Florian Marquardt},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2606.24808},
eprint = {2606.24808},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.24808},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Large-Language-Model Discovery of Quantum LDPC Codes through Structured Concept Evolution
AU - Zidu Liu
AU - Florian Marquardt
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2606.24808
UR - https://arxiv.org/abs/2606.24808
AB - Quantum low-density parity-check codes promise low-overhead error correction, but high-performing constructions remain hard to find. Here we introduce structured concept evolution, in which a large language model (LLM) evolves construction programs and their internal search strategies by modifying the finite group, protograph shapes or entry-assignment rule. We search for codes with fewer than $600$ data qubits and check weight at most $12$, optimizing kd^2/n or the circuit-level logical error rate. Our method improves on published lifted-product benchmarks in selected parameter regimes, with exactly certified distances for the leading results. Circuit-level optimization typically yields lower logical error rates than kd^2/n optimization, often despite smaller code distances. With the same evolution framework and step budget, the best LLM outperforms all random-mutation and hill-climbing runs on both objectives. Our results point to LLM-driven program search as an approach to designing general quantum LDPC codes.
ER -