{
  "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 $kd^2/n$ 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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.24808",
  "author_total": 2,
  "authors": [
    {
      "name": "Zidu Liu"
    },
    {
      "name": "Florian Marquardt"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6jf2raq2h0z1g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.24808",
  "fulltext_url": null,
  "id": "6jf2raq2h0z1g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.24808",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.AI"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7165756829",
  "pdf_url": "https://arxiv.org/pdf/2606.24808",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6jf2raq2h0z1g.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:20:55Z",
      "native_id": "2606.24808",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.24808"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Large-Language-Model Discovery of Quantum LDPC Codes through Structured Concept Evolution",
  "title_text": "Large-Language-Model Discovery of Quantum LDPC Codes through Structured Concept Evolution",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:10Z",
  "url": "https://research.draconitic.com/paper/6jf2raq2h0z1g",
  "venue": "arXiv",
  "versions": []
}