{
  "abstract": "Quantum LDPC codes promise to reduce the overhead of fault-tolerant quantum computation, but their practical use requires efficient logical gates, measurements, and access to non-Clifford resources. Here, we develop a complete set of computational primitives for La-cross hypergraph product codes. For a subclass of these codes, we show that seed automorphisms together with fold-transversal gates generate the full logical Clifford group up to Pauli corrections. We further prove that every rank one logical operator admits $D$ pairwise disjoint physical representatives, enabling parallel gauging and a space--time tradeoff for logical measurements. Finally, we construct an addressable surface code interface for injecting externally prepared resource states into selected logical qubits. Together, these results establish La-cross codes as a simple, low-connectivity generalisation of surface code computation, retaining analogous computational primitives while providing a complete Clifford+$T$ instruction set across multiple encoded qubits.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12685",
  "author_total": 5,
  "authors": [
    {
      "name": "Andrea Di Fini"
    },
    {
      "name": "Tom Hartweg"
    },
    {
      "name": "Laura Pecorari"
    },
    {
      "name": "Guido Pupillo"
    },
    {
      "name": "Samuel Crew"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/18mnv6jcr3mjc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12685",
  "fulltext_url": null,
  "id": "18mnv6jcr3mjc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12685",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7221553869",
  "pdf_url": "https://arxiv.org/pdf/2610.12685",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/18mnv6jcr3mjc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:36Z",
      "native_id": "2610.12685",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12685"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Fast computational primitives for La-cross qLDPC codes",
  "title_text": "Fast computational primitives for La-cross qLDPC codes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:36Z",
  "url": "https://research.draconitic.com/paper/18mnv6jcr3mjc",
  "venue": "arXiv",
  "versions": []
}