{
  "abstract": "Low-space-overhead fault-tolerant quantum computation requires not only high-rate quantum error-correcting codes but also space-efficient implementations of logical operations. Transversal and fold-transversal gates are promising since they limit error propagation and require no additional qubits. However, the logical operations they enable are typically restricted, and a central challenge is to construct codes that combine a complete set of logical Clifford gates with favorable code parameters. In this work, we introduce a family of quantum codes with an asymptotically constant encoding rate and sublogarithmically growing stabilizer weight, while supporting the entire logical Clifford group using only transversal and fold-transversal gates. Our construction is based on classical codes whose code spaces are absolutely irreducible Steinberg modules of their Tanner-graph automorphism groups. Taking hypergraph products of these classical codes yields quantum codes for which all logical Clifford operations can be synthesized from a fixed set of transversal and fold-transversal gates. Moreover, the slow growth of the stabilizer weight enables a high error-correcting performance in small instances. These results provide a path toward fault-tolerant quantum computation with low space overhead using transversal and fold-transversal gates.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37699",
  "author_total": 4,
  "authors": [
    {
      "name": "Takaya Matsuura"
    },
    {
      "name": "Yohji Chin"
    },
    {
      "name": "Shohei Kiryu"
    },
    {
      "name": "Kosuke Fukui"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/erpt7tsy5w16y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37699",
  "fulltext_url": null,
  "id": "erpt7tsy5w16y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37699",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7214972003",
  "pdf_url": "https://arxiv.org/pdf/2609.37699",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/erpt7tsy5w16y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:31Z",
      "native_id": "2609.37699",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37699"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Constant-rate quantum codes with low-weight stabilizers and full logical Clifford actions via transversal and fold-transversal gates",
  "title_text": "Constant-rate quantum codes with low-weight stabilizers and full logical Clifford actions via transversal and fold-transversal gates",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:31Z",
  "url": "https://research.draconitic.com/paper/erpt7tsy5w16y",
  "venue": "arXiv",
  "versions": []
}