{
  "abstract": "Recent work by Wills constructed codes with constant rate and transversal $T$. Extending this line of work, we construct asymptotically good CSS codes with \\textbf{fully addressable} transversal $T$, permitting selective control over which logical qubits receive a $T$ gate. We also give Pauli-LDPC codes with transversal $T$ and growing distance at vanishing rate; and a protected-subsystem construction with fully addressable transversal $T$, constant protected rate, distance $Ω(\\sqrt n)$, and sparse (non-Pauli) checks. More generally, we obtain asymptotically good binary codes with full transversal addressability for every fixed finite-order one-qubit gate, retaining CSS realizations for dyadic phase gates such as $\\sqrt T$ and using generally nonadditive codes for rotations such as $R_z(π/7)$. The remaining challenge is to construct asymptotically good Pauli-LDPC codes with fully addressable transversal non-Clifford one-qubit gates.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.38996",
  "author_total": 1,
  "authors": [
    {
      "name": "Alexander Meiburg"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0z2b41t67vnad.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.38996",
  "fulltext_url": null,
  "id": "0z2b41t67vnad",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.38996",
  "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": "W7215036482",
  "pdf_url": "https://arxiv.org/pdf/2609.38996",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0z2b41t67vnad.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.38996",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.38996"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Constant Rate Codes with Fully Addressable Transversal T: Good Codes, Sparse Checks",
  "title_text": "Constant Rate Codes with Fully Addressable Transversal T: Good Codes, Sparse Checks",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/0z2b41t67vnad",
  "venue": "arXiv",
  "versions": []
}