{
  "abstract": "Fault-tolerant quantum computation requires robust protection of encoded quantum information. In this work, we develop a representation-theoretic framework for constructing protected logical qudits in finite-group Kitaev quantum double models. By introducing $\\varepsilon$-stable irreducible representations, we establish a necessary and sufficient existence criterion and derive ribbon--projector commutation relations that yield a $d$-dimensional protected logical subspace. We apply this construction to symmetric and alternating groups, obtaining logical qubits for $S_n$ ($n\\ge 3$) and a logical qutrit for $A_4$. Moreover, the family $(\\mathbb Z_2)^d\\rtimes\\mathbb Z_d$ realizes protected logical qudits of arbitrary dimension $d\\ge 2$. Finally, for $D(A_4)$, we describe a scheme for universal logical qutrit computation using ribbon-based logical operations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.31011",
  "author_total": 2,
  "authors": [
    {
      "name": "Naihong Hu"
    },
    {
      "name": "Futao Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1f5mrzheyxnkn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.31011",
  "fulltext_url": null,
  "id": "1f5mrzheyxnkn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.31011",
  "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",
      "math.RT"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7204947222",
  "pdf_url": "https://arxiv.org/pdf/2608.31011",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1f5mrzheyxnkn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:41Z",
      "native_id": "2608.31011",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.31011"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Protected Logical Qudits in Kitaev Quantum Double Models via Stable Representations",
  "title_text": "Protected Logical Qudits in Kitaev Quantum Double Models via Stable Representations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/1f5mrzheyxnkn",
  "venue": "arXiv",
  "versions": []
}