{
  "abstract": "Recent work has shown that quantum double models can be used to circumvent the Bravyi-Koenig bound. In particular, this is achieved through code-switching protocols in which non-Pauli stabilizer phases appear as intermediate codes. We introduce the $X\\mathcal C^{(k)}_d$ stabilizer formalism, which generalizes the Pauli stabilizer formalism by combining Pauli-$X$ operators with diagonal operators drawn from a fixed level $k$ of the Clifford hierarchy on prime-dimensional qudits. This yields a natural class of beyond-Pauli stabilizer models, including many twisted quantum double phases. We classify a large class of these $X\\mathcal C^{(k)}_d$ stabilizer states, showing that they are uniform superpositions over affine-linear subspaces with diagonal phases. In particular, when the stabilizers of a state require operators from level $k$ of the Clifford hierarchy, we show that the diagonal gates required to produce the phases in the wavefunction sit one level higher. We further show that every 2D twisted quantum double ${\\cal D}^ω(\\mathbb{Z}_p^n)$ with $ω$ a product of type-III cocycles and $p$ an odd prime admits a realization using only Clifford ($k=2$) stabilizers, and we conjecture that phases where $ω$ contains a type-I or type-II cocycle require level-$p$ Clifford-hierarchy stabilizers for $p$-dimensional qudits. Finally, we demonstrate that a pair of qudit toric codes may be deterministically prepared in a logical magic state by measuring $X\\mathcal C^{(k)}_d$ stabilizers. Together, these results provide a concrete stabilizer framework for topological codes beyond Pauli stabilizer models and their logical gates.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00464",
  "author_total": 7,
  "authors": [
    {
      "name": "Christopher Fechisin"
    },
    {
      "name": "Kieran Cooney"
    },
    {
      "name": "Mathi Raja"
    },
    {
      "name": "Victor V. Albert"
    },
    {
      "name": "Dominic J. Williamson"
    },
    {
      "name": "Kyle Kawagoe"
    },
    {
      "name": "Seth Musser"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/414z9a22t07dx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00464",
  "fulltext_url": null,
  "id": "414z9a22t07dx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00464",
  "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",
      "cond-mat.str-el"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7216470777",
  "pdf_url": "https://arxiv.org/pdf/2610.00464",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/414z9a22t07dx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:03Z",
      "native_id": "2610.00464",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00464"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Clifford-hierarchy stabilizer formalism with applications to twisted quantum doubles",
  "title_text": "Clifford-hierarchy stabilizer formalism with applications to twisted quantum doubles",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:03Z",
  "url": "https://research.draconitic.com/paper/414z9a22t07dx",
  "venue": "arXiv",
  "versions": []
}