{
  "abstract": "The Clifford hierarchy is a nested sequence of sets of quantum gates that can be fault-tolerantly performed using gate teleportation within standard quantum error correction schemes. The importance of these gates has motivated numerous studies of their structure. Zeng-Chen-Chuang conjectured in 2007 that all hierarchy gates are generalised semi-Clifford, i.e. take the form $C_1 ΠD C_2$ for Clifford gates $C_1, C_2$, a permutation gate $Π$, and a diagonal gate $D$; Beigi-Shor proved in 2008 that this holds for all third-level gates. We construct a five-qubit gate that is in the fifth level of the Clifford hierarchy but is not generalised semi-Clifford. Rather than simply present and verify our counterexample to the generalised semi-Clifford conjecture, we show how its form can be deduced. Our counterexample also demonstrates that the Clifford hierarchy is not closed under inverses.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11903",
  "author_total": 2,
  "authors": [
    {
      "name": "Nadish de Silva"
    },
    {
      "name": "Oscar Lautsch"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/421kkecq22kwz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11903",
  "fulltext_url": null,
  "id": "421kkecq22kwz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11903",
  "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",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.QA"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7212281728",
  "pdf_url": "https://arxiv.org/pdf/2609.11903",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/421kkecq22kwz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:26Z",
      "native_id": "2609.11903",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11903"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "The generalised semi-Clifford conjecture is false",
  "title_text": "The generalised semi-Clifford conjecture is false",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/421kkecq22kwz",
  "venue": "arXiv",
  "versions": []
}