{
  "abstract": "Quantum cellular automata (QCAs) describe locality-preserving quantum dynamics and link quantum information, many-body physics, and topological quantum field theory (TQFT). Constructing a QCA from a TQFT, however, remains challenging: although a topological action yields a Hamiltonian with commuting terms that realizes the desired ground state, it does not by itself specify an automorphism of the full operator algebra. We develop a unified algebraic construction that extends such Hamiltonians to complete separator-flipper algebras on the full tensor-product Hilbert space, thereby defining the corresponding QCAs microscopically. In 3 spatial dimensions, our framework unifies all previously known QCA constructions associated with the $\\mathbb{Z}_8\\times\\mathbb{Z}_2$ subgroup of the Witt group, including the $U(1)_2$ and $U(1)_4$ QCAs. The same algebraic structure yields new infinite families of generalized $U(1)_2$ and $U(1)_4$ non-Clifford QCAs in spatial dimensions $d=4k-1$. We also reformulate the 4-dimensional $w_2w_3$ QCA and use it to construct QCAs from TQFTs associated with arbitrary products of Stiefel--Whitney classes. For example, we explicitly construct two infinite families: $w_2^nw_3^m$ QCAs in dimension $d=2n+3m-1$ and $w_2w_{4k-1}$ QCAs in dimension $d=4k$. For the 5-dimensional $w_3^2$ and $w_2^3$ QCAs, our construction gives finite-depth quantum circuits, consistent with the cobordism classification. More generally, we show that our construction yields a finite-depth quantum circuit whenever the corresponding Stiefel-Whitney number vanishes on every closed oriented manifold. Overall, these results convert invertible TQFTs into microscopic QCAs, provide higher-dimensional constructions beyond the Clifford setting, and open a systematic route to characterizing their stable structures and boundary anomalies.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.21697",
  "author_total": 5,
  "authors": [
    {
      "name": "Meng Sun"
    },
    {
      "name": "Zongyuan Wang"
    },
    {
      "name": "Bowen Yang"
    },
    {
      "name": "Nathanan Tantivasadakarn"
    },
    {
      "name": "Yu-An Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9nshf2khbk56y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.21697",
  "fulltext_url": null,
  "id": "9nshf2khbk56y",
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  "landing_url": "https://arxiv.org/abs/2607.21697",
  "language": null,
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  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.str-el"
    ],
    [
      "arxiv",
      "hep-th"
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    [
      "arxiv",
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    [
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      "math.QA"
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      "quant-ph"
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    [
      "openalex",
      "3107|Quantum many-body systems"
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  "openalex": "W7171473860",
  "pdf_url": "https://arxiv.org/pdf/2607.21697",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9nshf2khbk56y.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:15Z",
      "native_id": "2607.21697",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.21697"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Non-Clifford quantum cellular automata from invertible topological quantum field theories",
  "title_text": "Non-Clifford quantum cellular automata from invertible topological quantum field theories",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:51Z",
  "url": "https://research.draconitic.com/paper/9nshf2khbk56y",
  "venue": "arXiv",
  "versions": []
}