{
  "abstract": "Fermionic quantum cellular automata (QCA) are automorphisms of local fermionic operator algebras ($\\mathbb Z_2$-graded superalgebras) that have bounded spread: they map local operators to nearby operators. We prove that every 2-dimensional fermionic QCA on a locally finite-dimensional algebra is a composition of local automorphisms and a fermionic shift. This is implied by our result that every locally finite-dimensional fermionic invertible subalgebra in a one-dimensional lattice is Brauer trivial, \\textit{i.e.}, it is stably bounded-spread isomorphic to a tensor product fermionic algebra.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09317",
  "author_total": 3,
  "authors": [
    {
      "name": "Jeffrey Kwan"
    },
    {
      "name": "David M. Long"
    },
    {
      "name": "Jeongwan Haah"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/371mrvktw02xc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09317",
  "fulltext_url": null,
  "id": "371mrvktw02xc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09317",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.str-el"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7212124824",
  "pdf_url": "https://arxiv.org/pdf/2609.09317",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/371mrvktw02xc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:12Z",
      "native_id": "2609.09317",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09317"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Fermionic quantum cellular automata in 2d are trivial",
  "title_text": "Fermionic quantum cellular automata in 2d are trivial",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/371mrvktw02xc",
  "venue": "arXiv",
  "versions": []
}