{
  "abstract": "We study the operator entanglement of local operators in one-dimensional brickwork circuits whose two-site gate satisfies the braid relation; throughout this work, we call such a gate a Yang--Baxter gate. We establish upper bounds for several structured, overlapping classes of Yang--Baxter gates. We show that the operator Schmidt rank remains uniformly bounded in time for all qubit Yang--Baxter gates and, in arbitrary local dimension, for permutation gates obtained from non-degenerate Yang--Baxter maps. We also show that it grows at most polynomially for involutive dual-unitary Yang--Baxter gates and for arbitrary phase dressings of permutation gates obtained from non-degenerate Yang--Baxter maps. These results imply, respectively, constant and logarithmic upper bounds on the operator entanglement. Conversely, we construct a seven-state involutive Yang--Baxter gate without dual unitarity and a one-site operator whose exact operator Schmidt rank grows exponentially, although the corresponding operator entropies remain undetermined. Entanglement growth in the general Yang--Baxter case remains open. All proofs and selected examples were constructed by ChatGPT 5.6 Sol.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05121",
  "author_total": 1,
  "authors": [
    {
      "name": "Balázs Pozsgay"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fx92f97c41xww.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05121",
  "fulltext_url": null,
  "id": "fx92f97c41xww",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05121",
  "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",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "nlin.SI"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7208731938",
  "pdf_url": "https://arxiv.org/pdf/2609.05121",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fx92f97c41xww.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:03Z",
      "native_id": "2609.05121",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05121"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "On the growth of operator entanglement in brickwork circuits with Yang--Baxter gates",
  "title_text": "On the growth of operator entanglement in brickwork circuits with Yang--Baxter gates",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:03Z",
  "url": "https://research.draconitic.com/paper/fx92f97c41xww",
  "venue": "arXiv",
  "versions": []
}