{
  "abstract": "We investigate operator spreading in random quantum circuits with gates drawn from orthogonal-invariant or symplectic-invariant ensembles, revealing several key distinctions from the well-studied unitary-invariant case. We find that the ensemble-averaged Pauli-string weights relax to a ternary-valued structure, instead of the binary structure of unitary-invariant circuits. For orthogonal- or symplectic-invariant circuits, the domain wall separating trivial and scrambled regions has a finite width even for Haar-random gates, whereas domain walls are sharp for Haar-distributed random unitary circuits. We further find a fundamental dichotomy between random circuits with two-qubit gates from the two disconnected components of the orthogonal group: While the butterfly velocity for the special orthogonal ensemble lies between zero and the Haar value, the negative-determinant sector exhibits a non-zero lower bound for any gate distribution. Moreover, for qudit size $q=2$, the butterfly velocity can exceed that of the Haar-random ensemble.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Tan, Z., & Brouwer, P. W. (2026). Operator spreading in random unitary circuits with orthogonal/symplectic-invariant gate distributions. Physical Review B, 114(7), 074308",
  "arxiv": "2606.03956",
  "author_total": 2,
  "authors": [
    {
      "name": "Zhiyang Tan"
    },
    {
      "name": "Piet W. Brouwer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a6bxh62qhsdv7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.03956",
  "fulltext_url": null,
  "id": "a6bxh62qhsdv7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.03956",
  "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.stat-mech"
    ],
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      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2606.03956",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a6bxh62qhsdv7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:00Z",
      "native_id": "2606.03956",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.03956"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Operator spreading in random unitary circuits with orthogonal/symplectic-invariant gate distributions",
  "title_text": "Operator spreading in random unitary circuits with orthogonal/symplectic-invariant gate distributions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:00Z",
  "url": "https://research.draconitic.com/paper/a6bxh62qhsdv7",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1103/p5d4-dmj6",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}