{
  "abstract": "Reliable quantum computation requires methods for verifying quantum circuits. Level-synchronized tree automata (LSTAs) were recently introduced to represent sets of quantum states for this purpose. We study LSTAs along two axes relevant to verification: the complexity of their decision problems and the size of their representations under circuit operations. We prove that acyclic LSTAs have NP-complete nonemptiness and $Π_2^P$-complete language inclusion, and that general language inclusion is EXPSPACE-complete. We further prove inherent quadratic representation growth under individual quantum gates in a fixed qubit order, and give an adjacent-qubit reordering construction that preserves level synchronization. These results clarify the scope of applicability of the automata-theoretic toolbox for quantum circuit verification.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25138",
  "author_total": 4,
  "authors": [
    {
      "name": "Michael Blondin"
    },
    {
      "name": "Samy Chady Khoumsi-Kasmi"
    },
    {
      "name": "Guillermo A. Pérez"
    },
    {
      "name": "Marnix Suilen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a3ch2j9h3b90f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25138",
  "fulltext_url": null,
  "id": "a3ch2j9h3b90f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.25138",
  "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",
      "cs.FL"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1703|semigroups and automata theory"
    ]
  ],
  "openalex": "W7223053812",
  "pdf_url": "https://arxiv.org/pdf/2610.25138",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a3ch2j9h3b90f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:52Z",
      "native_id": "2610.25138",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25138"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "On the Complexity of Level-Synchronized Tree Automata for Quantum Circuit Verification",
  "title_text": "On the Complexity of Level-Synchronized Tree Automata for Quantum Circuit Verification",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:41Z",
  "url": "https://research.draconitic.com/paper/a3ch2j9h3b90f",
  "venue": "arXiv",
  "versions": []
}