{
  "abstract": "The dynamical Lie algebra (DLA) governs the controllability, expressibility, and simulation complexity of a quantum system. Explicitly computing it has been a major computational bottleneck: brute-force Lie closure scales exponentially in the number of qubits $n$. Many applications, however, consult only the isomorphism type of the DLA. We introduce PauLie, an open-source framework that decides this isomorphism type for DLAs generated by arbitrary Pauli strings, building on the anticommutation-graph reduction of Aguilar et al. PauLie runs in $O(n|\\mathcal{G}|\\max(n,|\\mathcal{G}|))$ time, where $|\\mathcal{G}|$ is the number of generators, turning DLA classification into a routine preprocessing step. We demonstrate its use as a structural oracle for routing Lie-algebraic simulation and Cartan decomposition, diagnosing barren plateaus in variational quantum algorithms, and engineering universal Pauli string generator sets with optimal generation rate.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30771",
  "author_total": 4,
  "authors": [
    {
      "name": "Oxana Shaya"
    },
    {
      "name": "Konstantin Golovkin"
    },
    {
      "name": "Mainak Roy"
    },
    {
      "name": "Vincent Russo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a27twg5xg8kta.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30771",
  "fulltext_url": null,
  "id": "a27twg5xg8kta",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30771",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7204912562",
  "pdf_url": "https://arxiv.org/pdf/2608.30771",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a27twg5xg8kta.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:41Z",
      "native_id": "2608.30771",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30771"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "PauLie: Fast Classification of Pauli Dynamical Lie Algebras",
  "title_text": "PauLie: Fast Classification of Pauli Dynamical Lie Algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:41Z",
  "url": "https://research.draconitic.com/paper/a27twg5xg8kta",
  "venue": "arXiv",
  "versions": []
}