{
  "abstract": "We show that every intermediate state of a broad class of non-Clifford quantum error-correction circuits is a third-order phase-polynomial state, even under stochastic Pauli noise. The class includes magic state distillation and cultivation, code switching and gauge fixing, transversal non-Clifford gates with syndrome extraction, and injection of diagonal magic states. Third-order phase-polynomial states strictly generalize stabilizer states, and we prove that they are exactly the stabilizer states of the diagonal-Clifford-and-Pauli (DCP) stabilizer formalism that we introduce. We characterize these states and show that their representations can be updated in polynomial time. This yields an exact polynomial-time simulation algorithm for these circuits and, more broadly, a framework for reasoning about their internal states and about magic states in general. We provide an open-source implementation, \\texttt{merlin}, and benchmark it against existing non-Clifford simulators on distillation, cultivation, and code switching circuits. The benchmarks demonstrate improved runtime and memory scaling as the number of logical outputs grows in Bravyi-Haah distillation, and simulation of a code switching circuit beyond the reach of all other tested simulators.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06811",
  "author_total": 3,
  "authors": [
    {
      "name": "Serban Cercelescu"
    },
    {
      "name": "Mark Koch"
    },
    {
      "name": "Arthur Pesah"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9gxfcjwf2psfa.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06811",
  "fulltext_url": null,
  "id": "9gxfcjwf2psfa",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06811",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7220718867",
  "pdf_url": "https://arxiv.org/pdf/2610.06811",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9gxfcjwf2psfa.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:05Z",
      "native_id": "2610.06811",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06811"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Polynomial-time simulation of non-Clifford quantum error correction",
  "title_text": "Polynomial-time simulation of non-Clifford quantum error correction",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:05Z",
  "url": "https://research.draconitic.com/paper/9gxfcjwf2psfa",
  "venue": "arXiv",
  "versions": []
}