{
  "abstract": "Quantum advantage is widely understood to rely on key quantum resources beyond entanglement, among which nonstabilizerness (quantum “magic”) plays a central role in enabling universal quantum computation. However, the deterministic evaluation of the second-order stabilizer Rényi entropy for generic many-body quantum states remains computationally challenging, with brute-force methods scaling as O ( 8 N ) = O ( d 3 ) for an N -qubit state with d = 2 N . Here, we develop an exact algebraic reformulation and a deterministic numerical algorithm, numerically exact up to floating-point roundoff, that reduces this cost to O ( N 4 N ) = O ( d 2 log 2 d ) while retaining natural parallelism. This is an exponential speedup, although the scaling remains exponential in the number of qubits. This advance enables high-precision calculations for generic state vectors at medium system sizes and provides a practical tool for investigating the scaling and nonequilibrium dynamics of quantum magic in many-body systems.",
  "abstract_shown": true,
  "affiliations": [
    "Shanghai University",
    "National University of Singapore"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 4,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Xuyang Huang"
    },
    {
      "affs": [
        0,
        1
      ],
      "name": "Han-Ze Li",
      "orcid": "0009-0006-0105-5216"
    },
    {
      "affs": [
        1
      ],
      "name": "Ching Hua Lee"
    },
    {
      "affs": [
        0
      ],
      "name": "Jian-Xin Zhong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5915c5e8s00mh.bib",
  "cited_by": 0,
  "doi": "10.1103/f7ss-6tl1",
  "fulltext_url": null,
  "id": "5915c5e8s00mh",
  "issns": [
    "2643-1564"
  ],
  "landing_url": "https://link.aps.org/doi/10.1103/f7ss-6tl1",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7117980241",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": "American Physical Society (APS)",
  "ris": "https://research.draconitic.com/paper/5915c5e8s00mh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:55Z",
      "native_id": "10.1103/f7ss-6tl1",
      "source": "crossref",
      "url": "https://link.aps.org/doi/10.1103/f7ss-6tl1"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "journal-openalex:3107|Quantum many-body systems",
      "subfield": "amo"
    }
  ],
  "title": "Fast and exact approach for stabilizer Rényi entropy via the XOR-FWHT algorithm",
  "title_text": "Fast and exact approach for stabilizer Rényi entropy via the XOR-FWHT algorithm",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:17:55Z",
  "url": "https://research.draconitic.com/paper/5915c5e8s00mh",
  "venue": "Physical Review Research",
  "versions": [
    {
      "doi": "10.48550/arxiv.2512.24685",
      "pid": null,
      "relation": "preprint",
      "title": null,
      "venue": null
    }
  ]
}