{
  "abstract": "Sampling-based quantum advantage raises a basic resource question: how much non-Gaussianity is needed to reproduce the random-matrix statistics often associated with quantum chaos? Passive fermionic linear optics preserves Gaussian structure, and even Haar-random mode mixing fails to anticoncentrate for Slater inputs. We show that overcoming this obstruction requires an extensive input resource. For any pure half-filled input state, the one-body defect $ν$, defined as the summed occupation variance of the natural orbitals, must scale linearly with system size. For products of bounded-size blocks on $4N$ modes, this condition is also sufficient, with normalized collision moment asymptotic to $2N/ν$, compared with the Porter-Thomas value 2. For four-mode products, the full Porter-Thomas moment hierarchy is recovered precisely when the defect density tends to its maximum. Assuming average-case hardness, approximate classical sampling remains hard near maximal density, with an error tolerance that increases with the density. Two-copy number fluctuations measure $ν$ directly, and the same quantity lower-bounds the combined cost of non-Gaussian resource modes and parity-preserving local gates in deterministic exact preparation. Fermionic randomness therefore carries an extensive magic cost, with a quantitative link between sampling statistics, preparation resources, and an experimentally accessible witness.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05093",
  "author_total": 3,
  "authors": [
    {
      "name": "Chenfeng Cao"
    },
    {
      "name": "Yifan Tang"
    },
    {
      "name": "Jens Eisert"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0yr93x9n7gara.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05093",
  "fulltext_url": null,
  "id": "0yr93x9n7gara",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05093",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7220664007",
  "pdf_url": "https://arxiv.org/pdf/2610.05093",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0yr93x9n7gara.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2610.05093",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05093"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "The magic cost of fermionic randomness",
  "title_text": "The magic cost of fermionic randomness",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:01Z",
  "url": "https://research.draconitic.com/paper/0yr93x9n7gara",
  "venue": "arXiv",
  "versions": []
}