{
  "abstract": "Reporting the Fisher geometry of a trained variational quantum model is routine; quoting the shot budget that would establish it is not. Certifying an empirical Fisher matrix to relative Frobenius error $\\varepsilon$ under coordinate-wise parameter shift costs $Θ(B p^{2} V/(\\varepsilon^{2} G))$ circuit executions, where $V$ is the measured readout variance and $G$ the measured squared gradient norm, with uniform allocation optimal in that class. One constant reproduces the cost of two circuit families whose exponents differ by a full power of $p$. The exponent is an identity in how $nV$ and $nG$ scale with the register, holding family by family to $0.001$ across 624 matrix-product-state cells once the finite-$p$ prefactor is removed. The cubic cost is therefore a finite-size window, set by whether the readout light cone grows with the register. A product family to 256 qubits gives $1.966$ (95% CI $1.934$--$1.997$); a brickwork entangler falls from $2.853$ below ten qubits to $1.715$ beyond sixty-four; a blocked entangler gives $1.984$ at a fixed cone width against $3.034$ at a proportional one. Fixed device connectivity fixes the cone, so a cubic budget from a small simulation overestimates a large machine, on top of hardware multipliers $2.07\\times$ ($1.41$--$3.02$), $2.38\\times$ and $1.91\\times$ on ibm_marrakesh, ibm_fez and ibm_kingston. Cost-optimal readout weights cut the measured shot budget by $2.67\\times$ ($1.33$--$4.00$) on hardware, flat from four to twelve qubits. A discrepancy model fitted on cheap circuits transfers its mean inside the calibration grid and, at six larger sizes named before the data, does not: nominal 90% intervals cover 36%, and split conformal is the only rung that stays near nominal.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14424",
  "author_total": 2,
  "authors": [
    {
      "name": "Pavel Sulimov"
    },
    {
      "name": "Claude Lehmann"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5yrzh8pkfqx33.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14424",
  "fulltext_url": null,
  "id": "5yrzh8pkfqx33",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14424",
  "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.LG"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7213340237",
  "pdf_url": "https://arxiv.org/pdf/2609.14424",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5yrzh8pkfqx33.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:25Z",
      "native_id": "2609.14424",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14424"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Certification cost of quantum models: measurement correlation, not parameter count",
  "title_text": "Certification cost of quantum models: measurement correlation, not parameter count",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:25Z",
  "url": "https://research.draconitic.com/paper/5yrzh8pkfqx33",
  "venue": "arXiv",
  "versions": []
}