{
  "abstract": "Zero-noise extrapolation (ZNE) reduces the bias of noisy quantum-circuit measurements, but Richardson coefficients and shot splitting increase their statistical error. This paper determines the noise strength at which Richardson ZNE starts to lower the mean-squared error relative to the unmitigated estimator at a fixed shot budget $B$. The boundary is set by the balance between the leading squared-bias improvement and the leading excess-variance penalty: depending on the variance exponent of the measurement, it shrinks with $B$, becomes a budget threshold, or disappears. For fixed Richardson extrapolation with linear leading bias, the Richardson order and the shot allocation change only constants; the boundary exponent is set by the measured observable and protocol. Deterministic stabilizer measurements and nonzero-variance Hamiltonian or variational-energy measurements have boundaries that shrink as $B^{-1}$ and $B^{-1/2}$, and for finite-outcome shot measurements these two classes are the only ones. Qiskit Aer simulations of Greenberger-Horne-Zeilinger (GHZ) and quantum approximate optimization algorithm (QAOA) circuits reproduce this separation, and on IBM Quantum hardware ZNE lowers the mean-squared error at equal budget in 75 of 101 instances.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.08251",
  "author_total": 1,
  "authors": [
    {
      "name": "Vicenzo Scavino Alfaro"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b2tsr5bg13pcv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.08251",
  "fulltext_url": null,
  "id": "b2tsr5bg13pcv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.08251",
  "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": "W7160914378",
  "pdf_url": "https://arxiv.org/pdf/2605.08251",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b2tsr5bg13pcv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:32Z",
      "native_id": "2605.08251",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.08251"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "A finite-shot mean-squared-error boundary for Richardson zero-noise extrapolation",
  "title_text": "A finite-shot mean-squared-error boundary for Richardson zero-noise extrapolation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:28Z",
  "url": "https://research.draconitic.com/paper/b2tsr5bg13pcv",
  "venue": "arXiv",
  "versions": []
}