{
  "abstract": "We study the limitations of black-box amplification in the quantum complexity class Q M A . Amplification is known to boost any inverse-polynomial gap between completeness and soundness to exponentially small error, and a recent result (Jeffery and Witteveen, 2025) shows that completeness can in fact be amplified to be doubly exponentially close to 1. We prove that this is optimal for black-box procedures: we provide a quantum oracle relative to which no Q M A verification procedure using polynomial resources can achieve completeness closer to 1 than doubly exponential, or a soundness which is super-exponentially small. This is proven by making the oracle separation from (Aaronson, 2009) between Q M A and Q M A 1 quantitative, using techniques from complex approximation theory.",
  "abstract_shown": true,
  "affiliations": [
    "University of Texas at Austin. Supported by the Simons Foundation",
    "University of Bonn",
    "QuSoft & CWI, Amsterdam"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Scott Aaronson"
    },
    {
      "affs": [
        1
      ],
      "name": "Phillip Harris"
    },
    {
      "affs": [
        2
      ],
      "name": "Freek Witteveen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1mp00ctjxm2mb.bib",
  "cited_by": 0,
  "doi": "10.22331/q-2026-10-06-2227",
  "fulltext_url": null,
  "id": "1mp00ctjxm2mb",
  "issns": [
    "2521-327X"
  ],
  "landing_url": "https://quantum-journal.org/papers/q-2026-10-06-2227/",
  "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": "W4414790552",
  "pdf_url": "https://quantum-journal.org/papers/q-2026-10-06-2227/pdf/",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": "Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften",
  "ris": "https://research.draconitic.com/paper/1mp00ctjxm2mb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:58Z",
      "native_id": "10.22331/q-2026-10-06-2227",
      "source": "crossref",
      "url": "https://quantum-journal.org/papers/q-2026-10-06-2227/"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "issn:2521-327X",
      "subfield": "quantum"
    }
  ],
  "title": "Limits to black-box amplification in QMA",
  "title_text": "Limits to black-box amplification in QMA",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:17:58Z",
  "url": "https://research.draconitic.com/paper/1mp00ctjxm2mb",
  "venue": "Quantum",
  "versions": []
}