{
  "abstract": "Primitive quantum speedups are interface-relative: they depend on the input access used to run the primitive and on the output contract used to consume its state or samples. This paper introduces a transcript-level admissibility relation \\(A_M\\preceq_{\\mathrm{int}}A_Q\\), defined relative to the declared implementation package of the quantum interface. It identifies which adaptive classical access transcripts that same package licenses, with all setup, transcript-generation, and precision overheads charged. The main application is an operational audit for normalized-Betti estimation in clique-complex TDA, separating three declared-interface regimes. Reversible indexed simplex interfaces certify matched classical simplex sampling and local Laplacian row access by evaluating their reversible routines on single computational branches. Membership-based preparations induce a rejection route of overhead \\(\\binom{n}{k+1}/|S_k|\\). Abstract spectral or block-encoding interfaces require an accompanying implementation package, transcript reduction, or shared representation. Under the indexed certificate and interface closure, the end-to-end cost is fixed by the imported estimator's spectral dependence on the gap \\(γ\\); the concretely realized bounded-treewidth family already admits exact \\(\\mathrm{poly}(n)\\) classical Betti computation by rank over \\(\\mathbb{Q}\\). A low-rank separation supports the role of access and output contracts.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09850",
  "author_total": 4,
  "authors": [
    {
      "name": "Pablo Herrero Gómez"
    },
    {
      "name": "Antonio Jimeno Morenilla"
    },
    {
      "name": "David Muñoz Hernández"
    },
    {
      "name": "Higinio Mora Mora"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9xjdch5pp8vb9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09850",
  "fulltext_url": null,
  "id": "9xjdch5pp8vb9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09850",
  "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",
      "cs.CC"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7212128858",
  "pdf_url": "https://arxiv.org/pdf/2609.09850",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9xjdch5pp8vb9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:12Z",
      "native_id": "2609.09850",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09850"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "When Does a Quantum Speedup Survive End-to-End?",
  "title_text": "When Does a Quantum Speedup Survive End-to-End?",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:12Z",
  "url": "https://research.draconitic.com/paper/9xjdch5pp8vb9",
  "venue": "arXiv",
  "versions": []
}