{
  "abstract": "We construct an oracle relative to which $\\mathsf{BQP} \\not\\subseteq \\mathsf{IP}$, resolving a long-standing open question in quantum complexity theory. Together with recent work due to Aaronson et al., our work also gives the first oracle separation between $\\mathsf{IP}$ and $\\mathsf{MIP}$, answering a question dating back to Fortnow's thesis. Our separation is based on the Forrelation problem, where given Boolean functions $f$ and $g$, the goal is to determine if $f$ is correlated with the Fourier spectrum of $g$. While this task is solvable by a query-efficient quantum algorithm, we show that it admits no classical interactive protocol with polynomial communication and a polynomial-query verifier. Our proof is based on (i) a new structural result showing how to approximate Avg-Max circuits (which are well-known to capture the power of interactive proofs in the oracular setting) by convex functions with small first and second derivatives and (ii) a novel analysis establishing that the Forrelation distribution suggested by Aaronson and Ambainis fools such functions. Our results imply that any prover-efficient classical interactive protocol for $\\mathsf{BQP}$ must rely on non-relativizing techniques. This might serve as a partial explanation for the lack of progress towards doubly-efficient, unconditionally sound classical verification of quantum computation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25680",
  "author_total": 5,
  "authors": [
    {
      "name": "Adam Bouland"
    },
    {
      "name": "Andrew Huang"
    },
    {
      "name": "Anand Natarajan"
    },
    {
      "name": "Itay Shalit"
    },
    {
      "name": "Avishay Tal"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0yasvw3yrtffn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25680",
  "fulltext_url": null,
  "id": "0yasvw3yrtffn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25680",
  "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.CC"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7214110283",
  "pdf_url": "https://arxiv.org/pdf/2609.25680",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0yasvw3yrtffn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:39Z",
      "native_id": "2609.25680",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25680"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "$\\mathsf{BQP} \\subseteq \\mathsf{IP}$ Does Not Relativize",
  "title_text": "BQP ⊆ IP Does Not Relativize",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:39Z",
  "url": "https://research.draconitic.com/paper/0yasvw3yrtffn",
  "venue": "arXiv",
  "versions": []
}