{
  "abstract": "Hao, Huang, and Liu (STOC'26) recently showed that optimal quantum query complexity may require large workspace even for short-output problems, and asked whether a quantum query advantage over classical computation can itself require space. We resolve this question by exhibiting an explicit total Boolean function with quantum query complexity $Q=\\widetildeΘ(M)$, and randomized query complexity $R=Θ(M^{21/20})$, whereas, for every fixed $0<η<1/100$ and $S\\le O(M^{1/100-η})$, its $S$-space quantum query complexity satisfies $Q_S=ω(M^{21/20})$. Consequently, $$ Q<R<Q_S, $$ so the unrestricted quantum query advantage disappears under sufficiently small workspace. The separation is obtained through a one-bit filtered-parity construction and a space-sensitive quantum lower bound based on compressed-oracle capacity and a new parity-to-capacity inequality, which may be of independent interest.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29497",
  "author_total": 3,
  "authors": [
    {
      "name": "Minbo Gao"
    },
    {
      "name": "Zhengfeng Ji"
    },
    {
      "name": "Ziyi Xie"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/029pja0807j4c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29497",
  "fulltext_url": null,
  "id": "029pja0807j4c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29497",
  "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": "W7214393122",
  "pdf_url": "https://arxiv.org/pdf/2609.29497",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/029pja0807j4c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:45Z",
      "native_id": "2609.29497",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29497"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Quantum Query Advantage Requires Space",
  "title_text": "Quantum Query Advantage Requires Space",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:45Z",
  "url": "https://research.draconitic.com/paper/029pja0807j4c",
  "venue": "arXiv",
  "versions": []
}