{
  "abstract": "In classical fine-grained complexity, the 3SUM Conjecture is used to prove a variety of conditional lower bounds on data structure and graph problems via an initial reduction to the SetDisjointness problem. However, there is an $\\tilde{O}(n)$-time quantum algorithm for 3SUM and a direct application of Grover's algorithm to SetDisjointness queries beats the state-of-the-art classical conditional bound by Kopelowitz, Pettie, and Porat (SODA 2016); this shows that these classical bounds do not apply in the quantum setting. Thus establishing analogous conditional lower bounds in the quantum setting requires applying the quantum 3SUM Conjecture to a \\emph{quantum} fine-grained reduction from 3SUM to SetDisjointness. We give the first sub-linear time quantum reductions from 3SUM to online SetDisjointness. Via our reduction, the quantum 3SUM conjecture implies a $p + 2q \\geqslant 1$ tradeoff bound for quantum SetDisjointness algorithms with $O(N^p)$ preprocessing time and $O(N^q)$ query time. We also give an analogous reduction from 3XOR. These results are derived from a general framework for fine-grained reductions to SetDisjointness which applies to any Abelian 3-Orthogonal Array (3OA) problem with suitable almost-linear hash functions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.40293",
  "author_total": 3,
  "authors": [
    {
      "name": "Jeremy Huang"
    },
    {
      "name": "Young Kun Ko"
    },
    {
      "name": "Chunhao Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cvpvxp67wpkzr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.40293",
  "fulltext_url": null,
  "id": "cvpvxp67wpkzr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.40293",
  "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",
      "cs.DS"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7215102427",
  "pdf_url": "https://arxiv.org/pdf/2609.40293",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cvpvxp67wpkzr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.40293",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.40293"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Quantum Fine-Grained Lower Bounds for SetDisjointness via Sub-Linear Reductions from 3SUM",
  "title_text": "Quantum Fine-Grained Lower Bounds for SetDisjointness via Sub-Linear Reductions from 3SUM",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/cvpvxp67wpkzr",
  "venue": "arXiv",
  "versions": []
}