{
  "abstract": "A tournament solution records a set of winners from a tournament, that is, from the outcomes of all pairwise comparisons among $N$ alternatives. We study the quantum query complexity of computing tournament solutions when the outcome of each comparison has to be learned by a query. Classically, the picture is uniform: the Copeland set, the uncovered set and the top cycle all require $Θ(N^2)$ queries, and so does finding a single vertex of maximum out-degree. We show that the quantum query complexity of the top cycle can be computed with $\\tildeΘ(N)$ queries, and a Condorcet winner can be found with $\\tilde Θ(\\sqrt N)$ queries. Finding a strong king requires $Θ(N^{3/2})$ queries, the same as finding a vertex of maximum out-degree. We also give a self-contained alternative proof of the known $Θ(N^{3/2})$ bound for finding a vertex of maximum degree, established by Gilani, Mande, Patro, and Raja. Our lower bounds reduce counting problems to tournament problems using Ambainis's adversary method. For the top cycle, we find a Hamiltonian path and locate the prefix forming the top cycle by divide and conquer.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39702",
  "author_total": 2,
  "authors": [
    {
      "name": "Pragya Arora"
    },
    {
      "name": "Udit Kumar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0e3wansa4btbq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39702",
  "fulltext_url": null,
  "id": "0e3wansa4btbq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39702",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39702",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0e3wansa4btbq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:23Z",
      "native_id": "2610.39702",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39702"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Quantum Query Complexity of Tournament Solutions",
  "title_text": "Quantum Query Complexity of Tournament Solutions",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:45Z",
  "url": "https://research.draconitic.com/paper/0e3wansa4btbq",
  "venue": "arXiv",
  "versions": []
}