{
  "abstract": "In the graph collision problem, the task is to decide whether a known graph on $n$ vertices contains an edge with both endpoints marked, given query access to the input bits specifying the marked vertices. We first refute the conjectured $Ω(n^{2/3})$ query lower bound with a bounded error quantum algorithm using $\\widetilde O(n^{92/139})$ queries. We then refine this approach to obtain a $\\widetilde O(n^{11/17})$ query algorithm. We also obtain a $\\widetilde O((nq)^{11/17})$ query bound for all (partial) Boolean output functions with positive certificate complexity at most 2 and alphabet size $q$, contrasting a known $Ω(n^{2/3})$ lower bound for such problems with large alphabet sizes. We complement these algorithms with an $Ω(\\sqrt{n\\log n})$ quantum query lower bound for graph collision, exceeding the $O(\\sqrt n)$ certificate complexity barrier for the positive adversary method.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.05356",
  "author_total": 6,
  "authors": [
    {
      "name": "Arjan Cornelissen"
    },
    {
      "name": "Amin Shiraz Gilani"
    },
    {
      "name": "Shiva Kintali"
    },
    {
      "name": "François Le Gall"
    },
    {
      "name": "Subhasree Patro"
    },
    {
      "name": "Xingyu Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fk9c9bh4g4mbc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.05356",
  "fulltext_url": null,
  "id": "fk9c9bh4g4mbc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.05356",
  "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",
      "cs.DS"
    ],
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.05356",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fk9c9bh4g4mbc.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:25Z",
      "native_id": "2611.05356",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.05356"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Breaking the quantum barriers for Graph Collision",
  "title_text": "Breaking the quantum barriers for Graph Collision",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/fk9c9bh4g4mbc",
  "venue": "arXiv",
  "versions": []
}