{
  "abstract": "Smoothed analysis is a central framework in classical algorithms for explaining the performance of algorithms beyond the worst case, often explaining why algorithms perform well in practice. We initiate a systematic study of its quantum counterpart and show the following results. $(1)$ We show that there is a total function whose smoothed quantum query complexity is exponentially smaller than its classical query complexity. $(2)$ We give near-tight characterizations of smoothed randomized and quantum query complexities for symmetric Boolean functions, unifying the worst-case complexity results of [Beals et al, FOCS'98] and average-case complexity results of [Ambainis and de Wolf, STACS'00]. $(3)$ We study string problems such as pattern matching and edit distance and, in various regimes, give polynomial to superpolynomial quantum speedups. Our main technical ingredients include a near-tight quantum algorithm for $\\varepsilon$-approximating the number of collisions between two non-repetitive strings, improving the result of Le Gall and Ng [QIC'22]. Together, our results show that smoothing can reveal larger quantum speedups than worst-case analysis suggests, opening a path towards quantum advantage on more realistic inputs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35580",
  "author_total": 3,
  "authors": [
    {
      "name": "Srinivasan Arunachalam"
    },
    {
      "name": "Yanlin Chen"
    },
    {
      "name": "Amin Shiraz Gilani"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eyk4cv035zjr8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35580",
  "fulltext_url": null,
  "id": "eyk4cv035zjr8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.35580",
  "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": "W7214775238",
  "pdf_url": "https://arxiv.org/pdf/2609.35580",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eyk4cv035zjr8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:12Z",
      "native_id": "2609.35580",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35580"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Quantum Query Complexity Beyond the Worst Case",
  "title_text": "Quantum Query Complexity Beyond the Worst Case",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:12Z",
  "url": "https://research.draconitic.com/paper/eyk4cv035zjr8",
  "venue": "arXiv",
  "versions": []
}