{
  "abstract": "Subgraph detection asks whether an $n$-vertex graph, accessed through queries to its adjacency matrix, contains a copy of a fixed graph $H$. We prove the first unconditional superlinear lower bounds on the bounded-error quantum query complexity of this problem, answering a longstanding open question. A copy of $H$ is a certificate of constant size, so the adversary method with nonnegative weights cannot prove superlinear lower bounds. For every fixed $r\\ge 4$, detecting the clique $K_r$ requires $n^{λ_r-o(1)}$ queries, where $λ_4=19/18$, the exponents $λ_r$ increase strictly with $r$, and $λ_r\\ge 2-4\\sqrt{2/r}+O(1/r)$. More generally, we prove superlinear lower bounds for detecting every fixed connected graph $H$ with chromatic number $c\\ge 4$. These bounds approach quadratic as $c$ grows: for sufficiently large $c$, detection requires $n^{2-O(\\sqrt{\\log\\log c/c})-o(1)}$ queries. Chromatic number alone does not characterize the quantum query complexity of subgraph detection: we show that detecting the complete bipartite graph $K_{r,r}$ requires $n^{β_r-o(1)}$ queries, where $β_{10}=181/180$ and $β_r\\ge 2-O(1/\\sqrt{r})$. Our main technical result is a lower bound for finding an all-ones certificate from a known family when the input bits are sampled independently. Its proof combines Zhandry's compressed oracle [CRYPTO 2019] with conditioning on a randomly planted certificate, adapting an argument of Belovs [FOCS 2026]. Our hard instances are built from graphs containing many copies of the desired subgraph with limited overlap. For cliques, we use a construction of Gowers and Janzer [CPC 2021]; for complete bipartite graphs, we use a random construction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.40263",
  "author_total": 2,
  "authors": [
    {
      "name": "Amin Shiraz Gilani"
    },
    {
      "name": "Xingyu Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/75nwgf8gerxrs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.40263",
  "fulltext_url": null,
  "id": "75nwgf8gerxrs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.40263",
  "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.DS"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7215123839",
  "pdf_url": "https://arxiv.org/pdf/2609.40263",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/75nwgf8gerxrs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2609.40263",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.40263"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Superlinear Quantum Query Lower Bounds for Subgraph Detection",
  "title_text": "Superlinear Quantum Query Lower Bounds for Subgraph Detection",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:01Z",
  "url": "https://research.draconitic.com/paper/75nwgf8gerxrs",
  "venue": "arXiv",
  "versions": []
}