{
  "abstract": "For a convex function $f \\colon \\mathbb{R}^d \\to \\mathbb{R}$, the problem of sampling from a distribution proportional to $e^{-f(x)}$ is called log-concave sampling. In many practical scenarios, the function $f(x)$ turns out to admit a local decomposition $f(x) = \\sum_{a=1}^R ψ_a(x_{S_a})$. In this paper, we consider log-concave sampling using local queries, i.e., evaluation and gradient queries to each clause $ψ_a(\\cdot)$, which can be computationally much cheaper than the queries to $f(x)$ itself. We show that if each coordinate appears in only a small number of clauses, there is a quantum algorithm for strongly log-concave sampling using $\\widetilde{O}(\\sqrtκd)$ local queries, where $κ$ is the condition number. This improves the prior best classical result $\\widetilde{O}(κd)$ due to Ascolani, Lavenant, and Zanella (Ann. Probab. 2026) and the quantum result $\\widetilde{O}(\\sqrtκ d^2)$ implied by Childs et al. (NeurIPS 2022). Our quantum sampler applies to a broad class of locally structured models from statistical computing and machine learning, with representative examples including Gaussian Markov random fields, finite-element latent Gaussian models, and sparse generalized linear models. These results demonstrate that local structure is not merely an implementation detail, but a quantum algorithmic resource for high-dimensional sampling.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20253",
  "author_total": 3,
  "authors": [
    {
      "name": "Chenghua Liu"
    },
    {
      "name": "Qisheng Wang"
    },
    {
      "name": "Zhengfeng Ji"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/37ffqnhh6rr3x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20253",
  "fulltext_url": null,
  "id": "37ffqnhh6rr3x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20253",
  "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.DS"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7213606262",
  "pdf_url": "https://arxiv.org/pdf/2609.20253",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/37ffqnhh6rr3x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:19Z",
      "native_id": "2609.20253",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20253"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Quantum Speedups for Log-Concave Sampling from Local Structure",
  "title_text": "Quantum Speedups for Log-Concave Sampling from Local Structure",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:19Z",
  "url": "https://research.draconitic.com/paper/37ffqnhh6rr3x",
  "venue": "arXiv",
  "versions": []
}