{
  "abstract": "We give a deterministic classical algorithm that estimates $|\\langle x|U|0^n\\rangle|^2$ to additive error $\\varepsilon$ in $\\mathrm{poly}(n, 1/\\varepsilon)$ time, where $U$ is a constant-depth quantum circuit comprised of gates with bounded fan-in and arbitrary connectivity, and $x$ is an arbitrary $n$-bit output string. This improves over prior state-of-the-art algorithms that takes $n^{O(log(n))}$ time for the same task, $n^{O(log(log(n))}$ when $U$ is geometrically local, and $n^{O(1)}$ for 2D geometrically-local circuits.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02146",
  "author_total": 5,
  "authors": [
    {
      "name": "Matthew Coudron"
    },
    {
      "name": "Michael J. Gullans"
    },
    {
      "name": "Jon Nelson"
    },
    {
      "name": "Joel Rajakumar"
    },
    {
      "name": "Shi Jie Samuel Tan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dvxdgv1hfn3a9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02146",
  "fulltext_url": null,
  "id": "dvxdgv1hfn3a9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02146",
  "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.CC"
    ],
    [
      "arxiv",
      "cs.DS"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7215831242",
  "pdf_url": "https://arxiv.org/pdf/2610.02146",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dvxdgv1hfn3a9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:03Z",
      "native_id": "2610.02146",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02146"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Polynomial-time additive-error estimation of output probabilities for shallow quantum circuits",
  "title_text": "Polynomial-time additive-error estimation of output probabilities for shallow quantum circuits",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:03Z",
  "url": "https://research.draconitic.com/paper/dvxdgv1hfn3a9",
  "venue": "arXiv",
  "versions": []
}