{
  "abstract": "Porter-Thomas statistics are a characteristic feature of the output distribution of random quantum states and, more broadly, chaotic quantum many-body systems. Convergence to Porter-Thomas plays a central role in random circuit sampling and experimental demonstrations of quantum advantage, where the output statistics of low-depth random quantum circuits are expected to be approximately Porter-Thomas, despite the absence of a rigorous proof of convergence. We show that the output distribution of polynomial-depth brickwork random circuits converges inverse-polynomially in total variation distance to the Porter-Thomas distribution. Specifically, consider the output probability distribution over a fixed bitstring of a local random quantum circuit, constructed from nearest-neighbor Haar random gates. Then, for any $m \\geq 0$, the distribution corresponding to circuits of depth $O(n^{2m+1}\\log(n))$ is at most $O(1/n^m)$ far in total variation distance from the Porter-Thomas distribution. Our proof uses moment bounds from approximate designs, analytic estimates for characteristic functions, and a local anticoncentration property for inverse moments.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02125",
  "author_total": 2,
  "authors": [
    {
      "name": "Aniruddha Sen"
    },
    {
      "name": "Nicholas Hunter-Jones"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fta3yrr1ahzzd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02125",
  "fulltext_url": null,
  "id": "fta3yrr1ahzzd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02125",
  "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",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7216341906",
  "pdf_url": "https://arxiv.org/pdf/2610.02125",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fta3yrr1ahzzd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:03Z",
      "native_id": "2610.02125",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02125"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Local random quantum circuits converge to the Porter-Thomas distribution in polynomial depth",
  "title_text": "Local random quantum circuits converge to the Porter-Thomas distribution in polynomial depth",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:03Z",
  "url": "https://research.draconitic.com/paper/fta3yrr1ahzzd",
  "venue": "arXiv",
  "versions": []
}