{
  "abstract": "We give an efficient algorithm for learning $k$-dimensional brickwork random quantum circuits using only copies of the output state obtained by applying $U$ to the all-zero input. For a depth-$d$ circuit on $n$ sites with random $2\\ell$-qubit gates, the algorithm learns the original circuit $U$ with high probability in $\\text{poly}(n,2^{\\ell d})$ time for every constant dimensional lattice. In particular, the algorithm is polynomial time as long as $\\ell d = O(\\log n)$. In one dimension, this reaches the natural boundary suggested by pseudorandomness: pseudorandom states require $\\ell d=ω(\\log n)$, and structured cryptographic constructions suggest that this scale may be achievable from above. In higher dimensions, it remains plausible that the same $\\ell d=ω(\\log n)$ scale remains the threshold for ancilla-free pseudorandomness, and our results help clarify the conditions under which pseudorandomness can arise in this setting. The main idea behind our algorithm is a local correlation criterion that identifies gates in the final layer without learning their entire backward light cones, avoiding a bottleneck in the previous approaches. A key technical ingredient is a Carbery-Wright type anticoncentration inequality for low-degree polynomials of Haar random unitaries whose small-ball exponent is independent of the matrix dimension. The dimension-independent exponent is crucial for handling gates of growing locality. This anticoncentration result may also be of independent interest.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.39821",
  "author_total": 3,
  "authors": [
    {
      "name": "Srinivasan Arunachalam"
    },
    {
      "name": "Qizhao Huang"
    },
    {
      "name": "Makrand Sinha"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bbeny3pjc11rj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.39821",
  "fulltext_url": null,
  "id": "bbeny3pjc11rj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.39821",
  "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": "W7215063613",
  "pdf_url": "https://arxiv.org/pdf/2609.39821",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bbeny3pjc11rj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.39821",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.39821"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Learning Random Quantum Circuits and the Emergence of Pseudorandomness",
  "title_text": "Learning Random Quantum Circuits and the Emergence of Pseudorandomness",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/bbeny3pjc11rj",
  "venue": "arXiv",
  "versions": []
}