{
  "abstract": "We consider quantum circuits consisting of $d$ layers of nearest-neighbor two-qubit gates acting on $n$ qubits arranged on a line, where every qubit is independently depolarized with a constant probability before each layer. We describe a randomized parallel algorithm which samples from the output distribution of any such circuit to within total variation error $δ$, with parallel runtime $2^{O(d)}\\log\\log(n/δ)$ and $n 2^{O(d)}$ elementary real-arithmetic operations. Without noise, the same approach gives an exact sampler with parallel runtime $O(\\log n)$. For constant depth, we further show that the input/output behavior of the noisy quantum circuit is reproduced up to a constant error by a randomized $\\mathsf{AC}^0$-circuit, that is, a Boolean circuit of polynomial size and constant depth with unbounded fan-in AND and OR gates and NOT gates. Consequently, every relation problem solved by a noisy constant-depth quantum circuit in one dimension is also solved, with essentially the same success probability, by a randomized $\\mathsf{AC}^0$-circuit. This rules out, for noisy circuits in one dimension, the unconditional quantum advantage established for noisy shallow circuits in two and three dimensions, where polynomial-size classical circuits over the same gate set require depth $Ω(\\log n/\\log\\log n)$. Our algorithm exploits the fact that depolarizing noise cuts a one-dimensional circuit into independent pieces of logarithmic width, each of which can be sampled exactly in parallel.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.39448",
  "author_total": 2,
  "authors": [
    {
      "name": "Robert Koenig"
    },
    {
      "name": "Marco Tomamichel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fetd5dd6cm5h6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.39448",
  "fulltext_url": null,
  "id": "fetd5dd6cm5h6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.39448",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7215119593",
  "pdf_url": "https://arxiv.org/pdf/2609.39448",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fetd5dd6cm5h6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.39448",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.39448"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Parallel classical simulation of noisy shallow circuits: no quantum advantage in 1D",
  "title_text": "Parallel classical simulation of noisy shallow circuits: no quantum advantage in 1D",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/fetd5dd6cm5h6",
  "venue": "arXiv",
  "versions": []
}