{
  "abstract": "We give a sampling problem that is solvable by shallow quantum circuits, hard for polynomial-time classical algorithms under lattice-based assumptions, and efficiently verifiable by a classical computer. The quantum sampler admits two implementations: one uses log-logarithmic-depth quantum circuits with one- and two-qubit gates, i.e., $\\mathsf{QNC}^0[\\log\\log]$ circuits, while the other uses constant-depth quantum circuits with unbounded fan-in gates, i.e., $\\mathsf{QAC}^0$ circuits. Our construction can be seen as compiling the Learning with Errors (LWE)-based single-round proof of quantumness of Arabadjieva et al. (2025) to very low depth. The price paid for this compilation is the reliance on less standard, though well-motivated, assumptions: in addition to the lattice knowledge assumption used by Arabadjieva et al. (2025), we require a strengthened variant of the adaptive-hardcore-bit property of LWE, for which we provide supporting evidence. Unlike previous low-depth proofs of quantumness, the quantum computation here requires no mid-circuit measurements or feed-forward: it consists only of running a shallow circuit and sampling from its output distribution. This shows that shallow quantum circuits have sufficient structure to solve certain classically hard tasks whose solutions can be verified efficiently.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01448",
  "author_total": 1,
  "authors": [
    {
      "name": "Alexandru Gheorghiu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4tbm6swfnhef8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01448",
  "fulltext_url": null,
  "id": "4tbm6swfnhef8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01448",
  "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.CR"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7206155622",
  "pdf_url": "https://arxiv.org/pdf/2609.01448",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4tbm6swfnhef8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:03Z",
      "native_id": "2609.01448",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01448"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Verifiable quantum advantage in extremely low depth",
  "title_text": "Verifiable quantum advantage in extremely low depth",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:03Z",
  "url": "https://research.draconitic.com/paper/4tbm6swfnhef8",
  "venue": "arXiv",
  "versions": []
}