{
  "abstract": "Random Clifford operators have numerous applications in quantum computing, including randomized benchmarking, classical shadows, and quantum authentication. However, sampling and implementing uniformly random $n$-qubit Clifford incur near-quadratic complexity due to the size of Clifford group. We introduce a cryptographic way to overcome these barriers: trapdoored Clifford operator distributions whose samples are computationally indistinguishable from uniformly random Cliffords, yet implementing them can be much faster given the trapdoor. We construct a distribution of trapdoored Clifford operators whose elements can be sampled and implemented in near-linear time under a variant of the learning parity with noise assumption. Our constructions allow fast tableau action on Pauli labels for classical simulation, and also can be optimized to admit polylogarithmic-depth implementation. Along the way, we construct trapdoored matrices over finite fields that support efficient multiplication by both a matrix and its inverse, resolving an open question left by Vaikuntanathan and Zamir [SODA'26]. We use these constructions to obtain faster protocols based on random Cliffords. We also explore their applications to the worst-case to average-case reductions for matrix and Clifford problems including the iterated matrix multiplication and Clifford circuit synthesis. In particular, we show the hardness of batching Clifford circuits: synthesizing circuits that apply the same Clifford to multiple registers is at least as hard as worst-case matrix multiplication, even when synthesis succeeds on a small constant fraction of random Cliffords. This extends to approximate implementations by general quantum circuits.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.01848",
  "author_total": 2,
  "authors": [
    {
      "name": "Minki Hhan"
    },
    {
      "name": "Hojune Lee"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9kxh9896wftrz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.01848",
  "fulltext_url": null,
  "id": "9kxh9896wftrz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.01848",
  "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.CC"
    ],
    [
      "arxiv",
      "cs.CR"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7216416503",
  "pdf_url": "https://arxiv.org/pdf/2610.01848",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9kxh9896wftrz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:03Z",
      "native_id": "2610.01848",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.01848"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Trapdoored Clifford Operators and Applications",
  "title_text": "Trapdoored Clifford Operators and Applications",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:03Z",
  "url": "https://research.draconitic.com/paper/9kxh9896wftrz",
  "venue": "arXiv",
  "versions": []
}