{
  "abstract": "We introduce a new exact classical sampling algorithm for Clifford+T circuits, called T-by-T sampling. For a circuit with T-count t, it reduces sampling to evaluating 2t amplitudes of circuits with successively increasing T-counts 1,2,...,t, without the need to compute costly marginal probabilities. Crucially, the number of amplitude evaluations is completely independent of the surrounding Clifford structure. This makes T-by-T sampling well suited for use together with low-rank stabiliser decompositions, which enable efficient amplitude evaluations as long as the T-count is not too high. In that sense, T-by-T sampling is an improvement over the gate-by-gate sampling technique introduced by Bravyi, Gosset, and Liu (Phys. Rev. Lett. 128, 2022), where the number of amplitudes instead scales with the number of non-monomial operations such as Hadamard gates, which can remain large even in circuits with low stabiliser rank. Concretely, T-by-T sampling offers significant speedups in regimes where T gates are embedded within large Clifford computations. This makes it well suited for applications such as simulating quantum error correction experiments, which typically have lower T complexity but involve extensive Clifford operations and measurements. In particular, we show how T-by-T sampling allows us to take samples from recent end-to-end magic state cultivation circuits with escape up to distance 19 in a couple of seconds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: EPTCS 456, 2026, pp. 207-218",
  "arxiv": "2611.06119",
  "author_total": 1,
  "authors": [
    {
      "name": "Mark Koch"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4m6k4sngctjbb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06119",
  "fulltext_url": null,
  "id": "4m6k4sngctjbb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06119",
  "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"
    ]
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  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.06119",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4m6k4sngctjbb.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:20:56Z",
      "native_id": "2611.06119",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06119"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Classical Clifford+T Sampling without Computing Marginals",
  "title_text": "Classical Clifford+T Sampling without Computing Marginals",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:19Z",
  "url": "https://research.draconitic.com/paper/4m6k4sngctjbb",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.4204/eptcs.456.8",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}