{
  "abstract": "It is well-known that learning a pure $n$-qubit stabilizer state $|ψ\\rangle$ both requires, and can be accomplished with, access to a number of copies of $|ψ\\rangle$ linear in $n$. However, the precise constant coefficient of this scaling does not appear to have been determined. Here we prove that $L_δ(n)$, the smallest number of copies from which a quantum procedure can identify any stabilizer state with failure probability at most $0<δ<1/8$, satisfies $n+\\lceil\\log_2(1/δ)\\rceil-3\\leq L_δ(n)\\leq n+\\left\\lceil\\log_2(1/δ)\\right\\rceil+4$. We present a polynomial-time quantum learning algorithm that saturates this bound, achieving a constant factor improvement in sample-complexity over previously known approaches. As an immediate corollary, we obtain via the Choi-Jamiolkowski isomorphism an algorithm for learning an unknown $n$-qubit Clifford unitary from $2n+\\left\\lceil\\log_2(1/δ)\\right\\rceil+4$ queries, the $n$-dependence of which we show to be optimal. Our proof technique, which involves Fourier analysis on the abelian group $\\mathbb{Z}_4^n \\times \\mathbb{F}_2^{n(n-1)/2}$, seems to be qualitatively different to previous approaches to stabilizer state learning, and may be of some independent interest; in particular, it admits natural generalisations to further problems in quantum learning theory.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10974",
  "author_total": 4,
  "authors": [
    {
      "name": "Rebecca Chang"
    },
    {
      "name": "Matthias C. Caro"
    },
    {
      "name": "Martin Larocca"
    },
    {
      "name": "Maxwell West"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/431sxkbzqtg4a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10974",
  "fulltext_url": null,
  "id": "431sxkbzqtg4a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10974",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7212258339",
  "pdf_url": "https://arxiv.org/pdf/2609.10974",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/431sxkbzqtg4a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:26Z",
      "native_id": "2609.10974",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10974"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Sample-optimal learning of stabilizer states",
  "title_text": "Sample-optimal learning of stabilizer states",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:26Z",
  "url": "https://research.draconitic.com/paper/431sxkbzqtg4a",
  "venue": "arXiv",
  "versions": []
}