{
  "abstract": "Stabilizer states are central to quantum computing, underlying quantum error correction, benchmarking, and efficient classical simulation. Yet their learnability exhibits a striking gap: an $n$-qubit stabilizer state can be learned from $Θ(n)$ copies using two-copy Bell measurements, whereas non-adaptive single-copy measurements require $Ω(n^2)$ copies. Here we show that adaptivity completely closes this gap. We give a polynomial-time adaptive algorithm that learns an arbitrary $n$-qubit stabilizer state from $Θ(n)$ single-copy Clifford measurements, matching the optimal sample complexity of Bell sampling without any multi-copy measurements. The same ideas yield a sample-optimal single-copy tolerant tester and, with $k$ qubits of quantum memory, the optimal testing tradeoff $Θ(n-k+1/\\varepsilon)$ at infidelity $\\varepsilon$. Finally, we show that this adaptive mechanism extends beyond exact stabilizer states: states of stabilizer nullity at most $r$, including states prepared by Clifford circuits with a bounded number of $T$ gates, can be learned using $O(n2^{r})$ single-copy measurements.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02031",
  "author_total": 5,
  "authors": [
    {
      "name": "L. Bittel"
    },
    {
      "name": "J. Eisert"
    },
    {
      "name": "W. Gong"
    },
    {
      "name": "A. A. Mele"
    },
    {
      "name": "L. Schatzki"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e4tnr5dwk32bt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02031",
  "fulltext_url": null,
  "id": "e4tnr5dwk32bt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02031",
  "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": "W7216173900",
  "pdf_url": "https://arxiv.org/pdf/2610.02031",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e4tnr5dwk32bt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:03Z",
      "native_id": "2610.02031",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02031"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Adaptivity is all you need: Optimal stabilizer learning using just single-copy measurements",
  "title_text": "Adaptivity is all you need: Optimal stabilizer learning using just single-copy measurements",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:03Z",
  "url": "https://research.draconitic.com/paper/e4tnr5dwk32bt",
  "venue": "arXiv",
  "versions": []
}