{
  "abstract": "We study the problem of learning a finite-range quantum Hamiltonian on an $n$-qubit $D$-dimensional lattice from copies of its Gibbs states at a known inverse temperature $β$ or its thermal metastable states. Existing efficient algorithms at arbitrary temperature have sample guarantees with an $e^{\\poly(β)}$ dependence, leaving open whether the exponent can be made linear in $β$. We achieve this improvement: for $β\\ge1$, our algorithm learns all Hamiltonian coefficients to $\\ell_\\infty$-error $ε$ with probability at least $1-δ$ using $\\tO\\bigl(e^{O(β)}ε^{-2}\\log(n/δ)\\bigr)$ copies and total time $\\tO\\bigl(n e^{O(β)}ε^{-2}\\log(n/δ)\\bigr)$. The measurements act on individual copies and are supported on balls of radius $O\\bigl(β^2+β\\log(1/ε)\\bigr)$. Our sample complexity achieves the optimal exponential order in $β$, with optimal $ε^{-2}$ dependence up to logarithmic factors. Building on the stationarity-test framework \\citep{Bergamaschi2026Stationarity}, we prove a unified Fisher-information coercivity bound showing that errors in the candidate Hamiltonian produce a detectable signal with only an $e^{-O(β)}$ loss in sensitivity. The key is a smooth frequency filter whose bandwidth remains independent of temperature, together with sharper estimates relating this signal to the Hamiltonian coefficients. For thermal metastable states, the guarantee holds under local drift $ζ\\le e^{-Cβ^{2D+1}}$, for a geometry-dependent constant $C>0$, and above an accuracy floor $\\tO(e^{O(β)}ζ)$. The argument applies to both Gibbs and thermal metastable states and, combined with local measurements and projected stochastic gradient descent (SGD), yields both learning guarantees.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01520",
  "author_total": 1,
  "authors": [
    {
      "name": "Tai Hsuan Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f544ps5ndekj9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01520",
  "fulltext_url": null,
  "id": "f544ps5ndekj9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01520",
  "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",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01520",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f544ps5ndekj9.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:20:59Z",
      "native_id": "2611.01520",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01520"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Near-Optimal Learning of Quantum Many-Body Systems from Gibbs and Thermal Metastable States via the Stationarity Test",
  "title_text": "Near-Optimal Learning of Quantum Many-Body Systems from Gibbs and Thermal Metastable States via the Stationarity Test",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/f544ps5ndekj9",
  "venue": "arXiv",
  "versions": []
}