{
  "abstract": "Learning quantum Hamiltonians from low-temperature thermal state measurements is a fundamental problem in quantum physics. Scalability of existing methods is limited by the complexity of semidefinite optimization problems or partition function computation. Here, we develop a quantum analog of classical score matching method that exploits generalized notions of derivatives and integration by parts in operator algebras. We introduce a new \\emph{Operator Score Matching} loss function that recovers Hamiltonian parameters by a simple gradient descent without the need to compute intractable normalization constants. Numerical experiments on the Gibbs states of the transverse-field Ising model, XXZ spin chain, Fermi-Hubbard model, and lattice $ϕ^4$ theory demonstrate efficient parameter recovery using finite-depth truncations of nested commutator expansions. Our results establish Operator Score Matching as a practical, partition-function-free framework for quantum Hamiltonian learning.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25246",
  "author_total": 3,
  "authors": [
    {
      "name": "Shreya Shukla"
    },
    {
      "name": "Abhijith Jayakumar"
    },
    {
      "name": "Andrey Y. Lokhov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/963e8tybnja09.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25246",
  "fulltext_url": null,
  "id": "963e8tybnja09",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25246",
  "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": "W7214083829",
  "pdf_url": "https://arxiv.org/pdf/2609.25246",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/963e8tybnja09.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:39Z",
      "native_id": "2609.25246",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25246"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Operator Score Matching for Learning Quantum Hamiltonians",
  "title_text": "Operator Score Matching for Learning Quantum Hamiltonians",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:39Z",
  "url": "https://research.draconitic.com/paper/963e8tybnja09",
  "venue": "arXiv",
  "versions": []
}