{
  "abstract": "When learning descriptions of many-body quantum systems, assuming locality of interactions can dramatically reduce the required number of observations and computational time compared to unstructured approaches. In this work, we uncover an infinite-dimensional instance of this phenomenon, initiating the study of Hamiltonian learning for positive-temperature bosonic Gaussian states. We present sample- and computationally efficient protocols for inferring the parameters and graph structure of underlying quadratic Hamiltonians, provided that temperature, squeezing, displacement, and the interaction graph's maximal degree are bounded. Notably, our protocol relies solely on heterodyne measurements, which are often experimentally feasible, and achieves a sample complexity that scales only logarithmically with the number of modes. Furthermore, our techniques allow for the learning of positive-temperature Gaussian states in trace distance with quadratic scaling in precision and polynomial scaling in the number of modes.",
  "abstract_shown": true,
  "affiliations": [
    "Inria, Télécom Paris - LTCI, Institut Polytechnique de Paris, Palaiseau, France. marco.fanizza@inria.fr.",
    "Department of Mathematical Sciences, University of Copenhagen, Copenhagen, Denmark. marco.fanizza@inria.fr.",
    "Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, Bellaterra (Barcelona), Spain. marco.fanizza@inria.fr.",
    "Inria, Télécom Paris - LTCI, Institut Polytechnique de Paris, Palaiseau, France.",
    "Department of Mathematical Sciences, University of Copenhagen, Copenhagen, Denmark.",
    "Univ Lyon, ENS Lyon, UCBL, CNRS, Inria, LIP, Lyon, France."
  ],
  "article_type": "research article",
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0,
        1,
        2
      ],
      "name": "Marco Fanizza",
      "orcid": "0000-0003-0802-8000"
    },
    {
      "affs": [
        3
      ],
      "name": "Cambyse Rouzé",
      "orcid": "0000-0001-7802-0616"
    },
    {
      "affs": [
        4,
        5
      ],
      "name": "Daniel Stilck França",
      "orcid": "0000-0001-9699-5994"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f2j3c3k6j6097.bib",
  "cited_by": 24,
  "doi": "10.1038/s41467-026-77405-3",
  "fulltext_url": "https://europepmc.org/articles/PMC13677717",
  "id": "f2j3c3k6j6097",
  "issns": [
    "2041-1723"
  ],
  "landing_url": "https://europepmc.org/article/MED/42893996",
  "language": "eng",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "1702|Quantum Information and Cryptography"
    ],
    [
      "openalex",
      "3107|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W4404390522",
  "pdf_url": "https://europepmc.org/articles/PMC13677717?pdf=render",
  "pmcid": "PMC13677717",
  "pmid": "42893996",
  "published": "2026-09-16",
  "publisher": "Nature Portfolio",
  "ris": "https://research.draconitic.com/paper/f2j3c3k6j6097.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:41Z",
      "native_id": "MED:42893996",
      "source": "europepmc",
      "url": "https://europepmc.org/article/MED/42893996"
    },
    {
      "first_seen": "2026-11-07T13:20:45Z",
      "native_id": "W4404390522",
      "source": "openalex",
      "url": "https://doi.org/10.1038/s41467-026-77405-3"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "openalex:3107|Quantum Information and Cryptography",
      "subfield": "quantum"
    }
  ],
  "title": "Efficient Hamiltonian, structure and trace distance learning of Gaussian states.",
  "title_text": "Efficient Hamiltonian, structure and trace distance learning of Gaussian states.",
  "type": "peer-reviewed",
  "updated_at": "2026-11-07T13:20:45Z",
  "url": "https://research.draconitic.com/paper/f2j3c3k6j6097",
  "venue": "Nature communications",
  "versions": []
}