{
  "abstract": "We present an efficient protocol for learning an unknown $k$-local Lindblad generator on $n$ qubits using only product-state preparations, short-time evolution, and single-qubit Pauli measurements, without prior knowledge of the interaction structure. For fixed $k$ and a supplied weighted interaction-strength bound $\\barα$, the protocol estimates all Hamiltonian and dissipative Pauli--GKSL coefficients with total coefficient error at each site at most $\\varepsilon$ with probability at least $1-δ$ using $\\widetilde{\\mathcal O}_k(\\barα^2n^{2k-2}\\varepsilon^{-2}\\log(n/δ))$ samples and polylogarithmically many distinct evolution times. This guarantee requires no degree, sparsity, or tail promise. A convex optimization converts these estimates into a valid $k$-local Lindblad generator with diamond-norm error at most $\\varepsilon$ using $\\widetilde{\\mathcal O}_k(\\barα^2n^{2k}\\varepsilon^{-2}\\log(n/δ))$ samples and polynomial-time classical postprocessing. With a supplied local effective-sparsity bound $r$ and a sufficiently small sitewise subthreshold tail $\\mathcal O_k(\\varepsilon)$, coefficient recovery requires only $\\widetilde{\\mathcal O}_k(\\barα^2r^2\\varepsilon^{-2}\\log(n/δ))$ samples, without a supplied threshold or coefficient locations and without a coefficient-gap assumption. In particular, exactly sparse bounded-degree models have logarithmic sample dependence on $n$. We also provide guard-band support recovery and complementary supplied-candidate guarantees, extend the guarantees to model misspecification, and prove complementary sample-complexity lower bounds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.23652",
  "author_total": 4,
  "authors": [
    {
      "name": "Tim Möbus"
    },
    {
      "name": "Thiago Bergamaschi"
    },
    {
      "name": "Daniel Stilck França"
    },
    {
      "name": "Cambyse Rouzé"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3zm34sj73vha8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.23652",
  "fulltext_url": null,
  "id": "3zm34sj73vha8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.23652",
  "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",
      "cs.IT"
    ],
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "arxiv",
      "math.NA"
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      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7165673944",
  "pdf_url": "https://arxiv.org/pdf/2606.23652",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3zm34sj73vha8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2606.23652",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.23652"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Robust Structure Learning of $k$-local Lindbladians",
  "title_text": "Robust Structure Learning of k-local Lindbladians",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:16Z",
  "url": "https://research.draconitic.com/paper/3zm34sj73vha8",
  "venue": "arXiv",
  "versions": []
}