{
  "abstract": "Learning an interacting many-body Hamiltonian at the Heisenberg limit generally requires control that preserves local information for evolution times of order $1/\\varepsilon$ to attain $\\varepsilon$ precision. To achieve this, existing protocols often rely on trusted many-qubit operations or increasingly rapid control pulses, creating a precision barrier when gates involve unknown multi-qubit interaction or have finite duration. We show that neither resource is necessary for geometrically local Hamiltonians. Our protocol applies only static single-qubit fields, whose strength is independent of system size and grows polylogarithmically with $1/\\varepsilon$. These fields generate emergent prethermal symmetries that suppress thermalization for the entire learning experiment while retaining informative symmetry-preserving dynamics. On a $d$-dimensional lattice of $n$ qubits, this enables learning every coefficient to accuracy $\\varepsilon$, with failure probability at most $δ$, using total evolution time $\\mathcal{O}(\\log^d(1/\\varepsilon)\\log^2(n/δ)/\\varepsilon).$ Thus, our learning protocol attains the information-theoretically optimal \\(1/\\varepsilon\\) dependence up to polylogarithmic factors using product-state preparation, single-qubit measurements, and non-adaptive experiments. More broadly, our results establish emergent prethermal symmetries as a resource for quantum learning, opening a route to Heisenberg-limited characterization of many-body systems where fast or trusted many-qubit control is unavailable.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27181",
  "author_total": 4,
  "authors": [
    {
      "name": "Myeongjin Shin"
    },
    {
      "name": "Junseo Lee"
    },
    {
      "name": "Iman Marvian"
    },
    {
      "name": "Yu Tong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6rw511pcp3vvh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27181",
  "fulltext_url": null,
  "id": "6rw511pcp3vvh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27181",
  "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",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7214207098",
  "pdf_url": "https://arxiv.org/pdf/2609.27181",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6rw511pcp3vvh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:56Z",
      "native_id": "2609.27181",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27181"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Emergent Prethermal Symmetries for Scalable Hamiltonian Learning",
  "title_text": "Emergent Prethermal Symmetries for Scalable Hamiltonian Learning",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/6rw511pcp3vvh",
  "venue": "arXiv",
  "versions": []
}