{
  "abstract": "We establish lower bounds for Hamiltonian property testing with access to the time-evolution operator but not its inverse. Each experiment may query the time-evolution operator multiple times, and distances between Hamiltonians are measured in the normalized Frobenius norm. In this model, we show that testing whether a Hamiltonian is $k$-local or $\\varepsilon$-far from every $k$-local Hamiltonian requires $Ω(1/\\varepsilon^2)$ total evolution time, matching the upper bound of Kallaugher and Liang (TQC'25). We also prove that testing whether an unknown Hamiltonian equals a target Hamiltonian or is $\\varepsilon$-far from it requires $Ω(1/\\varepsilon^2)$ total evolution time, matching the upper bound of Sinha and Tong (2025). These are the first lower bounds for natural problems in Hamiltonian learning and testing that rule out Heisenberg-limited scaling of $1/\\varepsilon$. As a third result, we show that amplitude estimation to precision $\\varepsilon$ requires $Ω(1/\\varepsilon^2)$ total time evolution, recovering the result of Tang and Wright (QIP'26) in the continuous-time query model. All three results follow from the hardness of distinguishing the zero Hamiltonian from a suitably chosen ensemble of random Hamiltonians. We establish this hardness by adapting the continuous-time adversary method to forward Hamiltonian evolution.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03205",
  "author_total": 3,
  "authors": [
    {
      "name": "Francisco Escudero Gutiérrez"
    },
    {
      "name": "Junseo Lee"
    },
    {
      "name": "Sebastian Zur"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/be4b0gtrmv2x6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03205",
  "fulltext_url": null,
  "id": "be4b0gtrmv2x6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03205",
  "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.CC"
    ],
    [
      "arxiv",
      "cs.DS"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7220474435",
  "pdf_url": "https://arxiv.org/pdf/2610.03205",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/be4b0gtrmv2x6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:36Z",
      "native_id": "2610.03205",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03205"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Hamiltonian locality testing and certification do not achieve the Heisenberg limit",
  "title_text": "Hamiltonian locality testing and certification do not achieve the Heisenberg limit",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:36Z",
  "url": "https://research.draconitic.com/paper/be4b0gtrmv2x6",
  "venue": "arXiv",
  "versions": []
}