{
  "abstract": "We develop an exact spectral-response theory for the Grover-type iterate \\(W_T=D_ξ\\exp(-\\mathrm{i} T H)\\), in which the evolution generated by a diagonal Ising Hamiltonian is used directly as a continuous phase oracle. An energy-grouped recurrence and its generating-function solution show how the empirical characteristic function determines the position, width, height, and saturation time of an energy-selective resonance. For an annealed Gaussian density of states, a high-density-tail resonance containing \\(M\\) configurations is reached after \\(Θ(\\sqrt{2^n/M})\\) oracle calls with success probability \\(Θ(1)\\), giving a quadratic query improvement over independent uniform sampling with classical energy evaluation. For correlated random Ising spectra, overlap-dependent covariances lead to a realization-dependent resonance shift with root-mean-square scale \\(O(n^{-3})\\), parametrically larger than the resonance width, and can also reduce the peak height. The shift is both an algorithmic detuning and a coherent probe of sample-specific spectral fluctuations whose ensemble statistics reflect the Ising overlap structure. Spectral symmetrization and iterative calibration can remove or compensate the resonance-center displacement for prescribed-energy targeting. We also clarify the relation to designed spectral filters and the precision and coherence requirements of this asymptotic primitive.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Phys. Rev. A 114, 042463 (2026)",
  "arxiv": "2606.03380",
  "author_total": 4,
  "authors": [
    {
      "name": "A. S. Plyashechnik"
    },
    {
      "name": "A. A. Zhukov"
    },
    {
      "name": "A. V. Lebedev"
    },
    {
      "name": "W. V. Pogosov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/88k9jqttafh9f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.03380",
  "fulltext_url": null,
  "id": "88k9jqttafh9f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.03380",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.dis-nn"
    ],
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2606.03380",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/88k9jqttafh9f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:32Z",
      "native_id": "2606.03380",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.03380"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Spectral theory of energy-selective quantum search with Ising Hamiltonian phase oracles",
  "title_text": "Spectral theory of energy-selective quantum search with Ising Hamiltonian phase oracles",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:49Z",
  "url": "https://research.draconitic.com/paper/88k9jqttafh9f",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1103/tgsx-5nz4",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}