{
  "abstract": "Accurate measurement of an intended conditional phase does not by itself place a multiqubit phase gate in its declared generalized-gate equivalence class. We cast the diagnosis as structured Hamiltonian learning of the diagonal successful block in a known basis: Ramsey measurements on a connected graph reconstruct a target-relative eigenphase map; a Walsh transform then yields the per-cycle stroboscopic error generator in a selected logarithm branch, whose branch-dependent coefficients alone cannot decide global equivalence. For diagonal Pauli-Z dressing of weight at most m we derive an exact branch-independent criterion from multiplicative Boolean-Mobius invariants, converted at finite shot counts into a pass/fail/unresolved decision under prespecified tolerances and simultaneous confidence, separate from model rejection. For shared-control C^mZ gates a circular target-face contrast isolates each intended conditional phase, yet a support theorem exhibits forbidden interactions invisible to every target face once multiple targets or external spectators are present. We derive a Cramer-Rao bound for arbitrary integer phase contrasts, recovering the 4^m attempted-circuit scaling of a uniform (m+1)-body face, and quantify degradation from visibility loss, heralded survival, readout confusion, and correlated noise, while systematic bias triggers model rejection. Seeded simulations implement the 4M-setting multiplexed acquisition end to end: for M=3,4,5 at a common budget its mean phase-map RMSE is 0.689-0.794 times a separately compiled statewise scan, and a blind-interaction test yields 300/300 global-audit rejections versus 1/300 for target faces. These results estimate the error generator of a diagonal successful block under a specified acquisition model; they are not unknown-basis Hamiltonian identification, arbitrary-channel tomography, or hardware certification.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27629",
  "author_total": 1,
  "authors": [
    {
      "name": "Xiu-Hao Deng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8d6e37rfsk3q8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27629",
  "fulltext_url": null,
  "id": "8d6e37rfsk3q8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27629",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7214215140",
  "pdf_url": "https://arxiv.org/pdf/2609.27629",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8d6e37rfsk3q8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:56Z",
      "native_id": "2609.27629",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27629"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Structured Hamiltonian Learning for Multiqubit Conditional Phase Gates",
  "title_text": "Structured Hamiltonian Learning for Multiqubit Conditional Phase Gates",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:56Z",
  "url": "https://research.draconitic.com/paper/8d6e37rfsk3q8",
  "venue": "arXiv",
  "versions": []
}