{
  "abstract": "A variational state optimized in a symmetry-projected space need not be the state prepared by exponentiating the corresponding unprojected parent generators. For an orthogonal target-space projector $P$, $Q=I-P$, and an anti-Hermitian generator $A$, exact equivalence for all amplitudes requires target-space invariance, $QAP=0$. We formulate this condition as a representation-equivalence audit for open-shell ADAPT-VQE. For a canonical CAS(15e,9o) type-1 Cu(II) Hamiltonian, 274 of 323 bare Hartree--Fock-origin single, double, and triple excitations violate this condition. Projected-doublet ADAPT reaches 1.5719 m$E_h$ with 121 operators, whereas the same amplitudes in the corresponding full-space sequence give 464.730 m$E_h$ error, 0.07343 fidelity with the projected state, and 54.45\\% quartet weight. Reoptimizing the same 121 parent generators in the same order under the hard constraint $p_D\\ge0.999$ reduces the best converged error to 8.482 m$E_h$, showing that the catastrophic same-angle failure is primarily a representation/parameter-transfer failure but is not completely repaired by full-space reoptimization of the fixed sequence. An independent 12-qubit NO benchmark exhibits the same mechanism more mildly. A spin-preserving generalized full-space construction removes the representation ambiguity and reaches 1.493 and 1.181 m$E_h$ at 18 and 24 qubits. For the 18-qubit positive control, selectively refining only four Suzuki-2 factors and re-transpiling with a fixed compiler seed passes the predeclared circuit-equivalence gate at 19,660 controlled-X (CX) gates and depth 23,016. Circuit synthesis and final-energy measurement therefore constitute separate validation layers. The contribution is a validation framework, not a new spin-adapted ADAPT algorithm.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.36060",
  "author_total": 2,
  "authors": [
    {
      "name": "Lucia Malíčková"
    },
    {
      "name": "Petr Klenovský"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4c9zkrcwp6dmb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.36060",
  "fulltext_url": null,
  "id": "4c9zkrcwp6dmb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.36060",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7214997421",
  "pdf_url": "https://arxiv.org/pdf/2609.36060",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4c9zkrcwp6dmb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:31Z",
      "native_id": "2609.36060",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.36060"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "From Projected Subspaces to Full-Space Implementations: Representation-Equivalence Audits for Open-Shell ADAPT-VQE",
  "title_text": "From Projected Subspaces to Full-Space Implementations: Representation-Equivalence Audits for Open-Shell ADAPT-VQE",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:31Z",
  "url": "https://research.draconitic.com/paper/4c9zkrcwp6dmb",
  "venue": "arXiv",
  "versions": []
}