{
  "abstract": "Variational quantum algorithms depend on the geometry of their parametrised circuits: metric-aware optimisation and time evolution require the Fubini--Study metric, which has hitherto demanded costly auxiliary measurements and ill-conditioned inversions. This work introduces a hardware-efficient $n$-qubit ansatz, which parametrises states by a binary tree and whose Hilbert-space pullback metric is diagonal in closed form. Quantum natural gradient on the tree parameters, variational imaginary- and real-time evolution, and exact unitary-invariant (Haar) sampling on a symmetry sector run with no auxiliary metric circuits or matrix inversion. When the target state is supported on a subspace of $k$ computational-basis states, the redundant tree parameters carry a gauge freedom a pruning compiler converts into circuits whose two-qubit count provably grows linearly in $k$; a variant reaches near-optimal $O(nk/\\log n)$ scaling with the closed-form metric intact. On electronic-structure calculations for small molecules and half-filled Hubbard quench dynamics, the method reaches reference-level accuracy with one to three orders of magnitude fewer two-qubit gates than leading alternatives. Interchangeable constructions (a Schur-transform dressing or internal reparameterisations) make the ansatz exactly spin-adapted, with fixed total spin at every parameter and no penalty terms. The bare ansatz is an exactly controllable, well-conditioned and barren-plateau-free primitive for preparing and sampling sector states: on its own, it is classically simulable in $k$ (a boundary proved for a general class of sector-sparse ansätze); composed with a classically hard dressing, it yields molecular ground states, sector-Haar benchmarking, thermal correlators, and exact effective Hamiltonians trained from energy measurements alone, with the composed circuit carrying the potential for quantum advantage.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.07942",
  "author_total": 1,
  "authors": [
    {
      "name": "Dario Picozzi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4hfm5a5d8gar7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.07942",
  "fulltext_url": null,
  "id": "4hfm5a5d8gar7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.07942",
  "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": "W7167903660",
  "pdf_url": "https://arxiv.org/pdf/2607.07942",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4hfm5a5d8gar7.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:30Z",
      "native_id": "2607.07942",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.07942"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "A hardware-efficient variational ansatz with an exact diagonal metric for real- and imaginary-time evolution and Haar sampling",
  "title_text": "A hardware-efficient variational ansatz with an exact diagonal metric for real- and imaginary-time evolution and Haar sampling",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:33Z",
  "url": "https://research.draconitic.com/paper/4hfm5a5d8gar7",
  "venue": "arXiv",
  "versions": []
}