{
  "abstract": "Parametrized gates in a variational quantum eigensolver (VQE) live on a product of unitary groups, which makes Riemannian optimization a natural candidate for improving training. We test this candidate in the clean per-gate setting: each single-qubit gate is optimized directly on U (2) and compared with Adam on an unconstrained Euler-angle chart representing the same physical gate, initialized from the same unitaries and tuned with a separate learning-rate sweep. On a validated hydrogen-chain benchmark, we find no measurable practical advantage from the Riemannian machinery. The direct manifold optimizer and the Euler-coordinate baseline are interleaved in final error and success rate; the classical coordinate baseline is not slower in iterations on the successful cells; and the choices of Riemannian metric, retraction, and momentum vector transport do not change the conclusion. We also identify four failure modes that can manufacture an apparent positive result: a trivial product-state benchmark, a projected-matrix Adam baseline that discards most of its own step, a non-unitary inherited Cayley retraction that lets the reported energy pass below the variational minimum, and a learning-rate grid whose optimum sits at its boundary. Each failure mode produced a plausible multi-seed result in our own workflow before being caught. The practical output of this paper is therefore a controlled null result and a validation checklist for VQE optimizer comparisons.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.17395",
  "author_total": 2,
  "authors": [
    {
      "name": "Polina Belozerova"
    },
    {
      "name": "Pavel Osinenko"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4bb074bxc397x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.17395",
  "fulltext_url": null,
  "id": "4bb074bxc397x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.17395",
  "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",
      "math.OC"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7221830026",
  "pdf_url": "https://arxiv.org/pdf/2610.17395",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4bb074bxc397x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:06Z",
      "native_id": "2610.17395",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.17395"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "A Controlled Null Result for Per-Gate Riemannian Optimization in VQE",
  "title_text": "A Controlled Null Result for Per-Gate Riemannian Optimization in VQE",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/4bb074bxc397x",
  "venue": "arXiv",
  "versions": []
}