{
  "abstract": "Analog quantum computers provides direct access to continuous many-body dynamics, but their native control Hamiltonians generate only a restricted operator space. Consequently, the fidelity with which they can reproduce a target Hamiltonian's dynamics depends not only on spectral agreement but on whether the physical controls can actually generate the required evolution. We introduce a geometry-independent framework for diagnosing and optimizing this compatibility between the spectral algebra generated by a target Hamiltonian $H$ and a Krylov-type operator space generated from the device's independently tunable control Hamiltonians and a fixed initial state. The encoding problem can be formulated as an optimization over the unitary orbit of the target Hamiltonian. We maximize a smooth subspace-overlap functional using Riemannian gradient descent on $U(d)$, thereby selecting a spectrally equivalent representation whose target algebra is better aligned with the native controls. We apply this framework to the deuteron Hamiltonian encoded on a Rydberg-atom analog processor. The standard binary encoding is strongly misaligned with this space for small system sizes, while principal-angle optimization substantially improves the algebraic compatibility of the encoding. Moreover, using a single geometry-independent optimized encoding substantially reduces the sensitivity of state-preparation fidelity to the atomic geometry. These results establish algebraic reachability as a useful preprocessing criterion for analog encoding design: it identifies representation-level incompatibilities before device-specific geometry and pulse optimization, while the distinction between algebra-level and state-level reachability clarifies when full encoding optimization is necessary and when geometry-dependent control resources can compensate for incomplete algebraic alignment.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11351",
  "author_total": 1,
  "authors": [
    {
      "name": "Mariane Mangin-Brinet"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ft8by31zxbj4z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11351",
  "fulltext_url": null,
  "id": "ft8by31zxbj4z",
  "issns": [],
  "landing_url": "https://hal.science/hal-05759396v1",
  "language": "en",
  "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"
    ],
    [
      "hal",
      "0.phys"
    ],
    [
      "hal",
      "1.phys.qphy"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7212300508",
  "pdf_url": "https://arxiv.org/pdf/2609.11351",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ft8by31zxbj4z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:37Z",
      "native_id": "hal-05759396",
      "source": "hal",
      "url": "https://hal.science/hal-05759396v1"
    },
    {
      "first_seen": "2026-10-30T12:20:26Z",
      "native_id": "2609.11351",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11351"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Optimizing quantum encodings for analog simulation through dynamical algebra reachability",
  "title_text": "Optimizing quantum encodings for analog simulation through dynamical algebra reachability",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:26Z",
  "url": "https://research.draconitic.com/paper/ft8by31zxbj4z",
  "venue": "HAL",
  "versions": []
}