{
  "abstract": "A quantum circuit for first-quantization-based Hamiltonian simulation, capable of running on a small-scale quantum computer emulator with fewer than 30 qubits, was constructed and demonstrated for one- and two-dimensional hydrogen-atom models, the simplest settings sufficient to check the proposed circuits without the confounding effects of electron-electron interaction and correlation. For these systems, Uniformly Controlled Rotation Z (UCRZ) circuits were found valuable for constructing a Coulomb potential circuit compact enough to fit on a small-scale emulator. Although this approach does not scale to larger models, we compare it against a conventional arithmetic-circuit implementation to identify the regime in which UCRZ is preferable. To deal with the Coulomb singularity, we propose regularizing it via a geometric average of the potential over a small circular region around the pole, avoiding divergence and minimizing the resulting energy error. To select parameters minimizing error for a given number of qubits, we determine the optimal spatial grid spacing from the trade-off between spatial discretization error and domain truncation error, and determine the time evolution step size not from the formal worst-case Trotter error bound, but from a sampling-theorem-based bound on the wave function’s maximum frequency component, avoiding unnecessary circuit depth without sacrificing accuracy. While the validity of a UCRZ-based circuit structure is restricted to the small-scale regime, the singularity treatment and parameter-selection procedure address the grid discretization itself and apply broadly to grid-based first-quantization simulations.",
  "abstract_shown": true,
  "affiliations": [
    "1Managed and Platform Services Business Division, Hitachi, Ltd., 292, Yoshida, Totsuka-ku, Yokohama 244-0817, Japan2Institute of Industrial Science, The University of Tokyo, 4-6-1, Komaba, Meguro-ku, Tokyo 153-8505, Japan",
    "2Institute of Industrial Science, The University of Tokyo, 4-6-1, Komaba, Meguro-ku, Tokyo 153-8505, Japan3Next Research, Research and Development Group, Hitachi, Ltd., Kokubunji, Tokyo 185-8601, Japan",
    "2Institute of Industrial Science, The University of Tokyo, 4-6-1, Komaba, Meguro-ku, Tokyo 153-8505, Japan4Tokyo Metropolitan College of Industrial Technology, 8-17-1, Minami-Senju, Arakawa-ku, Tokyo 116-8523, Japan",
    "2Institute of Industrial Science, The University of Tokyo, 4-6-1, Komaba, Meguro-ku, Tokyo 153-8505, Japan"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 5,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Hideo Takahashi",
      "orcid": "0009-0004-8948-9451"
    },
    {
      "affs": [
        1
      ],
      "name": "Tatsuya Tomaru",
      "orcid": "0000-0002-7645-8240"
    },
    {
      "affs": [
        2
      ],
      "name": "Toshiyuki Hirano",
      "orcid": "0000-0003-1856-8385"
    },
    {
      "affs": [
        3
      ],
      "name": "Saisei Tahara",
      "orcid": "0009-0009-2736-7332"
    },
    {
      "affs": [
        3
      ],
      "name": "Fumitoshi Sato",
      "orcid": "0000-0001-9110-8268"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d2csar5hwm5qa.bib",
  "cited_by": 0,
  "doi": "10.1063/5.0357248",
  "fulltext_url": "https://pubs.aip.org/aip/adv/article-pdf/doi/10.1063/5.0357248/21179891/105211_1_5.0357248.pdf",
  "id": "d2csar5hwm5qa",
  "issns": [
    "2158-3226"
  ],
  "landing_url": "https://doi.org/10.1063/5.0357248",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "lcc",
      "QC1-999"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7223333459",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": "AIP Publishing LLC",
  "ris": "https://research.draconitic.com/paper/d2csar5hwm5qa.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T13:44:19Z",
      "native_id": "becaeb14c3734d968ed7730cde7fd74e",
      "source": "doaj",
      "url": "https://doi.org/10.1063/5.0357248"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "lcc:QC1-999",
      "subfield": "general"
    }
  ],
  "title": "Grid-based quantum circuit simulation of the hydrogen atom: Coulomb singularity regularization and parameter-selection guidelines",
  "title_text": "Grid-based quantum circuit simulation of the hydrogen atom: Coulomb singularity regularization and parameter-selection guidelines",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T13:44:19Z",
  "url": "https://research.draconitic.com/paper/d2csar5hwm5qa",
  "venue": "AIP Advances",
  "versions": []
}