{
  "abstract": "Discretizing electronic degrees of freedom into atomic orbitals is the default choice to accurately model electrons in molecules in a compact and flexible way. We consider the task of simulating such electronic structure models on a quantum computer for $N$ orbitals, keeping the number of orbitals per atom constant. Atomic orbitals give rise to Hamiltonians with potentially up to $\\mathcal{O}(N^4)$ terms and little structure, which made it challenging to match the complexity of methods based on plane waves and real-space grids. In this work, we show that a Trotter step for atomic orbitals can be implemented in depth $\\mathcal{O}(\\mathrm{polylog}(N))$ without ancillas by combining a rigorous treatment of orbital localization, a hierarchical Hamiltonian decomposition based on the Fast Multipole Method, and shallow quantum Fourier arithmetic circuits. By bounding the Trotter error, we obtain sublinear simulation depth, and our total gate count $N^{5/3 + o(1)}$ matches the best scaling known for any basis.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00950",
  "author_total": 2,
  "authors": [
    {
      "name": "Jakob Günther"
    },
    {
      "name": "Aram W. Harrow"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8fggmhbzphh1p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00950",
  "fulltext_url": null,
  "id": "8fggmhbzphh1p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00950",
  "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": "W7215993288",
  "pdf_url": "https://arxiv.org/pdf/2610.00950",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8fggmhbzphh1p.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:03Z",
      "native_id": "2610.00950",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00950"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Sublinear-depth Quantum Simulation of Electrons with Atomic Orbitals",
  "title_text": "Sublinear-depth Quantum Simulation of Electrons with Atomic Orbitals",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:03Z",
  "url": "https://research.draconitic.com/paper/8fggmhbzphh1p",
  "venue": "arXiv",
  "versions": []
}