{
  "abstract": "Local interactions among electrons underlie many complex properties of correlated materials. While the Jordan-Wigner transformation can preserve this locality along one spatial dimension, interactions along the remaining dimensions typically incur substantial overhead. We show how to simulate all geometrically local interactions on an $N$-site two-dimensional fermion lattice with no asymptotic overhead in the number of interactions and no space overhead. The primary overhead of our method is circuit depth, which on a qubit lattice matches that of fermionic swap networks, scaling as $\\mathcal{O}(\\sqrt{N})$, but reduces to $\\mathcal{O}(\\log N)$ on reconfigurable qubit arrays and to $\\mathcal{O}(1)$ in lattice-surgery-based surface-code architectures. This is enabled by dynamically reorienting the Jordan-Wigner transformation to switch the lattice dimension along which locality is preserved. Furthermore, we study fermion routing, as required for the simulation of non-local interactions. When using qubit lattices, we reach resource scaling that asymptotically matches that of qubit routing, whilst on fully connected qubit devices, a depth scaling arbitrarily close to $\\mathcal{O}(\\log N)$ is reached. This allows the fermionic fast Fourier transform to be implemented on qubit lattices with asymptotically optimal resource scaling under these locality constraints. Notably, all of our constructions naturally extend to $d$-dimensional lattices. Beyond scaling improvements, we show explicit examples of our method, including Fermi-Hubbard-model simulations of the square-, Lieb- and kagome lattice and the fermionic fast Fourier transform.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.12600",
  "author_total": 4,
  "authors": [
    {
      "name": "Gregor Aigner"
    },
    {
      "name": "Berend Klaver"
    },
    {
      "name": "Martin Lanthaler"
    },
    {
      "name": "Wolfgang Lechner"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/45az8cqfzkp43.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.12600",
  "fulltext_url": null,
  "id": "45az8cqfzkp43",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.12600",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7161147995",
  "pdf_url": "https://arxiv.org/pdf/2605.12600",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/45az8cqfzkp43.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:52Z",
      "native_id": "2605.12600",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.12600"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Fermion lattices can be simulated by same-size qubit lattices with $\\mathcal{O}(1)$ interaction overhead",
  "title_text": "Fermion lattices can be simulated by same-size qubit lattices with 𝒪(1) interaction overhead",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:52Z",
  "url": "https://research.draconitic.com/paper/45az8cqfzkp43",
  "venue": "arXiv",
  "versions": []
}