{
  "abstract": "Evaluating spin Hamiltonians with dense, long-range interactions requires repeated global summation over many pairwise couplings, making energy evaluation costly on conventional electronic hardware. Here, we realize a planar optical architecture that evaluates such interaction energies directly in momentum space. For translationally structured couplings, the interaction kernel is encoded in the spatial transmission of a subwavelength-thick planar optical element placed in the Fourier plane. Pointwise spectral weighting followed by total-power detection reduces the quadratic spin Hamiltonian to a single optical signal, avoiding repeated digital multiply-accumulate operations during energy evaluation. We experimentally apply this approach to frustrated finite-range models and fully connected spin systems with oscillatory long-range couplings. The measured energies agree closely with numerical calculations, while optical annealing reproduces low-energy configurations and landscape statistics, reaching a normalized solution quality of 99.9%. These results establish momentum-space planar optics as a compact physical computing primitive for global-interaction problems in statistical physics and optimization.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25613",
  "author_total": 6,
  "authors": [
    {
      "name": "Huaqiang Li"
    },
    {
      "name": "Junxu Liu"
    },
    {
      "name": "Guangfeng Wang"
    },
    {
      "name": "Erez Hasman"
    },
    {
      "name": "Xianfeng Chen"
    },
    {
      "name": "Bo Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2kcnwk9d2cwfa.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25613",
  "fulltext_url": null,
  "id": "2kcnwk9d2cwfa",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25613",
  "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",
      "physics.optics"
    ],
    [
      "openalex",
      "1702|Neural Networks and Reservoir Computing"
    ]
  ],
  "openalex": "W7214098873",
  "pdf_url": "https://arxiv.org/pdf/2609.25613",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2kcnwk9d2cwfa.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:39Z",
      "native_id": "2609.25613",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25613"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.optics",
      "subfield": "optics-photonics"
    }
  ],
  "title": "Momentum-Space Planar Optics for Long-Range Spin Hamiltonians",
  "title_text": "Momentum-Space Planar Optics for Long-Range Spin Hamiltonians",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:39Z",
  "url": "https://research.draconitic.com/paper/2kcnwk9d2cwfa",
  "venue": "arXiv",
  "versions": []
}