Momentum-Space Planar Optics for Long-Range Spin Hamiltonians
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.
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BibTeX
@misc{li2026momentumspace,
title = {{Momentum-Space Planar Optics for Long-Range Spin Hamiltonians}},
author = {Huaqiang Li and Junxu Liu and Guangfeng Wang and Erez Hasman and Xianfeng Chen and Bo Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25613},
eprint = {2609.25613},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25613},
}
RIS
TY - UNPB
TI - Momentum-Space Planar Optics for Long-Range Spin Hamiltonians
AU - Huaqiang Li
AU - Junxu Liu
AU - Guangfeng Wang
AU - Erez Hasman
AU - Xianfeng Chen
AU - Bo Wang
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.25613
UR - https://arxiv.org/abs/2609.25613
AB - 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.
ER -