Momentum-Space-Engineered Spatial Photonic Ising Machine for Long-Range Interactions
Abstract
Long-range Ising models (LRIMs) with dense nonlocal and competing interactions are central to statistical physics, quantum simulation, and complex networks. Although the spatial photonic Ising machine (SPIM) exploits intrinsic optical parallelism for Ising computation, its ability to faithfully encode dense long-range couplings and capture the resulting thermodynamic signatures remains underexplored. Here, we present a momentum-space-engineered SPIM framework that maps prescribed long-range coupling kernels onto momentum-space masks for parallel Hamiltonian evaluation. Based on a high-fidelity optical field propagation model, the annealing dynamics of LRIMs with power-law and Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions are systematically investigated. For the power-law model, we investigate the modulation of the estimated critical temperature by the decay exponent σ and coupling cutoff radius R. For the RKKY model, we reproduce diverse ordered states induced by complex competing long-range interactions. A proof-of-principle experiment demonstrates the physical feasibility of our approach. This framework broadens the class of many-body systems accessible to the SPIM platform.
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BibTeX
@misc{zhou2026momentumspaceengineered,
title = {{Momentum-Space-Engineered Spatial Photonic Ising Machine for Long-Range Interactions}},
author = {Haijun Zhou and Hengyang Li and Maolin Wang and Yunru Chen and Yingxiong Qin and Xiahui Tang and Gang Xu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.07297},
eprint = {2609.07297},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.07297},
}
RIS
TY - UNPB
TI - Momentum-Space-Engineered Spatial Photonic Ising Machine for Long-Range Interactions
AU - Haijun Zhou
AU - Hengyang Li
AU - Maolin Wang
AU - Yunru Chen
AU - Yingxiong Qin
AU - Xiahui Tang
AU - Gang Xu
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.07297
UR - https://arxiv.org/abs/2609.07297
AB - Long-range Ising models (LRIMs) with dense nonlocal and competing interactions are central to statistical physics, quantum simulation, and complex networks. Although the spatial photonic Ising machine (SPIM) exploits intrinsic optical parallelism for Ising computation, its ability to faithfully encode dense long-range couplings and capture the resulting thermodynamic signatures remains underexplored. Here, we present a momentum-space-engineered SPIM framework that maps prescribed long-range coupling kernels onto momentum-space masks for parallel Hamiltonian evaluation. Based on a high-fidelity optical field propagation model, the annealing dynamics of LRIMs with power-law and Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions are systematically investigated. For the power-law model, we investigate the modulation of the estimated critical temperature by the decay exponent σ and coupling cutoff radius R. For the RKKY model, we reproduce diverse ordered states induced by complex competing long-range interactions. A proof-of-principle experiment demonstrates the physical feasibility of our approach. This framework broadens the class of many-body systems accessible to the SPIM platform.
ER -