The spatial-photonic Ising machine (SPIM) [D. Pierangeli et al., Phys. Rev. Lett. 122, 213902 (2019)] is a promising optical architecture utilizing spatial light modulation for solving large-scale combinatorial optimization problems efficiently. However, the SPIM can accommodate Ising problems with only rank-one interaction matrices, which limits its applicability to various real-world problems. In this Letter, we propose a new computing model for the SPIM that can accommodate any Ising problem without changing its optical implementation. The proposed model is particularly efficient for Ising problems with low-rank interaction matrices, such as knapsack problems. Moreover, the model acquires learning ability and can thus be termed a spatial-photonic Boltzmann machine (SPBM). We demonstrate that learning, classification, and sampling of the MNIST handwritten digit images are achieved efficiently using SPBMs with low-rank interactions. Thus, the proposed SPBM model exhibits higher practical applicability to various problems of combinatorial optimization and statistical learning, without losing the scalability inherent in the SPIM architecture.

翻译：空间光子伊辛机（SPIM）[D. Pierangeli 等，Phys. Rev. Lett. 122, 213902 (2019)] 是一种利用空间光调制高效求解大规模组合优化问题的有前途的光学架构。然而，SPIM 仅能容纳具有秩为一的交互矩阵的伊辛问题，这限制了其对各类现实问题的适用性。本文提出了一种适用于 SPIM 的新计算模型，该模型无需改变其光学实现即可容纳任意伊辛问题。该模型特别适用于具有低秩交互矩阵的伊辛问题，例如背包问题。此外，该模型具备学习能力，因此可称为空间光子玻尔兹曼机（SPBM）。我们证明了利用具有低秩交互的 SPBM 能够高效实现 MNIST 手写数字图像的学习、分类和采样。因此，所提出的 SPBM 模型在保持 SPIM 架构固有可扩展性的同时，对各类组合优化与统计学习问题展现出更高的实际适用性。