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. The primitive version of the SPIM, however, can accommodate Ising problems with only rank-one interaction matrices. 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, it acquires the learning ability of Boltzmann machines. We demonstrate that learning, classification, and sampling of the MNIST handwritten digit images are achieved efficiently using the model with low-rank interactions. Thus, the proposed 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等人，《物理评论快报》122, 213902 (2019)]是一种利用空间光调制的有前景的光学架构，可高效求解大规模组合优化问题。然而，原始版本的SPIM仅能处理秩为一的相互作用矩阵的伊辛问题。在本快报中，我们提出一种针对SPIM的新型计算模型，该模型无需改变其光学实现即可处理任意伊辛问题。所提出的模型对于低秩相互作用矩阵的伊辛问题（如背包问题）尤为高效。此外，它还具备玻尔兹曼机的学习能力。我们证明，利用该低秩相互作用模型可高效实现MNIST手写数字图像的训练、分类与采样。因此，所提出的模型在不牺牲SPIM架构固有可扩展性的前提下，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。