Low-rank combinatorial optimization and statistical learning by spatial photonic Ising machine

TL;DR

This paper introduces a new model for the spatial photonic Ising machine that handles any Ising problem, especially low-rank ones, and incorporates learning capabilities for tasks like image classification, enhancing its practical utility.

Contribution

The paper presents a novel computing model for SPIM that extends its capability to general Ising problems and integrates Boltzmann machine learning features.

Findings

Efficiently solves low-rank Ising problems like knapsack.

Achieves learning, classification, and sampling of MNIST images.

Maintains scalability of the original SPIM architecture.

Abstract

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.