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Spatial-photonic Boltzmann machines: low-rank combinatorial optimization and statistical learning by spatial light modulation
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.Comment: 7 pages, 5 figures (with a 3-page supplemental
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