Efficient Computation Using Spatial-Photonic Ising Machines: Utilizing Low-Rank and Circulant Matrix Constraints

TL;DR

This paper investigates how spatial-photonic Ising machines can efficiently solve complex optimization problems with low-rank and circulant matrices, expanding their applicability beyond traditional limitations.

Contribution

It introduces advanced decomposition techniques to enhance SPIM capabilities for a wider range of coupling matrices, including low-rank and circulant types, and assesses hardware precision impacts.

Findings

SPIM performance depends on matrix rank and precision.

Decomposition methods improve problem-solving range of SPIMs.

Low-rank approximations benefit real-world optimization tasks.

Abstract

We explore the potential of spatial-photonic Ising machines (SPIMs) to address computationally intensive Ising problems that employ low-rank and circulant coupling matrices. Our results indicate that the performance of SPIMs is critically affected by the rank and precision of the coupling matrices. By developing and assessing advanced decomposition techniques, we expand the range of problems SPIMs can solve, overcoming the limitations of traditional Mattis-type matrices. Our approach accommodates a diverse array of coupling matrices, including those with inherently low ranks, applicable to complex NP-complete problems. We explore the practical benefits of low-rank approximation in optimization tasks, particularly in financial optimization, to demonstrate the real-world applications of SPIMs. Finally, we evaluate the computational limitations imposed by SPIM hardware precision and suggest strategies to optimize the performance of these systems within these constraints.