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.

通过开发和评估先进的分解技术，我们扩大了空间光子伊辛机 (SPIMs) 所能解决的问题范围，克服了传统 Mattis 型矩阵的局限性。我们探讨了低秩近似在优化任务中的实际收益，特别是在金融优化中，以展示 SPIMs 的实际应用。最后，我们评估了 SPIM 硬件精度所带来的计算限制，并提出优化系统性能的策略。