Efficient computation using spatial-photonic Ising machines with low-rank and circulant matrix constraints

Spatial-photonic Ising machines (SPIMs) have shown promise as an energy-efficient Ising machine, but currently can only solve a limited set of Ising problems. There is currently limited understanding on what experimental constraints may impact the performance of SPIM, and what computationally intensive problems can be efficiently solved by SPIM. 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 the low-rank approximation in optimisation tasks, particularly in financial optimisation, to demonstrate the real-world applications of SPIMs. Finally, we evaluate the computational limitations imposed by SPIM hardware precision and suggest strategies to optimise the performance of these systems within these constraints.