The Ising model serves as a powerful tool for solving combinatorial optimization problems by searching the ground states of spin systems. However, the demand for computing power increases exponentially with spin system size expansion, which electronic processors rarely address due to their inherent limitations arising from the separation between storage and computation. Ising machines realized with photons instead of electrons have demonstrated significant potential in tackling large-scale combinatorial optimization problems. Among various routes, the spatial photonic Ising machine (SPIM) stands out as one of the most promising approaches due to its unique advantages in scalability and parallelism. However, the computational accuracy of SPIM is typically not high because of its analog nature, which severely hampers the further expansion of the spin system size. In this paper, we first establish a comprehensive physical model for the SPIM under various aberration conditions, and then propose a method that integrates aberration correction with a dynamic-cluster-flipping iterative algorithm to effectively enhance computational accuracy and, consequently, greatly expand the spin system size of the SPIM. Our results demonstrate that the enhanced SPIM can effectively emulate the ground-state search dynamics of fully connected nonuniform coupling Ising models with up to 360 000 spins. Furthermore, the proposed approach achieves faster convergence to the ground state with high accuracy.

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• Analog computation
• Optical coherence
• Optimization problems
• Photonics
• Spatial light modulators
• Combinatorics
• Ising model
• Optical computing