Yuto Hama, Daisuke Kitayama, Kensuke Inaba et al.
This paper proposes a novel optimization framework for discrete phase shifts of a reconfigurable intelligent surface (RIS) using a coherent Ising machine (CIM). Unlike conventional methods based on iterative convex approximation or combinatorial search with exponentially increasing complexity, the CIM physically explores the solution space of Ising Hamiltonians through collective mode competition in a network of optical oscillators, enabling efficient large-scale discrete optimization. We formulate the RIS discrete phase optimization problem as a quadratic Ising model, which supports both binary and quaternary phase shifts by appropriately mapping quantized phase states to spin variables. Using a real hardware CIM, we experimentally solve quadratic optimization problems for RISs with up to 22,201 elements. The results demonstrate that the proposed method achieves physically consistent beam patterns under both line-of-sight and non-line-of-sight environments and attains the theoretical gain when transitioning from binary to quaternary phase shift. To further enhance scalability, we introduce a spin-size reduction approach that removes spins deterministically fixed by dominant channel components. This technique efficiently reduces the problem size for CIM in line-of-sight conditions without performance loss. These results confirm that CIM-based optimization offers a practical and highly scalable solution for large RIS deployments with discrete phase shift constraints.