Scalable and Near-Optimal Discrete Phase Shift Optimization for Reconfigurable Intelligent Surfaces with Over 20,000 Elements

TL;DR

This paper introduces a CIM-based optimization framework for large-scale RIS with over 20,000 elements, enabling efficient discrete phase shift optimization and near-optimal beam pattern formation.

Contribution

It formulates RIS phase optimization as a quadratic Ising model and demonstrates hardware-based solutions for large-scale problems with improved scalability.

Findings

Successfully optimized RIS with over 22,000 elements using CIM.

Achieved physically consistent beam patterns in various environments.

Introduced spin-size reduction for scalable optimization without performance loss.

Abstract

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.