Quantum Optimization for Electromagnetics: Physics-Informed QAOA for Reconfigurable Intelligent Surfaces

Optimizing Reconfigurable Intelligent Surfaces (RIS) is a high-dimensional combinatorial challenge. Current quantum algorithms often simplify this problem by ignoring physical constraints like mutual coupling, which significantly degrades real-world performance. Rather than targeting a fully realistic RIS description, we embed progressively more physics-informed models of mutual coupling into Quadratic Unconstrained Binary Optimization (QUBO) formulations. We evaluate four Ising interaction models (Jij) for the Quantum Approximate Optimization Algorithm (QAOA), ranging from idealized phase-only to fully dense physical models. Analyzing a 5 × 5 grid, our results expose a critical trade-off between spatial pointing accuracy and quantum hardware feasibility. While complete global coupling maximizes beamforming precision, dense Hamiltonians introduce prohibitive routing overhead and complicate convergence on near-term processors. Ultimately, we demonstrate that while physics-informed quantum optimization is mathematically viable, sparse, distance-penalized models remain a necessary compromise for execution on current noisy intermediate-scale quantum (NISQ) devices.