Quantum-hardware spectral co-design framework for multifrequency Rydberg electrometry

This paper presents a spectral co-design framework for multifrequency Rydberg electrometry that directly couples a fabrication-constrained simultaneous perturbation stochastic approximation (SPSA)-Adam optimizer with full-wave finite-element eigenmode simulations. The method enables quantum hardware engineering without requiring analytical or adjoint gradients, operating over discrete design spaces. The approach addresses the general challenge of designing electromagnetic hardware to satisfy quantum-defined spectral constraints.