Dynamic Smoothing of Optimization Landscapes via High-Frequency Parametric Forcing in Hybrid Analog Computing

This work presents a theoretical framework for accelerating optimization dynamics in analog and hybrid quantum-classical systems using high-frequency parametric forcing. We model continuous-time optimization as overdamped Langevin dynamics in a rugged energy landscape. Using the method of multiple scales, we show that fast oscillatory forcing induces an effective renormalization of high-spatial-frequency components of the potential via a Bessel function dependence. This mechanism selectively suppresses local ruggedness while preserving the global structure of the landscape, leading to a reduction in effective barrier heights and a significant acceleration of escape dynamics. The model predicts a crossover from thermally activated, trap-dominated dynamics to a faster, drift-dominated regime as the forcing amplitude approaches a critical threshold. This work provides a physically motivated mechanism for improving convergence behavior in analog and hybrid optimization systems.