Optimal FALQON for Quantum Approximate Optimization via Layer-wise Parameter Tuning

Abstract

Feedback-based adaptive quantum optimization (FALQON) is a promising approach for combinatorial optimization on noisy intermediate-scale quantum devices, but prior studies report that standard fixed-parameter schedules can require relatively deep circuits to reach strong solution quality. We study Optimal FALQON, a layer-wise formulation that treats the time-step ${\delta }_k$ and scaling parameter $w_k$ as classical decision variables optimized per layer. The benchmark uses all 94 non-isomorphic 3-regular graphs with 12 vertices under 8192-shot simulation and compares standard FALQON, Optimal FALQON, and QAOA/QAOA-MA Powell runs warm-started from FALQON-derived schedules. Across approximation ratio, success probability, evaluation-normalized efficiency, and layer-normalized efficiency, Optimal FALQON substantially improves on standard FALQON, and Optimal-FALQON warm starts substantially improve on standard-FALQON warm starts.