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

TL;DR

This paper introduces Optimal FALQON, an adaptive quantum optimization method that optimizes layer-wise parameters to improve convergence speed and success probability on NISQ devices.

Contribution

It formulates FALQON as an optimization problem over hyperparameters, leading to significant empirical improvements over standard methods.

Findings

Optimal FALQON outperforms standard FALQON and QAOA variants in success probability.

It reduces the number of layers needed for acceptable solutions.

Initializing QAOA with Optimal FALQON parameters enhances warm-start performance.

Abstract

Feedback-based adaptive quantum optimization (FALQON) is a promising approach for solving combinatorial problems on noisy intermediate-scale quantum (NISQ) devices, requiring only single circuit evaluations per layer. However, standard FALQON relies on fixed hyperparameters that severely limit convergence speed, requiring hundreds to thousands of layers for acceptable solutions. This paper proposes Optimal FALQON, an optimization-based formulation that treats the per-layer time step ($\delta_k$) and scaling factor ($M_k$) as decision variables optimized via classical methods. We present a comprehensive empirical study on all 94 non-isomorphic 3-regular graphs with 12 vertices, comparing Optimal FALQON with standard FALQON and multiple QAOA variants. Results demonstrate statistically significant improvements in success probability, evaluation efficiency, and depth-normalized cost across the evaluated benchmarks. Furthermore, initializing QAOA with parameters from Optimal FALQON yields superior warm-start performance compared to fixed initialization.