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

2026-05-08

AI Summary

This work addresses the slow convergence of standard FALQON, which typically requires hundreds to thousands of layers to yield feasible solutions due to fixed hyperparameters. The authors propose the first approach that treats the time step and scaling factor at each FALQON layer as optimizable variables, adaptively tuning them via classical optimization algorithms. This adaptive strategy is leveraged to provide an efficient warm-start initialization for QAOA. By integrating feedback-based adaptive quantum optimization, classical optimization, and the QAOA framework, the method significantly enhances solution efficiency for combinatorial optimization problems on NISQ devices. Experiments on 94 twelve-vertex 3-regular graphs demonstrate clear advantages over standard FALQON and several QAOA variants in terms of success probability, evaluation efficiency, and depth-normalized cost.

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 ($δ_k$) 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.

Problem

• FALQON
• combinatorial optimization
• NISQ
• convergence speed
• quantum optimization

Innovation

• Optimal FALQON
• layer-wise parameter tuning
• quantum approximate optimization
• NISQ devices
• QAOA warm-start