Accelerating Feedback-based Algorithms for Quantum Optimization Using Gradient Descent

Feedback-based methods, built on Quantum Lyapunov Control (QLC), have gained significant attention as an alternative training paradigm for Variational Quantum Algorithms (VQAs) in solving combinatorial optimization problems such as MAX-CUT. These methods aim to reduce the training overhead associated with VQAs, and can mitigate barren plateaus. QLC methods often require long control sequences, and may show sensitivity to the evolution timestep, which can result in slow convergence compared to gradient-based VQA approaches. In this work, we address these challenges by proposing a hybrid method that incorporates per-layer gradient estimation to accelerate the convergence of QLC while preserving its low training overhead and stability guarantees. By leveraging layer-wise gradient information, our approach selects improved control parameters and achieves faster convergence rates compared to common QLC methods such as FALQON. We validate our algorithm through various empirical studies across a range of problem instances and optimization settings. We empirically show our algorithm's robustness against noise and variations in the timestep parameter. We also demonstrate a parameter initialization scheme for QAOA using our method that can lead to improved solution quality.