Accelerating Feedback-based Algorithms for Quantum Optimization Using Gradient Descent
This work addresses a bottleneck in quantum optimization for combinatorial problems like MAX-CUT, offering an incremental improvement to existing feedback-based methods.
The paper tackles the problem of slow convergence in feedback-based quantum optimization methods like Quantum Lyapunov Control (QLC) for QAOA, by proposing a hybrid approach that uses per-layer gradient estimation to accelerate convergence while maintaining low training overhead and stability, resulting in significantly faster convergence and improved robustness as validated through numerical experiments.
Feedback-based methods have gained significant attention as an alternative training paradigm for the Quantum Approximate Optimization Algorithm (QAOA) in solving combinatorial optimization problems such as MAX-CUT. In particular, Quantum Lyapunov Control (QLC) employs feedback-driven control laws that guarantee monotonic non-decreasing objective values, can substantially reduce the training overhead of QAOA, and mitigate barren plateaus. However, these methods might require long control sequences, leading to sub-optimal convergence rates. In this work, we propose 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, the proposed approach selects near-optimal control parameters, resulting in significantly faster convergence and improved robustness. We validate the effectiveness of the method through extensive numerical experiments across a range of problem instances and optimization settings.