用梯度信息加速量子优化反馈算法，提升收敛速度与稳定性。
Accelerating Feedback-based Algorithms for Quantum Optimization Using Gradient Descent
- 结合每层梯度估计，动态选择最优控制参数。
- 实验显示收敛速度显著加快，且保持低训练开销。
- 适合需要快速稳定优化的量子计算应用者。
反馈式方法作为求解组合优化问题（如MAX-CUT）中量子近似优化算法（QAOA）的一种替代训练范式，近年来受到广泛关注。其中，量子李雅普诺夫控制（QLC）通过反馈驱动的控制律，保证目标值单调不减，能显著降低QAOA的训练开销并缓解贫瘠平原问题。然而，这类方法可能需要较长的控制序列，导致收敛速率不足。本文提出一种混合方法，引入逐层梯度估计以加速QLC的收敛，同时保留其低训练开销和稳定性保障。通过利用层间梯度信息，所提方法可选取近似最优控制参数，实现更快收敛与更强鲁棒性。我们在多种问题实例与优化设置下进行了广泛数值实验，验证了该方法的有效性。
原文摘要 · Abstract (English)
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.
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