As industrial models and designs grow increasingly complex, the demand for optimal control of large-scale dynamical systems has significantly increased. However, traditional methods for optimal control incur significant overhead as problem dimensions grow. In this paper, we introduce an end-to-end quantum algorithm for linear-quadratic control with provable speedups. Our algorithm, based on a policy gradient method, incorporates a novel quantum subroutine for solving the matrix Lyapunov equation. Specifically, we build a quantum-assisted differentiable simulator for efficient gradient estimation that is more accurate and robust than classical methods relying on stochastic approximation. Compared to the classical approaches, our method achieves a super-quadratic speedup. To the best of our knowledge, this is the first end-to-end quantum application to linear control problems with provable quantum advantage.

翻译：随着工业模型和设计日益复杂，对大规模动态系统最优控制的需求显著增加。然而，传统的最优控制方法在问题维度增长时会产生显著的开销。本文提出了一种用于线性二次控制的端到端量子算法，并证明了其加速优势。我们的算法基于策略梯度方法，引入了一种新颖的量子子程序来求解矩阵李雅普诺夫方程。具体而言，我们构建了一个量子辅助的可微分模拟器，用于高效梯度估计，其精度和鲁棒性均优于依赖随机近似的经典方法。与经典方法相比，我们的方法实现了超二次加速。据我们所知，这是首个针对线性控制问题、具有可证明量子优势的端到端量子应用。