量子算法实现大规模线性控制，效率远超经典方法。
Differentiable Quantum Computing for Large-scale Linear Control
- 用量子子程序求解李雅普诺夫方程，构建可微分仿真器。
- 相比经典方法实现超二次加速，精度与鲁棒性更优。
- 首个证明有量子优势的端到端线性控制量子方案，适合控制领域研究者。
随着工业模型与设计日益复杂，对大规模动态系统最优控制的需求显著上升。然而，传统最优控制方法在问题维度增大时计算开销急剧增加。本文提出一种端到端的量子算法，用于线性-二次控制，并实现了可证明的加速优势。该算法基于策略梯度方法，引入一种新颖的量子子程序来求解矩阵李雅普诺夫方程。我们构建了量子辅助的可微分模拟器，用于高效梯度估计，其准确性和鲁棒性优于依赖随机近似的经典方法。与经典方法相比，本方法实现超二次加速。据我们所知，这是首个在大规模线性控制问题上实现可证明量子优势的端到端量子应用。
原文摘要 · Abstract (English)
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.
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