Differentiable Quantum Computing for Large-scale Linear Control
Abstract
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.
Cite
@article{arxiv.2411.01391,
title = {Differentiable Quantum Computing for Large-scale Linear Control},
author = {Connor Clayton and Jiaqi Leng and Gengzhi Yang and Yi-Ling Qiao and Ming C. Lin and Xiaodi Wu},
journal= {arXiv preprint arXiv:2411.01391},
year = {2024}
}