Differentiable Quantum Computing for Large-scale Linear Control
Connor Clayton, Jiaqi Leng, Gengzhi Yang, Yi-Ling Qiao, Ming Lin, Xiaodi Wu
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.
BibTeX
@inproceedings{
clayton2024differentiable,
title={Differentiable Quantum Computing for Large-scale Linear Control},
author={Connor Clayton and Jiaqi Leng and Gengzhi Yang and Yi-Ling Qiao and Ming Lin and Xiaodi Wu},
booktitle={The Thirty-eighth Annual Conference on Neural Information Processing Systems},
year={2024},
url={https://openreview.net/forum?id=GHqw3xLAvd}
}