Differentiable Quantum Computing for Large-scale Linear Control

TL;DR

This paper presents a quantum algorithm for large-scale linear control that offers super-quadratic speedups over classical methods, utilizing a novel quantum subroutine and differentiable simulation for efficient gradient estimation.

Contribution

It introduces the first end-to-end quantum algorithm for linear-quadratic control with provable quantum advantage and a quantum-assisted differentiable simulator for improved gradient estimation.

Findings

Achieves super-quadratic speedup over classical methods

Develops a quantum subroutine for solving matrix Lyapunov equations

Provides a more accurate and robust gradient estimation method

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.