# Differentiable Quantum Computing for Large-scale Linear Control

arXiv: https://arxiv.org/abs/2411.01391 · HTML: https://mlsanity.com/paper/2411.01391/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 59 references that are in the map.
- First posted on arXiv 3 Nov 2024.

## Builds on (most cited first, 23 of 23)

- [DiffTaichi: Differentiable Programming for Physical Simulation](https://mlsanity.com/paper/1910.00935/) (2019)
- [Global Convergence of Policy Gradient Methods for the Linear Quadratic Regulator](https://mlsanity.com/paper/1801.05039/) (2018)
- [On the Sample Complexity of the Linear Quadratic Regulator](https://mlsanity.com/paper/1710.01688/) (2017)
- [Learning Without Mixing: Towards A Sharp Analysis of Linear System Identification](https://mlsanity.com/paper/1802.08334/) (2018)
- [Accelerated Policy Learning with Parallel Differentiable Simulation](https://mlsanity.com/paper/2204.07137/) (2022)
- [gradSim: Differentiable simulation for system identification and visuomotor control](https://mlsanity.com/paper/2104.02646/) (2021)
- [Do Differentiable Simulators Give Better Policy Gradients?](https://mlsanity.com/paper/2202.00817/) (2022)
- [Online Linear Quadratic Control](https://mlsanity.com/paper/1806.07104/) (2018)
- [An End-to-End Differentiable Framework for Contact-Aware Robot Design](https://mlsanity.com/paper/2107.07501/) (2021)
- [Convergence and sample complexity of gradient methods for the model-free linear quadratic regulator problem](https://mlsanity.com/paper/1912.11899/) (2019)
- [FluidLab: A Differentiable Environment for Benchmarking Complex Fluid Manipulation](https://mlsanity.com/paper/2303.02346/) (2023)
- [Efficient Differentiable Simulation of Articulated Bodies](https://mlsanity.com/paper/2109.07719/) (2021)
- [The power of block-encoded matrix powers: improved regression techniques via faster Hamiltonian simulation](https://mlsanity.com/paper/1804.01973/) (2018)
- [Quantum SDP-Solvers: Better upper and lower bounds](https://mlsanity.com/paper/1705.01843/) (2017)
- [Rethinking Optimization with Differentiable Simulation from a Global Perspective](https://mlsanity.com/paper/2207.00167/) (2022)
- [Quantum Policy Iteration via Amplitude Estimation and Grover Search -- Towards Quantum Advantage for Reinforcement Learning](https://mlsanity.com/paper/2206.04741/) (2022)
- [Quantum Reinforcement Learning via Policy Iteration](https://mlsanity.com/paper/2203.01889/) (2022)
- [Near-Optimal Quantum Algorithms for Multivariate Mean Estimation](https://mlsanity.com/paper/2111.09787/) (2021)
- [Differentiable Hybrid Traffic Simulation](https://mlsanity.com/paper/2210.08046/) (2022)
- [Quantum Interior Point Methods for Semidefinite Optimization](https://mlsanity.com/paper/2112.06025/) (2021)
- [Differentiable Analog Quantum Computing for Optimization and Control](https://mlsanity.com/paper/2210.15812/) (2022)
- [Improved quantum algorithms for linear and nonlinear differential equations](https://mlsanity.com/paper/2202.01054/) (2022)
- [Efficient Quantum Algorithms for Quantum Optimal Control](https://mlsanity.com/paper/2304.02613/) (2023)

## Abstract (arXiv)

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.