Differentiable Quantum Computing for Large-scale Linear Control
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909376967606272 |
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| author | Clayton, Connor Leng, Jiaqi Yang, Gengzhi Qiao, Yi-Ling Lin, Ming C. Wu, Xiaodi |
| author_facet | Clayton, Connor Leng, Jiaqi Yang, Gengzhi Qiao, Yi-Ling Lin, Ming C. Wu, Xiaodi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_01391 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Differentiable Quantum Computing for Large-scale Linear Control Clayton, Connor Leng, Jiaqi Yang, Gengzhi Qiao, Yi-Ling Lin, Ming C. Wu, Xiaodi Quantum Physics Emerging Technologies Machine Learning Numerical Analysis Optimization and Control 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. |
| title | Differentiable Quantum Computing for Large-scale Linear Control |
| topic | Quantum Physics Emerging Technologies Machine Learning Numerical Analysis Optimization and Control |
| url | https://arxiv.org/abs/2411.01391 |