| 摘要: |
| Lyapunov equation is one of the most basic and important equations in control theory, which has various applications in, e.g., stability analysis and robust analysis of linear control systems. Inspired by the recent progresses of quantum algorithms, we find that solving Lyapunov equation can be exponentially accelerated by quantum algorithms rather than traditional classical algorithms. Our algorithm is more efficient especially when the system matrix is sparse and has a low condition number. The results presented in this paper open up new dimensions of research in controlling classical system by quantum information processors, which has rarely been considered in the existing literature. |
| 关键词: Quantum control, linear Lyapunov equation, large-scale complex system |
| DOI： |
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| 基金项目: |
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| Solving Lyapunov equation by quantum algorithm |
| H. Sun,J. Zhang |
| (Department of Automation, Tsinghua University, Beijing 100084, China) |
| Abstract: |
| Lyapunov equation is one of the most basic and important equations in control theory, which has various applications in, e.g., stability analysis and robust analysis of linear control systems. Inspired by the recent progresses of quantum algorithms, we find that solving Lyapunov equation can be exponentially accelerated by quantum algorithms rather than traditional classical algorithms. Our algorithm is more efficient especially when the system matrix is sparse and has a low condition number. The results presented in this paper open up new dimensions of research in controlling classical system by quantum information processors, which has rarely been considered in the existing literature. |
| Key words: Quantum control, linear Lyapunov equation, large-scale complex system |
