Lyapunov control methods of closed quantum systems |
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Authors: | Sen Kuang [Author Vitae] Shuang Cong [Author Vitae] |
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Affiliation: | a Department of Automation, University of Science and Technology of China, Hefei 230027, PR China b Key Laboratory of Quantum Information, USTC, Chinese Academy of Sciences, Hefei 230026, PR China |
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Abstract: | According to special geometric or physical meanings, the paper summarizes three Lyapunov functions in controlling closed quantum systems and their controller designing processes. Specially, for the average value-based method, the paper gives the generalized condition of the largest invariant set in the original reference and develops the construction method of the imaginary mechanical quantity; for the error-based method, this paper gives its strict mathematical proof train of thought on the asymptotic stability and the corresponding physical meaning. Also, we study the relations among the three Lyapunov functions and give a unified form of these Lyapunov functions. Finally, we compare the control effects of three Lyapunov methods by doing some simulation experiments. |
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Keywords: | Quantum system Feedback control Lyapunov function Asymptotic stability |
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