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On Exponential Stabilization of Spin-1/2 Systems

Abstract : In this paper, we study the stabilization problem of quantum spin-1/2 systems under continuous-time measurements. In the case without feedback, we show exponential stabilization around the excited and ground state by providing a lower bound of the convergence rate. Based on stochastic Lyapunov techniques, we propose a parametrized measurement-based feedback which ensures exponential convergence toward the excited state. Moreover, we give a lower bound of the convergence rate for this case. Then, we discuss the effect of each parameter appeared in the control law in the convergence rate. Finally, we illustrate the efficiency of such feedback law through simulations.
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Submitted on : Wednesday, November 27, 2019 - 6:10:18 PM
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  • HAL Id : hal-02010846, version 1
  • ARXIV : 1803.10632

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Weichao Liang, Nina Amini, Paolo Mason. On Exponential Stabilization of Spin-1/2 Systems. 57th IEEE Conference on Decision and Control (CDC 2018), Dec 2018, Miami, United States. ⟨hal-02010846⟩

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