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IEEE Conference on Cybernetics and Intelligent Systems

Lyapunov-based feedback control of two-level stochastic open quantum systems

Shahid Qamar, Shuang Cong, Bilal Riaz

Published Nov 1, 2017• 6 citations
Publisher

Abstract

In this paper, a Lyapunov-based feedback control (LFC) is proposed for the state transfer of a two-level stochastic quantum system. The quantum state is described in the Cartesian coordinate system. An exponential function is selected as the Lyapunov function to ensure the stability of the system. The Lyapunov-based feedback control strategy is designed according to the stochastic Lyapunov stability theorem. Numerical simulations results show that the proposed LFC strategy has the ability to transfer the stochastic system from any initial mixed state to the desired eigenstate, and the LFC has high convergence rate and high state transfer fidelity.

DOI
10.1109/iccis.2017.8274747

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A quantum state feedback control method is proposed in this paper. The state of a two-level open quantum system is estimated online based on the continuous weak measurement and the compressed sensing theory. Based on the state estimated online and the Lyapunov stability theorem, the state feedback control law used to transfer the quantum state is designed. Moreover, three numerical simulation experiments are implemented in the MATLAB environment: the state transfer from eigenstates to eigenstates, superposition states to superposition states, and superposition states to mixed states. The experimental results verify high performance of the proposed feedback control based on the state estimated online.
We propose a novel control strategy by combining state feedback and noise-assisted feedback to exponentially stabilize the target eigenstate for two-level stochastic quantum systems in this paper. The state space is divided into two subspaces, and the state feedback and noise-assisted feedback work in the corresponding subspace, respectively, to achieve the faster state convergence than that of using the two feedback strategies individually. Two kinds of continuous noise-assisted feedback controls are used to form the combined feedback strategies, respectively, and the exponential stabilization of target eigenstate is proved. The effectiveness and superiority of the combined feedback strategies are also verified in numerical simulations.
We propose a novel control strategy by combining state feedback and noise-assisted feedback to exponentially stabilize the target eigenstate for two-level stochastic quantum systems in this paper. The state space is divided into two subspaces, and the state feedback and noise-assisted feedback work in the corresponding subspace, respectively, to achieve the faster state convergence than that of using the two feedback strategies individually. Two kinds of continuous noise-assisted feedback controls are used to form the combined feedback strategies, respectively, and the exponential stabilization of target eigenstate is proved. The effectiveness and superiority of the combined feedback strategies are also verified in numerical simulations.
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