Feedback exponential stabilization of stochastic quantum systems based on state space division

Abstract

In this paper, the global exponential stabilization of two-level stochastic quantum systems is achieved by using measurement-based feedback strategies, including state feedback and noise-assisted feedback, and the state convergence rate is improved by dividing the state space into multiple subspaces and using different feedback controls in different state subspaces. For both the combination of two continuous noise-assisted feedback and the combination of state feedback and noise-assisted feedback, the state space is divided based on the comparison of real-time state convergence rate under different measurement-based feedback strategies, respectively. The global exponential convergence and the effect of dividing state space in improving state convergence rate for two-level quantum systems are proved in theory and verified in numerical simulations.