Finite-time stabilization control of quantum systems

Bo Bo

Zu-En Su, Sen Kuang, Daoyi Dong

In this paper, a novel continuous non-smooth control strategy is proposed to achieve finite-time stabilization of ladder quantum systems. We first design a universal fractional-order control law for a ladder n-level quantum system using a distance-based Lyapunov function, and then apply the Filippov solution in the sense of differential inclusions and the LaSalle's invariance principle to prove the existence and uniqueness of the solution of the ladder system under the continuous non-smooth control law. Both asymptotic stability and finite-time stability for the ladder system is rigorously established by applying Lyapunov stability theory and finite-time stability criteria. We also derive an upper bound of the time required for convergence to an eigenstate of the intrinsic Hamiltonian. Numerical simulations on a rubidium ladder three-level atomic system validate the effectiveness of the proposed method.

Xiaolei Li, Changyun Wen, Jian‐Ge Wang

In this paper, we consider the fixed-time stabilization control problem of quantum systems modeled by Schrödinger equations. Firstly, the Lyapunov-based fixed-time stability criterion is extended to finite-dimensional closed quantum systems in the form of coherence vectors. Then for a two-level quantum system with single control input, a non-smooth fractional-order control law is designed using the relative state distance. By integrating the fixed-time Lyapunov control technique and the bi-limit homogeneity theory, the quantum system is proved to be stabilized to an eigenstate of the inherent Hamiltonian in a fixed time. Comparing with existing methods in quantum system control, the proposed approach can guarantee stabilization in a fixed time without depending on the initial states.

M. R. James

Eram Taslima, Shyam Kamal, Ram Khelawan Saket

Robustness is a major issue in the stabilization control of quantum systems. A practical quantum system is often exposed to uncertainties and disturbances in external fields and system Hamiltonian. Sliding mode control is a powerful tool in designing robust control for classical systems to mitigate the effect of disturbances. This paper leverages the sliding mode control technique to design a finite-time reaching law for two-level quantum systems in the presence of uncertainties in the system Hamiltonian. A numerical example is presented to showcase the effectiveness of the theoretical results. This research contributes to advancing the robust control techniques for quantum systems, paving the way for enhanced stability in quantum computing and quantum information processing applications.

Hendra I. Nurdin, Naoki Yamamoto