Finite-time stabilization control of quantum systems.

This paper proposes a non-smooth control scheme to achieve finite-time convergence to an eigenstate of the internal Hamiltonian of a given closed quantum system. First, we define finite-time stability for quantum systems, and then present a Lyapunov stability criterion to identify the finite-time stability of quantum systems. Second, we propose a new non-smooth control law for two-level quantum systems by selecting a distance between quantum states as a Lyapunov function and using the Lyapunov stability theory, and prove the existence and uniqueness of solutions of the quantum system under the action of the non-smooth controller in the framework of Bloch vectors. Further, an equivalent transformation is made for the system model and the control target by expressing quantum states in terms of complex exponentials, and the finite-time stability of the system is proved by combining the finite-time Lyapunov stability criterion with the homogeneity theorem. Finally, we perform numerical simulations on a spin-1/2 particle system and demonstrate the effectiveness of the finite-time stabilization control scheme.