Finite-time stabilization control of quantum systems

TL;DR

This paper develops a finite-time stabilization control method for quantum systems, introducing a Lyapunov criterion, a non-smooth control law, and demonstrating effectiveness through numerical simulations on a spin-1/2 system.

Contribution

It presents a novel finite-time control approach for quantum systems using a Lyapunov criterion and a non-smooth control law with proven convergence.

Findings

Finite-time convergence to eigenstates demonstrated

Control law ensures system stability within finite time

Numerical results validate the proposed method

Abstract

The finite-time control problem of quantum systems is investigated in this paper. We first define finite-time stability and present a finite-time Lyapunov stability criterion for finite-dimensional quantum systems in coherence vector representation. Then, for two-level quantum systems, we design a continuous non-smooth control law with a state-dependent fractional power and prove the uniqueness of solutions of the system dynamics with the controller via the concept of transversality. By combining the finite-time Lyapunov stability criterion with the homogeneity theory, the finite-time convergence of the system to an eigenstate of its internal Hamiltonian is proved. Numerical results on a spin-1/2 system demonstrate the effectiveness of the proposed finite-time stabilization control scheme.