Finite-time stabilization control of quantum systems

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.Comment: 9 pages, 3 figure

Learning control of quantum systems using frequency-domain optimization algorithms

We investigate two classes of quantum control problems by using frequency-domain optimization algorithms in the context of ultrafast laser control of quantum systems. In the first class, the system model is known and a frequency-domain gradient-based optimization algorithm is applied to searching for an optimal control field to selectively and robustly manipulate the population transfer in atomic Rubidium. The other class of quantum control problems involves an experimental system with an unknown model. In the case, we introduce a differential evolution algorithm with a mixed strategy to search for optimal control fields and demonstrate the capability in an ultrafast laser control experiment for the fragmentation of Pr(hfac)$_3$ molecules.Comment: 11 pages, 11 figure