Rapid Lyapunov control for decoherence-free subspaces of Markovian open quantum systems

A Lyapunov-based rapid control scheme is proposed to drive a Markovian open quantum system to a decoherence-free subspace by constructing the control Hamiltonians of the system. Based on Lyapunov theory, we design a general form of control laws, which includes the standard Lyapunov control law. The convergence of the control system to the decoherence-free subspace is strictly proved. By analyzing the relationship between the LaSalle invariant set and the decoherence-free subspace, we propose a construction method for the control Hamiltonians to further speed up the control process. Simulation experiments on a three-level quantum system demonstrate that the rapid Lyapunov control scheme proposed in this paper has a good control performance.