Rapid stabilization of time delay stochastic quantum systems based on continuous measurement feedback

Abstract

Based on continuous measurement feedback, this paper addresses the rapid stabilization of eigenstates and Bell states for stochastic quantum systems, in which the time of computing control input is considered by using time delay control. For the rapidity of quantum state stabilization, a Lyapunov-LaSalle-like theorem is proposed, based on which the state space is divided into two subspaces, and two Lyapunov functions are constructed to be applied in the corresponding subspace. The desired target state is located in one subspace, while other equilibria are contained in the other subspace. The controls of rapidly stabilizing target state are designed based on the two Lyapunov functions, which can make sure the system trajectories only transit through the boundary between the two subspaces no more than 2 times from any initial state so that the stabilization time is shortened. The rapidity is proved, and numerical simulations are also performed to verify the rapidity by comparing with the existing controls in related literature.