Feedback Stabilization Control Of Stochastic Quantum Systems Based On Switching Strategies

In recent decades,more and more attention has been paid to research on quantum control.In quantum control,rapid control of quantum systems is particularly important since it can greatly recduce the manipulation time of quantum systems and the influence of decoherence.In the field of quantum systems,measurement is an important way to obtain effective information of the controlled system.Entanglement is an important characteristic in quantum mechanics.The preparation of entangled states of quantum systems is the basis of quantum control.At present,many achievements have been made in the research of quantum systems control,but there still exist many problems to be solved,for instance,the feedback stabilization of general N-dimensional quantum systems,and the rapid preparation of entanglement states of two-qubit quantum systems.Therefore,this paper will consider these problems.The main contents are as follows:1)The origin,background,and research status quo of quantum control,especially of quantum feedback control,are introduced;some unsolved problems in the existing literature are analyzed:and the main contents of this paper are listed.2)For an N-dimensional stochastic quantum system under the influence of continuous measurement,a switching control scheme of bang-bang form is proposed and any eigenstate of non-degenerate and degenerate measurement operators is asymptotically prepared respectively.In the proposed switching control scheme,the state space is divided into two parts:the set which includes the target state and its complement set.For non-degenerate and degenerate measurement operators,one and two control channels are used respectively.By analyzing the stability of the stochastic system under a constant Hamiltonian,a constant control law is designed and the conditions which the control Hamiltonian needs to satisfy are also given.Based on this,the stability of the whole closed-loop systems in these two cases is strictly analyzed and proved by using the stochastic LaSalle invariance principle and the continuous quantum measurement theory.Finally,some simulation experiments are performed on a finite-dimensional angular momentum system and a two-qubit quantum system to further verify the effectiveness of the proposed switching control scheme.3)For a two-qubit system under the measurement feedback,a control strategy that achieves the rapid stabilization of a target Bell state is proposed.Since the measurement operators in this case are usually degenerate,we use two control channels.First,based on the distance between the system state and the target state,the system state space is divided into two parts:the set containing the target state and its complement set.Then,according to the one or two-time switching theorem and via different Lyapunov functions,the corresponding control laws are designed in these two sets,and the control Hamiltonians of the system are constructed by ensuring the system convergence in each state set.This control strategy ensures that any system trajectory switches only one time between those two sets,and therefore greatly improves the convergence rate of the system trajectory to the target state.Finally,some numerical simulation experiments are carried out on a specific two-qubit system to verify the proposed control scheme.