| Quantum information technology is developing rapidly nowadays.In the process of quantum information processing,decoherence or dissipation effects caused by environment will make quantum systems under consideration become open systems.For an open quantum system,its dynamics evolution is no longer unitary,which may lead to errors or even a leakage of quantum information stored in the system.It is of great interest to study the control methods of open quantum systems so as to decrease the impact of docoherence and achieve the efficient manipulation of quantum states for the development of quantum information technology.For Markovian open quantum systems,this thesis studies the decoherence and state control based on Lyapunov methods.Main research content includes the following several aspects:1)The development of quantum control will be summarized.In particular,the state-of-the-art of open quantum system control will be introduced in detail,including coherence control and state control.2)Rapid Lyapunov control for decoherence-free subspaces of Markovian open quantum systems.A decoherence-free subspace is defined as a collection of states that undergo unitary evolution in the presence of couplings to the environment.Driving quantum states into decoherence-free subspaces is an effective method to avoid decoherence.Based on the Lyapunov methods,a rapid control scheme is proposed to drive a Markovian open quantum system to a decoherence-free subspace.In this scheme,we firstly design control laws based on Lyapunov methods.In particular,an approximate bang-bang Lyapunov control law as a rapid control law will be designed.Then,the convergence of the whole system with the control fields to a decoherence-free subspace is strictly proved mathematically.Further,we propose a construction method for the control Hamiltonians to speed up convergence rate by analyzing the relationship between the LaSalle invariant set and the decoherence-free subspace.Finally,simulation experiments on a three-dimensional open quantum system will be performed to demonstrate the control effect of the proposed rapid Lyapunov control scheme.3)State convergent control of open quantum systems.Based on the construction of the system Hamiltonian,this thesis proposes a Hamiltonian control method to make an open quantum system converge to a target state.Firstly,for an open quantum system with an unknown Hamiltonian and known dissipative operators,we solve the system equation with the unknown Hamiltonian to obtain a stable solution,and then design the Hamiltonian by comparing the stable solution with the target state.Secondly,we transform the nonlinear model for the original system into an affine linear model via the coherent vector framework.Thus,we obtain the stability conditions for the original system by analyzing the stability of the latter one.Finally,we perform simulation experiments on a two-level quantum system to demonstrate the effectiveness of the proposed control scheme. |
