Characteristics Analysis And State Preservation For Open Quantum Systems

Quantum systems are grouped into closed systems and open systems according to whether the systems interact with their environment. Closed quantum systems generally refers to quantum systems at absolute zero or quantum systems that have not any interaction with the external environment. Many quantum systems are considered as open quantum systems because the systems interact with the environment, such as bath or measurement. The systems are called Markovian open quantum systems if the environment’s memory effects could be ignored, or else, they are considered as non-Markovian open systems. The quantum systems are classified as stochastic open quantum systems while they are under measurements which bring noise to the systems.This dissertation mainly studies two aspects, one is characteristics analysis of the models and the state feedback control of stochastic open quantum systems, the other is state preservation for open quantum systems.1. Models and feedback control characteristics analysis of stochastic open quantum systems. The stochastic open quantum system models undergoing continuous measurement in different cases are analyzed including stochastic master equation in. Schrodinger Picture which describe the stochastic evolution of state estimation, the master stochastic equations considering the effect of the decoherence and time delay in the control loop and the linear master equation in optimal control. The condition of the use, the composition of model component, and the effect caused, the process of model simplifying, as well as the relationship between these different models, are studied.Based on these stochastic master equations, the characteristics of designing different feedback control laws for the stochastic open quantum system based on state estimation are analyzed comparatively. When there is no control applied to stochastic open quantum systems, randomly, the state will convergence to the eigenstate of the measurement operator, while the state will certainly convergence to the determined eigenstates under control. For the simple angular momentum quantum system, the structure of switch control laws and the continuous control laws designed by Lyapunov stability theorem are analyzed. The different parts of the control laws will make sure the state in different sets associated with target state will convergence to the target state. For linear stochastic master equation, analytic expression of the control law could be given based on the performance function and the master equation. The designing of feedback controllers under the influence of decoherence arose from environment and time delay,as well as general form stochastic master equations are also considered.2. In the case of fixed system frequency and ambient temperature, we design a Lyapunov-based controller to transfer and maintain states for the Time-convolution-less (TCL) master equation of two-level non-Markovian open quantum systems. Basis on the state transferring from the superposition state to superposition state, we maintain the state in the superposition state. The system simulation experiments are implemented under the MATLAB environment. The comparison experiments of the fault-tolerant performance before and after maintaining state demonstrate the superiority of the designed controller. At the same time, the influence of control parameters to length of time maintaining the state of the system are analyzed, and the best control parameters are given.