State Estimation And Feedback Control Of Open Quantum Systems

With the advancement and understanding the quantum dynamic behavior,the promis?ing applications of quantum phenomena have been proposed in literature,which has promoted the quantum control theory development.On the other side,the uniqueness of quantum systems behavior makes quantum feedback control a challenging research area.Despite the achievements in literature about the control of quantum system be?havior,but still need more effective and more efficient way to develop the framework of quantum theory of feedback control.The main purpose of this thesis is development of online state estimation process and new methods to the problem of feedback control in quantum technology applications.In this thesis,firstly a Lyapunov-based feedback control(LFC)is design for the known initial state of the two-level open stochastic quantu,m system(OSQS).It is known that the state transfer of OSQS is a difficult task in the presence of the decoherence factor(spontaneous emission)and the environmental disturbances.Therefore,the purpose of the LFC is to steer the state of OSQS from any arbitrary state to the desired quantum system to get the high state transfer fidelity.The feedback control law based on measurement results is very important in the quantum control theory.Therefore,in the second part,an estimator-based Lyapunov feedback control(ELFC)is design for the two-level bilinear Markovian OSQS.The es-timator is developed to estimate the system'unknown state information,and the feed-back control signal is altered based on the online estimation result to achieve satisfac-tory control performance.The state of the proposed state-dependent differential Riccati equation(SDDRE)nonlinear state estimator(NSE)is continuously updated by the con-tinuous weak measurement data to converge to the system state.The proposed ELFC Jaw is design based on the estimated state of SDDRE NSE.Furthermore,the positive effects of quantum measurements in state transfer are illustrated by investigating state transfer of OSQS to the desired state from arbitrary initial state with high fidelity.Finally,the state-dependent Riccati equation is introduced to design a nonlinear op-timal feedback tracking control(NOFTC)strategy based on the nonlinear state estimator(NSE)for a two-level bilinear open non-Markovian stochastic quantum system(ONM-SQS).The estimated state variables are used to design NOFTC for the both stabilization and output tracking of a reference model.The output state of reference model is chosen as the desired performance of NOFTC for ONMSQS.The numerical simulation results verify the achievability of proposed NOFTC strategy in terms of state estimation and the tracks the given reference trajectory,i.e.,final reference target state with high state transfer success rate.The importance of the proposed online method NSE and NOFTC lies in the fact that it provides basic support for developing a general framework for online nonlinear quantum state estimation and nonlinear feedback control.