Summary In this paper, a switching optimal adaptive controller for tracking a time‐dependent trajectory in finite‐dimensional closed quantum systems is proposed. The issue of intrinsic singularities in trajectory tracking control of quantum systems leads to a sharp rise in the control amplitude. To overcome this drawback, a switching optimal adaptive quantum controller is designed based on Lyapunov stability theory and optimal quantum control approach. A state‐dependent strategy is considered to select the switching signal. The new switching controller adjusts the quantum state so that its population traces the desired dynamic trajectory and simultaneously eliminates the effects of singularities and reduces the control amplitude. The proposed controller is tested successfully for population transfer in a 4‐level closed quantum system in a simulation experiment. Both issues of reduction of the tracking error and control intensity along with a significant decrease in the number of singular points are well illustrated by simulation experiment as the advantages of the proposed method.Summary In this paper, a switching optimal adaptive controller for tracking a time‐dependent trajectory in finite‐dimensional closed quantum systems is proposed. The issue of intrinsic singularities in trajectory tracking control of quantum systems leads to a sharp rise in the control amplitude. To overcome this drawback, a switching optimal adaptive quantum controller is designed based on Lyapunov stability theory and optimal quantum control approach. A state‐dependent strategy is considered to select the switching signal. The new switching controller adjusts the quantum state so that its population traces the desired dynamic trajectory and simultaneously eliminates the effects of singularities and reduces the control amplitude. The proposed controller is tested successfully for population transfer in a 4‐level closed quantum system in a simulation experiment. Both issues of reduction of the tracking error and control intensity along with a significant decrease in the number of singular points are well illustrated by simulation experiment as the advantages of the proposed method.

Optimal Control Applications and MethodsFeb 13, 20188 citations

A unified trajectory tracking control for of N-dimensional closed quantum systems

Yu-Qiu Zhou, Shuang Cong, Fangfang Meng

A Lyapunov-based unified control method for quantum state trajectory tracking control is proposed in this paper. By inducing the error between the controlled state and the target state as error state, the trajectory tracking control problem of the quantum system is transformed into the regular control problem of systematic error state. Through an interaction picture transformation, the spin effect is eliminated. The unified control method is designed in the trajectory tracking control for the quantum system which can also solve the problems caused by the non-ideal quantum systems, where the free Hamiltonian of the system is not strongly regular and (or) not commutes with the target state, and (or) the control Hamiltonian is not fully connected. The unified trajectory tracking control proposed can drive the system from an arbitrary initial state to an arbitrary target state and achieve the purpose of tracking. The numerical simulation experiments and results analyses are given.A Lyapunov-based unified control method for quantum state trajectory tracking control is proposed in this paper. By inducing the error between the controlled state and the target state as error state, the trajectory tracking control problem of the quantum system is transformed into the regular control problem of systematic error state. Through an interaction picture transformation, the spin effect is eliminated. The unified control method is designed in the trajectory tracking control for the quantum system which can also solve the problems caused by the non-ideal quantum systems, where the free Hamiltonian of the system is not strongly regular and (or) not commutes with the target state, and (or) the control Hamiltonian is not fully connected. The unified trajectory tracking control proposed can drive the system from an arbitrary initial state to an arbitrary target state and achieve the purpose of tracking. The numerical simulation experiments and results analyses are given.

Chinese Control Conference (CCC)Jul 25, 20220 citations

Robust $H_{\infty }$ Uncertainties-Tolerant Observer-Based Reference Quantum Trajectory Tracking Control for Lindblad Master EquationRobust $H_{\infty }$ Uncertainties-Tolerant Observer-Based Reference Quantum Trajectory Tracking Control for Lindblad Master Equation

Shin-Yi Wen, Bor-Sen Chen, Chun-Liang Lin

Robust output feedback reference quantum trajectory tracking control design is proposed by the simultaneous continuous weak measurement of non-commuting observables. Using the robust $H_\infty$ uncertainties-tolerant observer-based reference quantum trajectory tracking control (UTOBRQTTC) design strategy, the proposed method can robustly estimate the quantum trajectory and robustly track a sequence of any reference quantum states against undesired uncertainties and potential unavailable fault signals. Smoothed signal models are embedded into the augmented bilinear quantum system derived from Lindblad master equation. With the regression of unavailable system and sensor fault signal by smoothed models, the proposed $H_\infty$ UTOBRQTTC design of the augmented bilinear quantum system can proactively compensate for the corruption of fault signals. Therefore, robust quantum trajectory estimation and reference quantum trajectory tracking can be achieved simultaneously via the proposed robust $H_\infty$ UTOBRQTTC design strategy. Furthermore, the nonlinear Hamilton-Jacobi inequality (HJI)-constrained optimization problem of optimal robust $H_\infty$ UTOBRQTTC design strategy can be treated as an LMIs-constrained optimization problem by the upper bound of spectral radius of augmented bilinear quantum system and the proposed two-step procedure, which can be efficiently solved with the help of MATLAB LMI TOOLBOX. Finally, several simulation examples of two-level bilinear quantum systems represented by the Lindblad master equation are provided to demonstrate the estimation performance of quantum trajectory and fault signals and any arbitrary signal tracking performance for more practical applications of bilinear quantum systems.Robust output feedback reference quantum trajectory tracking control design is proposed by the simultaneous continuous weak measurement of non-commuting observables. Using the robust$H_\infty$uncertainties-tolerant observer-based reference quantum trajectory tracking control (UTOBRQTTC) design strategy, the proposed method can robustly estimate the quantum trajectory and robustly track a sequence of any reference quantum states against undesired uncertainties and potential unavailable fault signals. Smoothed signal models are embedded into the augmented bilinear quantum system derived from Lindblad master equation. With the regression of unavailable system and sensor fault signal by smoothed models, the proposed$H_\infty$UTOBRQTTC design of the augmented bilinear quantum system can proactively compensate for the corruption of fault signals. Therefore, robust quantum trajectory estimation and reference quantum trajectory tracking can be achieved simultaneously via the proposed robust$H_\infty$UTOBRQTTC design strategy. Furthermore, the nonlinear Hamilton-Jacobi inequality (HJI)-constrained optimization problem of optimal robust$H_\infty$UTOBRQTTC design strategy can be treated as an LMIs-constrained optimization problem by the upper bound of spectral radius of augmented bilinear quantum system and the proposed two-step procedure, which can be efficiently solved with the help of MATLAB LMI TOOLBOX. Finally, several simulation examples of two-level bilinear quantum systems represented by the Lindblad master equation are provided to demonstrate the estimation performance of quantum trajectory and fault signals and any arbitrary signal tracking performance for more practical applications of bilinear quantum systems.

IEEE Transactions on Quantum EngineeringDec 18, 20251 citation

Robust

H_{\infty }

Uncertainties-Tolerant Observer-Based Reference Quantum Trajectory Tracking Control for Lindblad Master Equation

Robust output feedback reference quantum trajectory tracking control design is proposed by the simultaneous continuous weak measurement of non-commuting observables. Using the robust

H_\infty

uncertainties-tolerant observer-based reference quantum trajectory tracking control (UTOBRQTTC) design strategy, the proposed method can robustly estimate the quantum trajectory and robustly track a sequence of any reference quantum states against undesired uncertainties and potential unavailable fault signals. Smoothed signal models are embedded into the augmented bilinear quantum system derived from Lindblad master equation. With the regression of unavailable system and sensor fault signal by smoothed models, the proposed

H_\infty

UTOBRQTTC design of the augmented bilinear quantum system can proactively compensate for the corruption of fault signals. Therefore, robust quantum trajectory estimation and reference quantum trajectory tracking can be achieved simultaneously via the proposed robust

H_\infty

UTOBRQTTC design strategy. Furthermore, the nonlinear Hamilton-Jacobi inequality (HJI)-constrained optimization problem of optimal robust

H_\infty

UTOBRQTTC design strategy can be treated as an LMIs-constrained optimization problem by the upper bound of spectral radius of augmented bilinear quantum system and the proposed two-step procedure, which can be efficiently solved with the help of MATLAB LMI TOOLBOX. Finally, several simulation examples of two-level bilinear quantum systems represented by the Lindblad master equation are provided to demonstrate the estimation performance of quantum trajectory and fault signals and any arbitrary signal tracking performance for more practical applications of bilinear quantum systems.