Dynamical trajectory tracking control in quantum systems

Shuang Cong, Jianxiu Liu

Liu, Cong Cong, Zhu

Cong Cong, Shuang, Liu +1 more

Zeinab Sahebi, Majid Yarahmadi

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.

Xueming Qian, Baotong Cui

In this paper, the finite time tracking issue for a class of closed quantum systems under the action of impulsive control fields is addressed. The aim is to steer the state of the quantum system to the trajectory of a periodic time-varying target. By using the Lyapunov direct method and considering a finite-time control strategy, the modified impulsive tracking controllers are designed such that the error dynamical system converges to zero in finite time. While finite-time tracking implies optimality in convergence time and has better disturbance rejection. Numerical simulations are given to illustrate the effects of system’s trajectory tracking, and also given to demonstrate the superiority of the control laws which are proposed.

Wusheng Zhu, Martina Smit, HERSCHEL A. RABITZ

Singularities can arise in the external field obtained by tracking control of quantum mechanical systems. Whether or not the trajectory is disturbed by the presence of a singular point is shown to mainly depend on the average momentum along the trajectory at the moment of passing the singular point. If the singularity occurs on a turning point, the tracking will be quite unstable since the direction taken by the trajectory is very sensitive to field errors. The theoretical analysis of these situations yields detailed conclusions about the impact of field singularities in quantum tracking control. A rank index is defined to characterize nontrivial singularities, and the rank is shown to play an important role in determining the tracking quality while passing over a singular turning point where the field has a unique solution. A special class of nontrivial singularities is identified by the ability to remove the singularity under a proper limiting process. These insights into the nature and influence of singularities in tracking control of quantum systems are beneficial for developing numerical schemes and for designing controls.