Learning-based Landscape Control Of Open Quantum Systems

With its significant advance over the last few decades, quantum technology is developing rapidly and it related closely to the physical, chemical and control science. The quantum control, as an emerging study within the field of quantum technology, is gathering increasing attentions. The quantum control landscape is a physical objective defined as a functional of the time dependent controls. Numerous studies of quantum control theory are considered only on the closed systems, which are based on the assumption that quantum system has no energy dissipation with the external environment. However, this assumption is hard to achieve in laboratory, because the quantum system will inevitably interact with the external environment, which makes it more complex and more difficult to realize the state transition problem of open quantum system. Moreover, quantum ensemble, which consists of numerous single quantum systems, has been widely used in the emerging quantum technology. The control objective of quantum ensemble is to apply a set of control fields to steer all the elements of ensemble from a common quantum state to the expect target state. This makes it even more complex when compared with the single quantum system’s control problem, therefore, to study the state transition control problem is of great importance.This dissertation firstly focused on the control problem of single quantum system. The Lindblad equation was analyzed, and then the objective function, along with the first-order derivative of the objective function to the external control field were derived accordingly. Then the gradient descent (GD) method, genetic algorithm (GA) and the differential evolution (DE) algorithm were carried out to optimize the open quantum system at different levels and the optimal control strategies for transferring the system status are presented. The parameters for different learning algorithms and different energy levels are analyzed with respect to the optimization results. From the results we found that the gradient descent method outperforms the other algorithms. However, when the system model is unknown, the gradient descent method is unable to used, while the DE and GA method can achieved best optimization results.On account of the status transfer control of open quantum ensemble that consists of a large number of elements, the control strategies for single quantum system were fed to the quantum control ensemble as the initial controls in order to shorten the optimization time. Moreover, the control period was carried out using the Sampling based Learning Control method that took a training procedure and an examining procedure to obtain the optimal control strategy for the status transfer of quantum ensemble. The experimental results show that the training procedure is of great importance. The iterations and the tuning of parameters affected the optimization results to a large extent and thus if choose properly, the better realization of status transfer control of the quantum ensemble should be achieved.