Studies On Quantum Control Strategies And Learning Control Algorithms

More general and practical quantum control technologies and methods should be explored under the direction of quantum control theory, which is an important step to lead us into the quantum information industry era and is also significant for bond-selective chemistry, gene engineering and nanotechnology. Nowadays, quantum control is an international prosperous research area, in which quantum control strategies and control algorithms have become important research missions. After the survey of the current main developments of quantum control, we study in this thesis the control problems of quantum systems from the point of view of information theory and control theory, and our attention is paid to quantum control strategies and learning control algorithms. The main work and contributions of this thesis are as follows.(1) The representation methods of states of quantum control systems are introduced and some kinds of general models describing the evolution of quantum states in quantum control are discussed, in which we detailedly discuss finite dimensional bilinear model and master equation model. Mechanism modeling and quantization modeling methods.are analyzed for the modeling of specific quantum control systems and a modeling method called analogy quantization is presented.(2) In view of quantum control of electron spin, a time quantum control scheme is presented, in which the electron spin can effectively be controlled to the given objective quantum state through controlling acting time of external control field. The analytic relation between quantum state and acting time is also obtained. For quantum oscillator control system, perturbation theory is used to analyze and design quantum control problem and a class of perturbation model of quantum control is obtained. In this method, control solution is approximate and it is suitable to analyze the quantum control problem with weak input. The two examples can be used to give a demonstration for open-loop quantum control design process.(3) Using the method of pattern recognition and looking upon every encoding state of quantum information systems as a quantum information pattern, this thesis presents two clustering and recognition algorithms based on pattern-distance. In our method, pattern-distance is used as a measurement of comparability of different quantum states. A simple recognition algorithm and its geometrical explanation are given for objective pattern being known. When objective pattern is unknown, a kind of effective clustering algorithm for quantum information is proposed. In the two algorithms, the comparability of quantum states and the phases and occurrence probabilities of their eigenstates are related, and the results show that these algorithms accord to intuitionistic explanation in physics. Besides the application to quantum feedback control in our thesis, this...