MODELING OF QUANTUM CONTROL SYSTEMS BASED ON QUANTIZATION

摘要

It is getting more and more important to manipulate and control quantum states with rapid development of quantum information theory in the last two decades. There are many differences between the control of quantum systems and that of classical systems, so the control of quantum states must be guided by quantum control theory. Quantum control theory is a new interdiscipline, which mainly studies the control of quantum states for systems in the microworld. To get better control results, it is necessary to study modeling of quantum control systems. In classical system control theory, models of many control systems are given, and there are also corresponding relations between quantum mechanical operators (such as momentum operator, energy operator) and classical physical quantities, so the application of quantization may be considered. In this paper, the method of quantization is introduced, by which the models of quantum control systems can be derived from corresponding classical control systems. Three methods are discussed: direct quantization, indirect quantization and analogy quantization. Direct quantization is that the models of quantum control systems are directly derived from classical control systems through the corresponding relations between quantum operators and classical physical quantities. Indirect quantization is that the models of quantum control systems are indirectly derived via Lagrangian and Hamiltonian systems within the framework of Lagrangian and Hamiltonian formalisms. And analogy quantization is that the models of quantum control systems are derived by analogy with the classical control systems which are easily quantized. The method of quantization joints quantum control and classical control, and it is possible to extend some conclusions in classical control to quantum control domain.