Quantum Control Systems

Daoyi Dong, Zonghai Chen

Quantum control theory is a new interdiscipline, which mainly concerns how to control quantum states of microsystems. To get better control results, it is necessary to study the modeling and simulation of the systems. With the consideration of the characteristics of quantum control, direct mechanism modeling and quantization modeling for quantum control systems are studied, and simulation of quantum control systems is also analyzed. Direct mechanism modeling uses the mechanism information of systems in quantum physics and suitably models some quantum control systems with the known mechanism. Quantization modeling makes the most of the corresponding relations between quantum operators and classical physical quantities, and uses the information of models in classical control to establish the corresponding models in quantum control.

En-Bing Lin

Dong Daoyi, Zonghai Chen

Perturbation theory, an important method in both classical control theory and quantum mechanics, is used to quantum control theory. Perturbation model of quantum control system with weak control input is introduced when the Hamiltonian of control system can be written into two parts: the free Hamiltonian of unperturbed system and the interaction Hamiltonian between the controlled system and its external control. As an example, the quantum control problem of oscillator control system with weak input is analyzed and its second-order approximate quantum control input is found by perturbation method.

G. Huang

DongDaoyi, ChenZonghai

Formal state space models of quantum control systems are deduced and a scheme to establish formal state space models via quantization could been obtained for quantum control systems is proposed. State evolution of quantum control systems must accord with Schrodinger equations, so it is foremost to obtain Hamiltonian operators of systems. There are corresponding relations between operators of quantum systems and corresponding physical quantities of classical systems,such as momentum, energy and Hamiltonian, so Schrodinger equation models of corresponding quantum control systems via quantization could been obtained from classical control systems, and then establish formal state space models through the suitable transformation from Schrodinger equations for these quantum control systems. This method provides a new kind of path for modeling in quantum control.

J. W. Clark, Dennis G. Lucarelli, Tzyh‐Jong Tarn