Modeling of Quantum Control Systems; Examples

Domenico D'Alessandro

Quantum systems whose dynamics depends on one or more control functions will be named quantum control systems. In a typical situation the objects of control are charged particles while the control functions are appropriately shaped electromagnetic fields. Therefore, to derive the models, in this chapter we describe elements of the theory of field-particle interaction. We start with the classical theory of electrodynamics and show how to obtain the quantum mechanical description through a process called canonical quantization. We present physical examples of (finite dimensional) quantum control systems of interest in applications and we highlight the fact that such systems have a common mathematical structure, as bilinear systems whose evolution is determined by an element of the Lie group of unitary matrices. In a parallel to classical control theory, we identify a state, an input, and an output in our description of quantum control systems.

Wen-Bin Dong, Re-Bing Wu, Xiaohu Yuan +2 more

John Edward Gough

Domenico D’Alessandro

Quantum systems whose dynamics depends on one or more control functions are called quantum control systems. This chapter describes elements of the theory of field-particle interaction. It starts with the classical theory of electrodynamics and shows how to obtain the quantum mechanical description through a process called canonical quantization. The chapter presents physical examples of quantum control systems of interest in applications and highlights the fact that such systems have a common mathematical structure. In the external system, the motion of the charges, are fixed and independent of the field. Canonical quantization is the process which associates quantities in classical mechanics with operators in quantum mechanics.

TZYH JONG TARN, Garng M. Huang, J. W. Clark

Hamza Jirari, W. Pötz

The interaction of a quantum system with a bath, usually referred to as dissipation, can be controlled if one can establish quantum interference between the system--bath interaction and a coupling of the system to an external control field. This is demonstrated for the example of the spin-boson model in the strong coupling limit for the system--bath interaction. It is shown that driving and trapping of the spin system leads to an optimum control problem which is nonlinear in the external control field. Using an indirect optimization strategy introducing a Lagrange-type adjoint state, we show that the spin system can be trapped in otherwise unstable quantum states and that it can be driven from a given initial state to a specified target state with high fidelity.