Modelling of quantum mechanical control systems

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

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.

Navin Khaneja

Control and manipulation of quantum mechanical systems using electromagnetic fields is a widely studied subject in areas of physics and chemistry, including spectroscopy, atomic molecular, and optical physics, and quantum chemistry.This article attempts to provide a glimpse into the rich class of bilinear control systems that are ubiquitous in these problems.In this article, we use control of spin systems in magnetic resonance as a model system to highlight characteristic feature of problems in quantum control.Background information is provided to enable the reader to appreciate new results and developments, where principled use of ideas from control theory have provided new insights into finding optimal ways to control and manipulate quantum mechanical systems.The study of deterministic and stochastic models that arise in problems in measurement and manipulation of quantum mechanical systems may foster new developments in control.

En-Bing Lin

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

Shuang Cong

A model of quantum mechanical systems and its ensemble are established from control theory viewpoint. The state vector of wave function and density matrix of quantum mechanical systems are transformed into evolution matrix state of geometry space. The manipulation problem of an abstract physical concept is changed into a control design problem on a state of geometry space, which is easy to deal with mathematically and suitable for control. (Finally,) five basic problems about quantum sysetms control, which may be solved based on the model, are (presented.)