Directions in the Theory of Quantum Control

Jeffrey L. Krause

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.

Jincheng Zhang

This paper introduces a novel adaptive quantum control theory designed to achieve high-precision measurement by dynamically adjusting control strategies based on the observed state of a quantum system. The core mechanism relies on quantum feedback control, enabling real-time monitoring and adjustment of control parameters according to the system's state. This approach overcomes the limitations of traditional static quantum control methods, offering enhanced performance in achieving accurate measurement outcomes. The theoretical framework is presented, focusing on the mathematical formulation of the adaptive control process and the key equations governing the system's dynamics. The paper culminates in a discussion of potential applications and future research directions within the field of quantum measurement and control.

Shuang Cong

Stuart David Wilson

The use of control theory in a LQG form for quantum mechanical situations has revealed a new conceptualization of knowledge, measurement and feedback. The benefits of state estimation by the Kalman filter has shown up in theoretical calculations for cooling and confining of an atom in a harmonic potential, surpassing previous proposals of direct feedback. The goal of this thesis is to explore the possible application of a new form of filter/controller, the risk-sensitive LEQG filter, which has been shown to enjoy a sense of robustness against model uncertainties. An investigation is launched into some simple models, and a computer simulation has highlighted circumstances where the LEQG filter does provide better control.

S. G. Schirmer