Quantum controllability

Daoyi Dong, Ian R. Petersen

This study presents a survey on quantum control theory and applications from a control systems perspective. Some of the basic concepts and main developments (including open-loop control and closed-loop control) in quantum control theory are reviewed. In the area of open-loop quantum control, the paper surveys the notion of controllability for quantum systems and presents several control design strategies including optimal control, Lyapunov-based methodologies, variable structure control and quantum incoherent control. In the area of closed-loop quantum control, this study reviews closed-loop learning control and several important issues related to quantum feedback control including quantum filtering, feedback stabilisation, linear-quadratic-Gaussian control and robust quantum control.

Sonia G. Schirmer, I. C. H. Pullen, A. I. Solomon

政宏 柳澤

Seth Lloyd

This paper discusses fully coherent quantum feedback control, in which the sensors, controller, and actuators are quantum systems and interact coherently with the system to be controlled: as a result, the entire feedback loop is coherent. Unlike conventional semiclassical feedback control of quantum systems, feedback control by quantum controllers is not stochastic, preserves the initial state of the controlled system, and can control quantum systems in ways that are not possible using conventional, incoherent feedback control. In particular, the target state to which the quantum controller drives the system can be entangled with another quantum system. This paper investigates quantum controllers and states necessary and sufficient conditions for a Hamiltonian quantum system to be observable and controllable by a quantum controller.

Fei Xue, Sixia Yu, Che Sun

We describe quantum controllability under the influences of the quantum decoherence induced by the quantum control itself. It is shown that, when the controller is considered as a quantum system, it will entangle with its controlled system and then cause quantum decoherence in the controlled system. In competition with this induced decoherence, the controllability will be limited by some uncertainty relation in a well-armed quantum control process. In association with the phase uncertainty and the standard quantum limit, a general model is studied to demonstrate the possibility of realizing a decoherence-free quantum control with a finite energy within a finite time. It is also shown that if the operations of quantum control are to be determined by the initial state of the controller, then due to the decoherence which results from the quantum control itself, there exists a low bound for quantum controllability.

James James