Quantum control theory and applications: A survey

This paper 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, the paper reviews closed-loop learning control and several important issues related to quantum feedback control including quantum filtering, feedback stabilization, LQG control and robust quantum control.Comment: 38 pages, invited survey paper from a control systems perspective, some references are added, published versio

Sampled-data design for robust control of a single qubit

This paper presents a sampled-data approach for the robust control of a single qubit (quantum bit). The required robustness is defined using a sliding mode domain and the control law is designed offline and then utilized online with a single qubit having bounded uncertainties. Two classes of uncertainties are considered involving the system Hamiltonian and the coupling strength of the system-environment interaction. Four cases are analyzed in detail including without decoherence, with amplitude damping decoherence, phase damping decoherence and depolarizing decoherence. Sampling periods are specifically designed for these cases to guarantee the required robustness. Two sufficient conditions are presented for guiding the design of unitary control for the cases without decoherence and with amplitude damping decoherence. The proposed approach has potential applications in quantum error-correction and in constructing robust quantum gates.Comment: 33 pages, 5 figures, minor correction

A Quantum Langevin Formulation of Risk-Sensitive Optimal Control

In this paper we formulate a risk-sensitive optimal control problem for continuously monitored open quantum systems modelled by quantum Langevin equations. The optimal controller is expressed in terms of a modified conditional state, which we call a risk-sensitive state, that represents measurement knowledge tempered by the control purpose. One of the two components of the optimal controller is dynamic, a filter that computes the risk-sensitive state. The second component is an optimal control feedback function that is found by solving the dynamic programming equation. The optimal controller can be implemented using classical electronics. The ideas are illustrated using an example of feedback control of a two-level atom