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

Mathematical control of complex systems

Copyright © 2013 ZidongWang et al.This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

Control of stochastic chaos using sliding mode method

AbstractStabilizing unstable periodic orbits of a deterministic chaotic system which is perturbed by a stochastic process is studied in this paper. The stochastic chaos is modeled by exciting a deterministic chaotic system with a white noise obtained from derivative of a Wiener process which eventually generates an Ito differential equation. It is also assumed that the chaotic system being studied has some model uncertainties which are not random. The sliding mode controller with some modifications is used for stochastic chaos suppression. It is shown that the system states converge to the desired orbit in such a way that the error covariance converges to an arbitrarily small bound around zero. As some case studies, the stabilization of 1-cycle and 2-cycle orbits of chaotic Duffing and Φ6 Van der Pol systems is investigated by applying the proposed method to their corresponding stochastically perturbed systems. Simulation results show the effectiveness of the method and the accuracy of the statements proved in the paper

Sliding Mode Control of Two-Level Quantum Systems

This paper proposes a robust control method based on sliding mode design for two-level quantum systems with bounded uncertainties. An eigenstate of the two-level quantum system is identified as a sliding mode. The objective is to design a control law to steer the system's state into the sliding mode domain and then maintain it in that domain when bounded uncertainties exist in the system Hamiltonian. We propose a controller design method using the Lyapunov methodology and periodic projective measurements. In particular, we give conditions for designing such a control law, which can guarantee the desired robustness in the presence of the uncertainties. The sliding mode control method has potential applications to quantum information processing with uncertainties.Comment: 29 pages, 4 figures, accepted by Automatic

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

Event-triggered distributed H∞ state estimation with packet dropouts through sensor networks

This study is concerned with the event-triggered distributed H∞ state estimation problem for a class of discrete-time stochastic non-linear systems with packet dropouts in a sensor network. An event-triggered communication mechanism is adopted over the sensor network with hope to reduce the communication burden and the energy consumption, where the measurements on each sensor are transmitted only when a certain triggering condition is violated. Furthermore, a novel distributed state estimator is designed where the available innovations are not only from the individual sensor, but also from its neighbouring ones according to the given topology. The purpose of the problem under consideration is to design a set of distributed state estimators such that the dynamics of estimation errors is exponentially mean-square stable and also the prespecified H∞ disturbance rejection attenuation level is guaranteed. By utilising the property of the Kronecker product and the stochastic analysis approaches, sufficient conditions are established under which the addressed state estimation problem is recast as a convex optimisation one that can be easily solved via available software packages. Finally, a simulation example is utilised to illustrate the usefulness of the proposed design scheme of event-triggered distributed state estimators.This work was supported in part by Royal Society of the UK, the National Natural Science Foundation of China under Grants 61329301, 61203139, 61473076, 61374127 and 61422301, the Shanghai Rising-Star Program of China under Grant 13QA1400100, the ShuGuang project of Shanghai Municipal Education Commission and Shanghai Education Development Foundation under Grant 13SG34, the Fundamental Research Funds for the Central Universities, DHU Distinguished Young Professor Program, and the Alexander von Humboldt Foundation of Germany