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.
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.
This review concerns quantum control results and methods that, over the years, have been used in the various operations involving quantum systems. Most of these methods have been originally developed outside the context of quantum physics, and, then, adapted to take into account the specificities of the various quantum physical platforms. Quantum control consists in designing adequate control signals required to efficiently manipulate systems conforming the laws of quantum mechanics in order to ensure the associated desired behaviours and performances. This work attempts to provide a thorough and self-contained introduction and review of the various quantum control theories and their applications. It encompasses issues spanning quantum control modelling, problem formulation, concepts of controllability, as well as a selection of the main control theories. Given the vastness of the field, we tried our best to be as concise as possible, and, for the details, the reader is pointed out to a profusion of references. The contents of the review are organized in the three major classes of control problems - open-loop control, closed-loop learning control, and feedback control - and, for each one of them, we present the main developments in quantum control theory. Finally, concerning the importance of attaining robustness and reliability due to inherent fragility of quantum systems, methods for quantum robust control are also surveyed.
For most practical quantum control systems, it is important and difficult to attain robustness and reliability due to unavoidable uncertainties in the system dynamics or models. Three kinds of typical approaches (e.g., closed-loop learning control, feedback control, and robust control) have been proved to be effective to solve these problems. This work presents a self-contained survey on the closed-loop and robust control of quantum systems, as well as a brief introduction to a selection of basic theories and methods in this research area, to provide interested readers with a general idea for further studies. In the area of closed-loop learning control of quantum systems, we survey and introduce such learning control methods as gradient-based methods, genetic algorithms (GA), and reinforcement learning (RL) methods from a unified point of view of exploring the quantum control landscapes. For the feedback control approach, the paper surveys three control strategies including Lyapunov control, measurement-based control, and coherent-feedback control. Then such topics in the field of quantum robust control as H(∞) control, sliding mode control, quantum risk-sensitive control, and quantum ensemble control are reviewed. The paper concludes with a perspective of future research directions that are likely to attract more attention.
The scope of this work is to provide a self-contained introduction to a selection of basic theoretical aspects in the modeling and control of quantum mechanical systems, as well as a brief survey on the main approaches to control synthesis. While part of the existing theory, especially in the open-loop setting, stems directly from classical control theory (most notably geometric control and optimal control), a number of tools specifically tailored for quantum systems have been developed since the 1980s, in order to take into account their distinctive features: the probabilistic nature of atomic-scale physical systems, the effect of dissipation and the irreversible character of the measurements have all proved to be critical in feedback-design problems. The relevant dynamical models for both closed and open quantum systems are presented, along with the main results on their controllability and stability. A brief review of several currently available control design methods is meant to provide the interested reader with a roadmap for further studies.
In this review paper, we survey the main concepts and some of the recent developments in quantum feedback control. For consistency and clarity, essential ideas and notations in the theory of open quantum systems and quantum stochastic calculus, as well as continuous measurement theory are developed. We give a general description of quantum feedback control, set up a coherent model and compare it to open-loop designs. Objectives which can be achieved by feedback, such as rapid state preparation and purification or entanglement generation are formulated and analyzed, based on the relevant literature. The connection between quantum feedback and quantum chaos is also described and unravelled which, apart from its theoretical curiosity, can shed more light on some of the intrinsic properties of this control paradigm.
Optimal Control Theory is a powerful mathematical tool, which has known a rapid development since the 1950s, mainly for engineering applications. More recently, it has become a widely used method to improve process performance in quantum technologies by means of highly efficient control of quantum dynamics. This review aims at providing an introduction to key concepts of optimal control theory which is accessible to physicists and engineers working in quantum control or in related fields. The different mathematical results are introduced intuitively, before being rigorously stated. This review describes modern aspects of optimal control theory, with a particular focus on the Pontryagin Maximum Principle, which is the main tool for determining open-loop control laws without experimental feedback. The different steps to solve an optimal control problem are discussed, before moving on to more advanced topics such as the existence of optimal solutions or the definition of the different types of extremals, namely normal, abnormal, and singular. The review covers various quantum control issues and describes their mathematical formulation suitable for optimal control. The optimal solution of different low-dimensional quantum systems is presented in detail, illustrating how the mathematical tools are applied in a practical way.
This paper surveys some recent results on the feedback control of quantum linear systems and the robustness properties of these systems. Quantum linear systems are a class of systems whose dynamics, which are described by the laws of quantum mechanics, take the specific form of a set of linear quantum stochastic differential equations (QSDEs). These systems can also be described in terms of a Hamiltonian operator H and a coupling operator L, which in the case of quantum linear systems have a specific quadratic and linear form respectively. Such systems commonly arise in the area of quantum optics and related disciplines. Systems whose dynamics can be described or approximated by linear QSDEs include interconnections of optical cavities, beam-splitters, phase-shifters, optical parametric amplifiers, optical squeezers, and cavity quantum electrodynamic systems. An important approach to the feedback control of quantum linear systems involves the use of a controller which itself is a quantum linear system. This approach to quantum feedback control, referred to as coherent quantum feedback control, has the advantage that it does not destroy quantum information, is fast, and has the potential for efficient implementation. The paper discusses recent results concerning the synthesis of coherent quantum controllers such as in coherent quantum H∞ control. Another important issue in the design of quantum feedback controllers is the robustness of the closed loop quantum system to perturbations in the quantum plant dynamics arising from perturbations in the system Hamiltonian H and the system coupling operator L. The paper discusses recent robust stability results for such perturbed quantum systems which take the form of a quantum small gain theorem and a quantum Popov stability criterion. These results are usefu