This paper provides a brief review of Rosenbrock's recent work on generating quantum mechanics using dynamic programming, some background knowledge of quantum mechanics and some general issues and problems in developing feedback quantum control.
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.
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.
Quantumcontrolasabrandnewacademicfield is emerging fast. A survey on this new topicispresented.Firstofall,abrief historical review of the origin and the development of the quantum control is provided. Then a quick introduction to the quantum mechanics is given. It provides the theoretical fundation and the framwork for the quantum control. The relationship between the quantum control and the control theory is discussed. The model and major control problems in the quantum control are presented, and the current research situation abroad is described. Finally, a brief prospect is given.
This brief paper continues a development in earlier publications by Rosenbrock, in which results in quantum mechanics were obtained by adding a random disturbance to Hamilton's principle. The disturbance is complex, and the resulting variational problem is solved by dynamic programming, which computes the causal relations needed to accomplish a purpose. It is shown here that this procedure leads to many results that agree with those obtained in the standard theory of quantum mechanics, but also to some that are not readily obtained in that theory. For example, certain changes at a time t m to the end condition x f , which will be reached at t f >t m , can instantaneously change some aspects of the particle's behaviour at t m while it is still in transit. This accounts for Einstein's `spooky action at a distance'. An approach is also given to interference and entanglement, which is simpler than the standard account and may therefore be useful in quantum control and quantum computation.
In the last two decades there has been an enormous progress in the experimental investigation of single quantum systems. This progress covers fields such as quantum optics, quantum computation, quantum cryptography, and quantum metrology, which are sometimes summarized as `quantum technologies'. A key issue there is entanglement, which can be considered as the characteristic feature of quantum theory. As disparate as these various fields maybe, they all have to deal with a quantum mechanical treatment of the measurement process and, in particular, the control process. Quantum control is, according to the authors, `control for which the design requires knowledge of quantum mechanics'. Quantum control situations in which measurements occur at important steps are called feedback (or feedforward) control of quantum systems and play a central role here. This book presents a comprehensive and accessible treatment of the theoretical tools that are needed to cope with these situations. It also provides the reader with the necessary background information about the experimental developments. The authors are both experts in this field to which they have made significant contributions. After an introduction to quantum measurement theory and a chapter on quantum parameter estimation, the central topic of open quantum systems is treated at some length. This chapter includes a derivation of master equations, the discussion of the Lindblad form, and decoherence – the irreversible emergence of classical properties through interaction with the environment. A separate chapter is devoted to the description of open systems by the method of quantum trajectories. Two chapters then deal with the central topic of quantum feedback control, while the last chapter gives a concise introduction to one of the central applications – quantum information. All sections contain a bunch of exercises which serve as a useful tool in learning the material. Especially helpful are also various separate boxes presenting important background material on topics such as the block representation or the feedback gain-bandwidth relation. The two appendices on quantum mechanics and phase-space and on stochastic differential equations serve the same purpose. As the authors emphasize, the book is aimed at physicists as well as control engineers who are already familiar with quantum mechanics. It takes an operational approach and presents all the material that is needed to follow research on quantum technologies. On the other hand, conceptual issues such as the relevance of the measurement process for the interpretation of quantum theory are neglected. Readers interested in them may wish to consult instead a textbook such as Decoherence and the Quantum-to-Classical Transition by Maximilian Schlosshauer. Although the present book does not contain applications to gravity, part of its content might become relevant for the physics of gravitational-wave detection and quantum gravity phenomenology. In this respect it should be of interest also for the readers of this journal.