Abstract The development of quantum information science has brought great changes to the fields of computer and communication, and deepened people’s understanding of basic physical problems. The core problems of overcoming decoherence, preparing and manipulating quantum states are quantum control problems in essence, so the research on quantum control will attract more and more attention and be important in the development of quantum information. This paper studies several applications of quantum Lyapunov control and quantum feedback control in quantum information processing by using Schrodinger equation, and some principal equations as tools for finite-dimensional systems. In this paper, a brief introduction of quantum control and its applications is presented to review the recent development and its prospect.
Abstract The development of quantum information science has brought great changes to the fields of computer and communication, and deepened people’s understanding of basic physical problems. The core problems of overcoming decoherence, preparing and manipulating quantum states are quantum control problems in essence, so the research on quantum control will attract more and more attention and be important in the development of quantum information. This paper studies several applications of quantum Lyapunov control and quantum feedback control in quantum information processing by using Schrodinger equation, and some principal equations as tools for finite-dimensional systems. In this paper, a brief introduction of quantum control and its applications is presented to review the recent development and its prospect.
The introduction of control theory in quantum mechanics has created a rich, new interdisciplinary scientific field, which is producing novel insight into important theoretical questions at the heart of quantum physics. Exploring this emerging subject, Introduction to Quantum Control and Dynamics presents the mathematical concepts and fundamental physics behind the analysis and control of quantum dynamics, emphasizing the application of Lie algebra and Lie group theory. To advantage students, instructors and practitioners, and since the field is highly interdisciplinary, this book presents an introduction with all the basic notions in the same place. The field has seen a large development in parallel with the neighboring fields of quantum information, computation and communication. The author has maintained an introductory level to encourage course use. After introducing the basics of quantum mechanics, the book derives a class of models for quantum control systems from fundamental physics. It examines the controllability and observability of quantum systems and the related problem of quantum state determination and measurement. The author also uses Lie group decompositions as tools to analyze dynamics and to design control algorithms. In addition, he describes various other control methods and discusses topics in quantum information theory that include entanglement and entanglement dynamics. Changes to the New Edition: New Chapter 4: Uncontrollable Systems and Dynamical Decomposition New section on quantum control landscapes A brief discussion of the experiments that earned the 2012 Nobel Prize in Physics Corrections and revised concepts are made to improve accuracy Armed with the basics of quantum control and dynamics, readers will invariably use this interdisciplinary knowledge in their mathematics, physics and engineering work.
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.
Quantum information science has blossomed into a major research field over the past decade or so. In doing so, it has established links with several other areas of physics, computer science, and engineering. One of these areas is quantum control – the extension of control theory to physical systems whose dynamics are governed by quantum mechanics. Quantum control, like quantum information, is a fairly young field with remarkable technological consequences, and this cross-pollination is proving to be stimulating. In this thesis we explore some of the connections between quantum information and quantum control. In particular, (i) we examine quantum error correction from a quantum feedback control perspective, and demonstrate new continuous time implementations of quantum error correcting codes; (ii) we consider performing quantum feedback control experiments on a solid-state quantum computing architecture – circuit QED – and propose new measurement schemes that would enable such experiments; and (iii) we consider the problem of optimally estimating quantum processes, and in particular, analyze in detail the problem of optimally estimating a one-parameter quantum process.
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.
Quantum physics is the cornerstone of contemporary science,and has led to a revolution in high-tech development. Its combination with information science has resulted in the interdisciplinary field of quantum information. It provides a new train of thought for overcoming the limits of computer chip size. Since 1987,our investigations on quantum open system theory,quantum ecoherence,and the fundamental problems of quantum physics have kept pace with the rapid development of quantum information science in the last decade. Starting with Huan-Wu Peng's important research on open quantum systems (the quantum damped harmonic oscillator) at the end of the 1970s,we will review the basic concepts and scientific importance of this field. At the same time,we will give a brief description of our series of studies on the theory of quantum open systems and its applications in quantum information.
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.