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Chinese Journal of Quantum Electronics

Progress of the research on quantum feedback control

Zonghai Chen

Published Jan 1, 2005• 1 citation
OpenAlex

Abstract

The idea of feedback to actively control of quantum systems is introduced into quantum feedback control theory, which becomes more and more important part in quantum optics, atomic physics and quantum information theory. In consideration of differences between several feedback strategies, the progress of the research on quantum feedback control theory is reviewed, Markovian quantum feedback, Bayesian quantum feedback, non-Markovian quantum feedback with time delay and coherent quantum feedback are analyzed and expounded, and the four feedback strategies are also compared.

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The idea of feedback to actively control of quantum systems is introduced into quantum feedback control theory, which becomes more and more important part in quantum optics, atomic physics and quantum information theory. In consideration of differences between several feedback strategies, the progress of the research on quantum feedback control theory is reviewed, Markovian quantum feedback, Bayesian quantum feedback, non-Markovian quantum feedback with time delay and coherent quantum feedback are analyzed and expounded, and the four feedback strategies are also compared.
Quantum control theory is profitably reexamined from the perspective of quantum information, two results on the role of quantum information technology in quantum feedback control are presented and two quantum feedback control schemes, teleportation-based distant quantum feedback control and quantum feedback control with quantum cloning, are proposed. In the first feedback scheme, the output from the quantum system to be controlled is fed back into the distant actuator via teleportation to alter the dynamics of system. The result theoretically shows that it can accomplish some tasks such as distant feedback quantum control that Markovian or Bayesian quantum feedback can not complete. In the second feedback strategy, the design of quantum feedback control algorithms is separated into a state recognition step, which gives "on-off" signal to the actuator through recognizing some copies from the cloning machine, and a feedback (control) step using another copies of cloning machine. A compromise between information acquisition and measurement disturbance is established, and this strategy can perform some quantum control tasks with coherent feedback.
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.
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.
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.
In this paper, an overview of research in quantum control is presented. Examples of work in the first theme include numerous applications of semi-definite programming and relaxation methods in quantum information theory. Examples of the second include applications of feedback control in the development of new receiver designs for quantum-optical telecom. The third theme is just beginning to emerge as an active research area, linking fundamental issues in quantum field theory with new challenges for applied and computational mathematics in non-commutative stochastic analysis and optimization.
This chapter provides fundamental concepts and problems in quantum control theory. It discusses physical mechanisms behind quantum control theory. The chapter introduces modeling and analysis problems and summarizes open-loop and feedback control methods. In principle, Bayesian feedback may outperform the Markovian feedback because more information extracted from the measurement history can be used to determine the control. The fusion of control theory and quantum physics calls for collaborations between physicists and engineers. In contrast to classical control theory, the body of literature on open-loop control is much larger than that of feedback control. In quantum optimal control theory, all algorithms may suffer from the possible existence of false traps, that is, the search may converge to an undesired locally optimal solution that is not globally optimal. Quantum optimal control theory has been proven to be effective for finite-level or simple few-body systems.