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IEEE Conference on Decision and Control (CDC)

Algorithms for closed loop control of quantum dynamics

HERSCHEL A. RABITZ

Published Nov 11, 2002• 12 citations
Publisher

Abstract

Most quantum systems considered for control by external fields are plagued by a serious lack of complete information about the underlying Hamiltonian. Traditional feedback control techniques are generally not appropriate due to the latter problem, as well as the ultrafast nature of typical quantum dynamics phenomena and the fact that observations of the quantum system will inevitably lead to a disturbance which may often be contradictory to the desired control. In contrast, learning control techniques have a special role to play in the manipulation of quantum dynamics phenomena. The unique capabilities of quantum systems making them amenable to learning control are (a) the ability to have very large numbers of identical systems for submission to control, (b) the high duty cycle of laboratory laser controls, and (c) the ability to observe the impact of trial controls at ultrafast time scales. Various learning algorithms have been proposed to guide this control process. The paper discusses these proposals, as well as some new perspectives.

DOI
10.1109/cdc.2000.912893

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Most quantum systems considered for control by external fields are plagued by a serious lack of complete information about the underlying Hamiltonian. Traditional feedback control techniques are generally not appropriate due to the latter problem, as well as the ultrafast nature of typical quantum dynamics phenomena and the fact that observations of the quantum system will inevitably lead to a disturbance which may often be contradictory to the desired control. In contrast, learning control techniques have a special role to play in the manipulation of quantum dynamics phenomena. The unique capabilities of quantum systems making them amenable to learning control are (a) the ability to have very large numbers of identical systems for submission to control, (b) the high duty cycle of laboratory laser controls, and (c) the ability to observe the impact of trial controls at ultrafast time scales. Various learning algorithms have been proposed to guide this control process. The paper discusses these proposals, as well as some new perspectives.
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In recent years, great strides have been made in controlling quantum phenomena through the use of tailored laser pulses. This paper discusses several issues that lie ahead, drawing on the ability to perform massive numbers of closed-loop laser control experiments. Particular attention is given to the robustness of these experiments, the capability of deducing control mechanisms and the introduction of special closed-loop control techniques to reveal Hamiltonian information. All these prospects point towards an increasing ability to control and understand quantum systems through close-loop laboratory techniques.
This paper presents a novel approach to dynamic quantum control utilizing feedback learning algorithms. The core idea is to develop a system capable of real-time adjustment of control parameters based on feedback information obtained from the quantum system itself. This approach addresses the inherent challenges in precisely controlling quantum systems, which are often highly sensitive to environmental noise and difficult to model accurately. The proposed framework leverages the principles of quantum control and feedback learning to achieve optimal control performance. The system architecture incorporates a closed-loop control mechanism where the system's output is continuously monitored, and the control parameters are adjusted accordingly. Mathematical formulations detailing the control process, feedback mechanisms, and optimization strategies are provided. This work contributes to advancements in quantum control by offering a robust and adaptable method for manipulating quantum states, with potential applications in quantum computing, quantum sensing, and quantum communication. The algorithm is designed to minimize the influence of external disturbances and maximize the accuracy of state preparation and manipulation. The presented approach provides a pathway towards more reliable and efficient quantum control strategies.
Interest in the control of quantum dynamics phenomena has grown in recent years, with laboratory studies showing increasing successes. The role of theory in the control of quantum phenomena encompasses the design of laser controls, the development of algorithms to guide the laboratory studies, and the means to analyze the ensuing dynamics observations. Laboratory laser control instrumentation has the special capability of performing massive numbers of experiments in a short period of time, to rapidly search for controls that meet the objectives. This unique laboratory feature needs to be factored in when considering how to best utilize theoretical analyses. The present paper reviews the role that theory is playing, as well as suggests some future avenues for theory in the laser control of quantum phenomena.
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.