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Chinese Journal of Quantum Electronics

Quantum control theory

Daoyi Dong

Published Jan 1, 2004• 4 citations
OpenAlex

Abstract

Quantum control theory is a new interdiscipline, which mainly studies the control of quantum states for systems in the microworld. First, quantum control theory is elicited through quantum information theory. Then the research contents and characteristics of quantum control theory and measurement theory in quantum control are expounded. Current research of quantum control theory is also summarized. And last, advanced research on quantum control theory is proposed.

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Quantum control theory is a new interdiscipline, which mainly studies the control of quantum states for systems in the microworld. First, quantum control theory is elicited through quantum information theory. Then the research contents and characteristics of quantum control theory and measurement theory in quantum control are expounded. Current research of quantum control theory is also summarized. And last, advanced research on quantum control theory is proposed.
Aiming at development trend of quantum communication and quantum computing,the importance embranchment of quantum system science——quantum control theory is expounded.Quantum control theory is a brand-new interdiscipline,which mainly studies the control of quantum states for systems in the microworld.First,quantum control theory is elicited through quantum information theory.Then in turn the definition,characteristics,current research state and research contents of quantum control are systemically expounded.And at last some new ideas for advanced research are proposed.
Quantum control theory is a new interdiscipline, which mainly concerns how to control quantum states of microsystems. To get better control results, it is necessary to study the modeling and simulation of the systems. With the consideration of the characteristics of quantum control, direct mechanism modeling and quantization modeling for quantum control systems are studied, and simulation of quantum control systems is also analyzed. Direct mechanism modeling uses the mechanism information of systems in quantum physics and suitably models some quantum control systems with the known mechanism. Quantization modeling makes the most of the corresponding relations between quantum operators and classical physical quantities, and uses the information of models in classical control to establish the corresponding models in quantum control.
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.
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.
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 paper explores the potential of leveraging chaos theory for precise control of quantum systems. The core claim posits that the inherent sensitivity to initial conditions within chaos theory can be harnessed to achieve highly accurate control over quantum systems. The proposed mechanism involves designing a chaos-based control method, exploiting this sensitivity to precisely manipulate quantum states. This represents a novel approach, bridging the traditionally distinct fields of quantum mechanics and chaos theory. We present a theoretical framework outlining the principles and potential challenges associated with this control strategy, emphasizing the need for further research and development. The control strategy utilizes feedback loops, incorporating measurements of the quantum system's state to iteratively refine the control parameters based on the chaotic dynamics. We discuss the potential for enhanced control precision and explore the limitations imposed by the inherent complexity of quantum systems. This research contributes to a deeper understanding of quantum control and opens new avenues for technological advancements. ---