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Intelligent Control and Automation

Continuous Controller Design for Quantum Shannon Entropy

Yifan Xing, Wensen Huang, Jinhui Zhao

Published Jan 1, 2016• 1 citation
Publisher

Abstract

This paper proposes the continuous controller design method for quantum Shannon entropy, which can continuously drive the entropy to track a desired trajectory. We also analyzed the controllability of Shannon entropy in very short time interval. Simulations are done on five dimensional quantum system, which can verify the validation of the method.

DOI
10.4236/ica.2016.73007

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This paper proposes the continuous controller design method for quantum Shannon entropy, which can continuously drive the entropy to track a desired trajectory. We also analyzed the controllability of Shannon entropy in very short time interval. Simulations are done on five dimensional quantum system, which can verify the validation of the method.
This paper proposes a new quantum control method which controls the Shannon entropy of quantum systems. For both discrete and continuous entropies, controller design methods are proposed based on probability density function control, which can drive the quantum state to any target state. To drive the entropy to any target at any prespecified time, another discretization method is proposed for the discrete entropy case, and the conditions under which the entropy can be increased or decreased are discussed. Simulations are done on both two- and three-dimensional quantum systems, where division and prediction are used to achieve more accurate tracking.
For quantum state trajectory tracking of density matrix in Liouville equation of quantum systems, with the help of concept in quantum system control, one can apply unitary transformation both to controlled system and free-evolutionary target system such as to change the time-variant and non-stationary target system into a stationary state. Therefore, the quantum state trajectory tracking problem becomes a steering one. State steering control law of the system transformed is designed by means of the Lyapunov stability theorem. Finally, numerical simulation experiments are given for a five-level energy quantum system. The comparison analysis of original system’s trajectory tracking with other method illustrates the advantage in control time of the method proposed.
A Lyapunov-based approach of trajectory tracking in Liouville equation for quantum systems is proposed. By selecting density matrix of controlled system as the system state, and defining the error between controlled state and target one as an error state, the paper regards this error as a new controlled state of system. In such a way the quantum state trajectory tracking problem is changed into the state regulation problem by driving the error state to zero. The control law is designed according to the Lyapunov stability theorem, which can be applied to track different kinds of quantum states including pure state, superposition state and mixed-state. Finally, numerical simulation experiments and results analysis are given.
This paper explores a novel approach to quantum control, termed information entropy gradient-driven quantum control. The central premise is that the rate of change of information entropy within a quantum system provides a fundamentally different and potentially more robust control signal compared to traditional methods relying on precise target state definitions. We propose a methodology where the gradient of the information entropy is continuously measured and utilized to drive the system towards desired quantum states. This approach aims to mitigate the inherent challenges associated with achieving high-fidelity control in quantum systems, particularly those stemming from measurement uncertainty and the difficulty of specifying precise target states. The theoretical framework presented outlines the key equations and concepts underlying this method, highlighting its potential advantages for applications in quantum computing, quantum communication, and quantum sensing. The core claim is that leveraging quantum system information entropy changes as control signals can enable efficient state manipulation, avoiding the precision issues encountered in traditional control methods. The core mechanism involves precise measurement of the quantum system's information entropy and feedback to the system for fine-tuning and state transfer. We demonstrate, through mathematical modeling, the feasibility and potential benefits of this approach.
There is a fundamental limit to what is knowable about atomic and molecular scale systems. This fuzziness is not always due to the act of measurement. Other contributing factors include system parameter uncertainty, functional uncertainty that originates from input functions, and sensors noises to mention a few. This indeterminism has led to major challenges in the development of accurate control methods for atomic scale systems. To address the probabilistic and uncertain nature of these systems, this work proposes a novel control framework that considers the representation of the quantum system states and the quantification of its physical properties following a probabilistic approach. Our framework is fully probabilistic. It uses the Shannon relative entropy from information theory to design optimal randomised controllers that can achieve a desired outcome of an atomic scale system. Two experiments are carried out to illustrate the applicability and effectiveness of the proposed approach.