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International Journal of Psychosocial Rehabilitation

TRACKING CONTROL OF QUANTUM VON NEUMANN ENTROPY

YIFAN XING

Published Feb 28, 2020• 0 citations
Publisher

Abstract

This paper provides the accurate tracking control of the von-Neumann entropy of quantum systems. The closed form of the accurate time derivative of the entropy is presented. Based on this, controller design method for time-dependent decay rate is provided, which can directly drive the entropy to track a desired trajectory. Simulations are done on two-level quantum system.

DOI
10.37200/ijpr/v24i4/pr201061

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This paper provides the accurate tracking control of the von-Neumann entropy of quantum systems. The closed form of the accurate time derivative of the entropy is presented. Based on this, controller design method for time-dependent decay rate is provided, which can directly drive the entropy to track a desired trajectory. Simulations are done on two-level quantum system.
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.
The orbit tracking problem of a free-evolutionary target system in closed quantum systems is solved by changing it into the state transferring problem with the help of unitary transformation.The control law designed by the Lyapunov stability theorem employs a carefully constructed virtual mechanical quantity P to ensure the system convergence.The virtual mechanical quantity P is chosen by two approaches according to the forms of limit set,where P = —pf is suitable for regular limit set and a new different P is constructed for irregular one.The proposed tracking control theory is demonstrated on a four-level quantum system by means of numerical simulation experiments.
This article is devoted to developing an approach for manipulating the von Neumann entropy S(ρ(t)) of an open two-qubit system with coherent control and incoherent control inducing time-dependent decoherence rates. The following goals are considered: (a) minimizing or maximizing the final entropy S(ρ(T)); (b) steering S(ρ(T)) to a given target value; (c) steering S(ρ(T)) to a target value and satisfying the pointwise state constraint S(ρ(t))≤S¯ for a given S¯; (d) keeping S(ρ(t)) constant at a given time interval. Under the Markovian dynamics determined by a Gorini-Kossakowski-Sudarshan-Lindblad type master equation, which contains coherent and incoherent controls, one- and two-step gradient projection methods and genetic algorithm have been adapted, taking into account the specifics of the objective functionals. The corresponding numerical results are provided and discussed.
This paper is concerned with the tracking control problem for the closed single spin-1/2 quantum ensembles. Based on the Liouville-von Neumann equation, mathematical model of dynamics for single spin-1/2 quantum ensembles are formulated as a bilinear form with states evolving on Bloch sphere. An associated matrix Lie group equation describing transfers from the initial state being an identity matrix is naturally introduced. The tracking problem for the system in question is transformed to a stabilization problem such that the control techniques are able to be used. In order to deal with the tracking problem, the Lyapunov-based feedback design method is employed to obtain the control such that the dynamics of system can converge to the reference trajectory.
The measurement-based feedback (MBF) control offers several powerful means for preparing the desired target quantum state. Therefore, it is important to investigate fundamental properties of MBF. In particular, how the entropy of the controlled system under the MBF behaves is of great interest. In this study, we examine this problem by deriving a sufficient condition that the time derivative of the von Neumann entropy is nonnegative under the MBF control. This result is rigorously characterized by the variance of the system observable and the quantumness of a given decoherence. We show the validity of the result and physical interpretation in the example of qubit stabilizing.