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The Scientific World JOURNAL

Hybrid Impulsive Control for Closed Quantum Systems

Shouwei Zhao, Jitao Sun, Hai Lin

Published Jan 1, 2013• 0 citations
Publisher

Abstract

The state transfer problem of a class of nonideal quantum systems is investigated. It is known that traditional Lyapunov methods may fail to guarantee convergence for the nonideal case. Hence, a hybrid impulsive control is proposed to accomplish a more accurate convergence. In particular, the largest invariant sets are explicitly characterized, and the convergence of quantum impulsive control systems is analyzed accordingly. Numerical simulation is also presented to demonstrate the improvement of the control performance.

DOI
10.1155/2013/545091

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The state transfer problem of a class of nonideal quantum systems is investigated. It is known that traditional Lyapunov methods may fail to guarantee convergence for the nonideal case. Hence, a hybrid impulsive control is proposed to accomplish a more accurate convergence. In particular, the largest invariant sets are explicitly characterized, and the convergence of quantum impulsive control systems is analyzed accordingly. Numerical simulation is also presented to demonstrate the improvement of the control performance.
We investigate the Lyapunov control of finite-dimensional quantum systems with impulsive control fields, where the studied quantum systems are governed by the Schrödinger equation. By three different Lyapunov functions and the invariant principle of impulsive systems, we study the convergence of quantum systems with impulsive control fields and propose new results for the mentioned quantum systems in the form of sufficient conditions. Two numerical simulations are presented to illustrate the effectiveness of the proposed control method.
In this paper, the finite time tracking issue for a class of closed quantum systems under the action of impulsive control fields is addressed. The aim is to steer the state of the quantum system to the trajectory of a periodic time-varying target. By using the Lyapunov direct method and considering a finite-time control strategy, the modified impulsive tracking controllers are designed such that the error dynamical system converges to zero in finite time. While finite-time tracking implies optimality in convergence time and has better disturbance rejection. Numerical simulations are given to illustrate the effects of system’s trajectory tracking, and also given to demonstrate the superiority of the control laws which are proposed.
A Lyapunov-based method is presented for stabilizing and controlling of closed quantum systems. The proposed method is constructed upon a novel quantum Lyapunov function of the system state trajectory tracking error. A positive-definite operator in the Lyapunov function provides additional degrees of freedom for the designer. The stabilization process is analyzed regarding two distinct cases for this operator in terms of its vanishing or non-vanishing commutation with the Hamiltonian operator of the undriven quantum system. To cope with the global phase invariance of quantum states as a result of the quantum projective measurement postulate, equivalence classes of quantum states are defined and used in the proposed Lyapunov-based analysis and design. Results show significant improvement in both the set of stabilizable quantum systems and their invariant sets of state trajectories generated by designed control signals. The proposed method can potentially be applied for high-fidelity quantum control purposes in quantum computing frameworks.
Quantum Lyapunov control is a feedback control methodology to determine control fields applied to control quantum systems. In this paper, with the help of the invariant principle of impulsive systems, we investigate the trajectory tracking for quantum systems with impulsive control fields by two Lyapunov functions based on the distance of quantum states and the average value of Hermitian operator which can be regarded as an observable of a quantum system, propose new control fields to drive the quantum systems in the form of sufficient conditions. One numerical simulation is presented to illustrate the effectiveness of the proposed control method.