Title: Design of a new hybrid linearising-backstepping controller using quantum state equations and quantum spins

Authors: Nadjet Zioui; Aicha Mahmoudi; Mohamed Tadjine

Addresses: Laboratoire d'Intelligence Artificielle Appliquée (LI2A), Département de Génie Mécanique, Université du Québec à Trois-Rivières, 3351 Boulevard des Forges, Trois-Rivières, QC G8Z 4M3, Canada ' Projet Véo, Université de Sherbrooke, 2500 Bd de l'Université, Sherbrooke, QC J1K 2R1, Canada ' Laboratoire de Commande des Processus (LCP), École Nationale Polytechnique d'Alger, 10 Rue des Frères OUDEK, El Harrach 16200, Algeria

Abstract: Automatic control theory has brought many new innovative process control strategies and solutions to stability and trajectory tracking problems in engineering, for linear as well as for nonlinear systems. With the emergence of quantum computing concepts and technologies, quantum versions of conventional modelling techniques, control tools and strategies are needed to take full advantage of the future quantum computers. This work presents firstly the new quantum formulation of a special class of state-space equations. Secondly, quantum state feedback making it possible to control a desired qubit state is introduced based on quantum spins. This new method uses the Hermitian quantum rotations operators. The state variables can also be computed using the inherent property of reversibility of the quantum operators. Thirdly, simulation results considering both constant and time-varying references demonstrated the effectiveness of the method compared to the conventional competitor with very satisfactory results in terms of speed and resources use efficiency.

Keywords: qubit states; quantum spins; state space equations; quantum linearising control; QLC; backstepping methodology; quantum state feedback control.

DOI: 10.1504/IJAAC.2023.131754

International Journal of Automation and Control, 2023 Vol.17 No.4, pp.397 - 417

Received: 03 Jun 2022
Accepted: 31 Aug 2022

Published online: 30 Jun 2023 *

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