Implementation of logical gates on infinite dimensional quantum oscillators

Nabile Boussaid (1) , Marco Caponigro (2, 3) , Thomas Chambrion (2, 3)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
2 CORIDA - Robust control of infinite dimensional systems and applications
3 IECN - Institut Élie Cartan de Nancy

In this paper we study the error in the approximate simultaneous controllability of the bilinear Schrodinger equation. We provide estimates based on a tracking algorithm for general bilinear quantum systems and on the study of the finite dimensional Galerkin approximations for a particular class of quantum systems, weakly-coupled systems. We then present two physical examples: the perturbed quantum harmonic oscillator and the infinite potential well.

Keywords: averaging theory; Bilinear Schrodinger equation; quantum control; geometric control theory; averaging theory.

Domains: Optimization and Control [math.OC]

Nabile Boussaid, Marco Caponigro, Thomas Chambrion. Implementation of logical gates on infinite dimensional quantum oscillators. American Control Conference (ACC) 2012, Jun 2012, Montreal, Canada. pp.5825-5830. ⟨hal-00637115⟩