Implementation of logical gates on infinite dimensional quantum oscillators
Nabile Boussaid (LM-Besan\c{c}on), Marco Caponigro (INRIA Lorraine /, IECN / MMAS, IECN), Thomas Chambrion (INRIA Lorraine / IECN / MMAS, IECN)
TL;DR
This paper investigates the controllability of infinite-dimensional quantum oscillators, providing error estimates and practical examples like the quantum harmonic oscillator and potential well.
Contribution
It introduces a tracking algorithm for controlling bilinear quantum systems and analyzes finite-dimensional approximations for weakly-coupled systems.
Findings
Error bounds for approximate controllability
Effective control strategies for quantum harmonic oscillator
Insights into finite-dimensional approximation accuracy
Abstract
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.
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