  We establish a uniform comparison between the spectrum of the rough Laplacian
(acting on sections of a vector bundle of complex rank one or of harmonic
curvature) with the spectrum of a discrete operator (a generalization of a
discrete magnetic Laplacian added with a potential) acting on a finite
dimensional space coming from a discretization process. As an application, we
obtain a comparison of the first positive eigenvalue of the rough Laplacian
with the holonomy.
