  Minimizing the effect of decoherence on a quantum register must be a central
part of any strategy to realize scalable quantum information processing. Apart
from the strength of the coupling to the environment, the decoherence rate is
determined by the the system level structure and by the spectral composition of
the noise trace that the environment generates. Here, we discuss a relatively
simple model that allows us to study these different effects quantitatively in
detail. We evaluate the effect that the perturbation has on an NMR system while
it performs a Grover search algorithm.
