  In this work we study several models of decoherence and how different quantum
maps and algorithms react when perturbed by them. Following closely Ref. [1],
generalizations of the three paradigmatic one single qubit quantum channels
(these are the depolarizing channel, the phase damping channel and the
amplitude damping channel) for the case of an arbitrarily-sized
finite-dimensional Hilbert space are presented, as well as other types of noise
in phase space. More specifically, Grover's search algorithm's response to
decoherence is analyzed; together with those of a family of quantum versions of
chaotic and regular classical maps (the baker's map and the cat maps). A
relationship between how sensitive to decoherence a quantum map is and the
degree of complexity in the dynamics of its associated classical counterpart is
observed; resulting in a clear tendency to react the more decoherently the more
complex the associated classical dynamics is.
