  We analyze the stability of a quantum algorithm simulating the quantum
dynamics of a system with different regimes, ranging from global chaos to
integrability. We compare, in these different regimes, the behavior of the
fidelity of quantum motion when the system's parameters are perturbed or when
there are unitary errors in the quantum gates implementing the quantum
algorithm. While the first kind of errors has a classical limit, the second one
has no classical analogue. It is shown that, whereas in the first case
(``classical errors'') the decay of fidelity is very sensitive to the dynamical
regime, in the second case (``quantum errors'') it is almost independent of the
dynamical behavior of the simulated system. Therefore, the rich variety of
behaviors found in the study of the stability of quantum motion under
``classical'' perturbations has no correspondence in the fidelity of quantum
computation under its natural perturbations. In particular, in this latter case
it is not possible to recover the semiclassical regime in which the fidelity
decays with a rate given by the classical Lyapunov exponent.
