  The speed-up provided by quantum algorithms with respect to their classical
counterparts is at the origin of scientific interest in quantum computation.
However, the fundamental reasons for such a speed-up are not yet completely
understood and deserve further attention. In this context, the classical
simulation of quantum algorithms is a useful tool that can help us in gaining
insight. Starting from the study of general conditions for classical
simulation, we highlight several important differences between two
non-equivalent classes of quantum algorithms. We investigate their performance
under realistic conditions by quantitatively studying their resilience with
respect to static noise. This latter refers to errors affecting the inital
preparation of the register used to run an algorithm. We also compare the
evolution of the entanglement involved in the different computational
processes.
