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The speed-up provided by quantum algorithms with respect to their classicalcounterparts is at the origin of scientific interest in quantum computation.However, the fundamental reasons for such a speed-up are not yet completelyunderstood and deserve further attention. In this context, the classicalsimulation of quantum algorithms is a useful tool that can help us in gaininginsight. Starting from the study of general conditions for classicalsimulation, we highlight several important differences between twonon-equivalent classes of quantum algorithms. We investigate their performanceunder realistic conditions by quantitatively studying their resilience withrespect to static noise. This latter refers to errors affecting the initalpreparation of the register used to run an algorithm. We also compare theevolution of the entanglement involved in the different computationalprocesses.Comment: 10 pages, 9 figures, RevTeX

Noise resilience and entanglement evolution in two nonequivalent classes of quantum algorithms