In practice, several things can impact the ideal and limit speed-ups. The most obvious one being the number of triggered high level steps. It is easy to realize that for large values of N , the number of triggered high level steps will tend towards a system dependent number, in most cases larger than zero. Such that one cannot achieve arbitrarily large speed-ups simply by increasing N . From a more practical point of view, the physics of the system (vibrational frequencies) will be the first parameter to consider as a limitation for the value of N and thus for the speed-up (too large values of N would lead to artifacts such as resonances 30 ). A less straightforward impact on the effective (or real) speed-up is given by the overhead due timings. For comparison the ideal and limit speed-ups as defined in eqs. ( ) and ( ), respectively, are also reported.