We study how the Monte Carlo simulations of the critical dynamics of two-dimensional Ising lattices are affected by the quality (as compared to true randomness) of the pseudo-randomness used in them by computing an observable known to be sensitive to it: the dynamic critical exponent z. To this end, we first present a review of the literature and then perform the same simulations with different pseudo-randomness sources. We control the quality of the random streams by physically reseeding the generators and observe that while the mean value of the measured observable is slightly affected by the correlations within them, its variance does get a severe impact. By studying this affectation and how such pseudo-random streams perform under standard randomness tests based on statistical analysis, we conclude that the new protocol is able to detect other types of correlations and can thus be used as an additional test. On the other hand, we present the first (to the best of our knowledge) computation of the dynamic critical exponent with a perfectly random quantum random number generator (QRNG) and hypothesize that the presented strategy may point toward a route to establish quantum advantage based on the quality of results as complementary to those strategies based on the speed of the computational task.
