Effects of the entropy source on Monte Carlo simulations

In this paper we show how different sources of random numbers influence the outcomes of Monte Carlo simulations. We compare industry-standard pseudo-random number generators (PRNGs) to a quantum random number generator (QRNG) and show, using examples of Monte Carlo simulations with exact solutions, that the QRNG yields statistically significantly better approximations than the PRNGs. Our results demonstrate that higher accuracy can be achieved in the commonly known Monte Carlo method for approximating $\pi$. For Buffon's needle experiment, we further quantify a potential reduction in approximation errors by up to $1.89\times$ for optimal parameter choices when using a QRNG and a reduction of the sample size by $\sim 8\times$ for sub-optimal parameter choices. We attribute the observed higher accuracy to the underlying differences in the random sampling, where a uniformity analysis reveals a tendency of the QRNG to sample the solution space more homogeneously. Additionally, we compare the results obtained with the QRNG and PRNG in solving the non-linear stochastic Schr\"odinger equation, benchmarked against the analytical solution. We observe higher accuracy of the approximations of the QRNG and demonstrate that equivalent results can be achieved at 1/3 to 1/10-th of the costs.