Anton Lebedev, Annika Möslein, Olha I. Yaman, Del Rajan, Philip Intallura
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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.