Effects of the entropy source on Monte Carlo simulations

TL;DR

This study compares the impact of different entropy sources on Monte Carlo simulation accuracy, showing that quantum random number generators improve approximation precision over traditional pseudo-random generators.

Contribution

It demonstrates that quantum random number generators enhance Monte Carlo simulation accuracy and efficiency compared to pseudo-random generators, with quantifiable improvements in specific experiments.

Findings

QRNG yields statistically better approximations than PRNGs

Potential reduction in approximation errors up to 1.89x with QRNG

Sample size reduction by approximately 8x using QRNG

Abstract

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.