[Paper Review] Quantum Random Number Generators : Benchmarking and Challenges

David Cirauqui, Miguel Ángel García-March+6 more|arXiv (Cornell University)|Jun 10, 2022

Advanced Data Storage Technologies4 citations

TL;DR

This paper benchmarks Quantum Random Number Generators (QRNGs) by evaluating their performance in simulating critical dynamics in 2D Ising lattices using FPGAs and GPUs, comparing them to classical pseudo-random number generators (PRNGs). It identifies that QRNGs outperform PRNGs in detecting correlations at moderate lattice sizes (128×128), establishing quantitative requirements for speed, access time, and efficiency to achieve quantum advantage in random number generation.

ABSTRACT

We discuss the current state of the art of Quantum Random Number Generators (QRNG) and their possible applications in the search for quantum advantages. To this aim, we first discuss a possible way of benchmarking QRNG by applying them to the computation of complicated and hard to realize classical simulations, such as critical dynamics in two-dimensional Ising lattices. These are performed with the help of computing devices based on field-programmable gate arrays (FPGAs) or graphic processing units (GPUs). The results obtained for QRNG are compared with those obtained by classical pseudo-random number generators (PRNG) of various qualities. Monte Carlo simulations of critical dynamics in moderate lattice sizes (128$ imes$128) start to be sensitive to the correlations present in pseudo-random numbers sequences, allowing us to detect them. By comparing our analysis with that of Ref. [PRE {\bf 93}, 022113 (2016)], we estimate the requirements for QRNGs in terms of speed, rapidity of access, and efficiency to achieve the objective of quantum advantage with respect to the best PRNGs. We discuss the technical challenges associated with this objective.

Motivation & Objective

• To evaluate the performance of Quantum Random Number Generators (QRNGs) in simulating complex classical systems, specifically critical dynamics in 2D Ising lattices.
• To identify the limitations of classical pseudo-random number generators (PRNGs) in capturing long-range correlations in Monte Carlo simulations.
• To establish quantitative benchmarks for QRNGs—specifically speed, access time, and efficiency—required to achieve quantum advantage over the best classical PRNGs.
• To assess the feasibility of using QRNGs in high-precision simulations where statistical correlations in PRNGs degrade simulation accuracy.
• To provide a methodology for distinguishing high-quality randomness using dynamic critical exponents derived from Monte Carlo simulations.

Proposed method

• Simulating critical dynamics in 2D Ising lattices (128×128) using Monte Carlo methods on FPGA- and GPU-based computing platforms.
• Employing both QRNGs and multiple classes of PRNGs (with varying correlation lengths) as input random number sources in the simulations.
• Analyzing the dynamic critical exponent $ z $ via finite-size scaling and fitting to power-law behavior to detect deviations caused by PRNG correlations.
• Calculating $ \log(\tau_0) $ from fitting the relaxation time to extract sensitivity to randomness quality, with lower values indicating higher correlation.
• Comparing results from QRNGs and PRNGs against known theoretical and numerical benchmarks from the literature to validate simulation accuracy.
• Using the dynamic exponent $ z $ as a sensitive probe to detect subtle statistical correlations in random number sequences.

Experimental results

Research questions

• RQ1 Can QRNGs detect correlations in Monte Carlo simulations that classical PRNGs fail to avoid, even at moderate lattice sizes?
• RQ2 What are the minimum performance requirements (speed, access time, efficiency) for QRNGs to outperform the best classical PRNGs in simulating critical dynamics?
• RQ3 How does the dynamic critical exponent $ z $ serve as a sensitive indicator of randomness quality in simulation outputs?
• RQ4 To what extent do different PRNGs with varying correlation lengths affect the accuracy of Monte Carlo simulations of the 2D Ising model?
• RQ5 Can the simulation of critical dynamics be used as a benchmarking tool for evaluating the quality of random number generators in high-stakes applications?

Key findings

• Monte Carlo simulations of 128×128 2D Ising lattices become sensitive to PRNG correlations, allowing detection of statistical flaws that are undetectable in smaller systems.
• The QRNG produced $ \log(\tau_0) = -0.362 $, significantly lower than all tested PRNGs, indicating superior randomness quality and reduced correlation effects.
• PRNGs with longer correlation lengths (e.g., PRNG3 $ k=2 $, $ \log(\tau_0) = -0.2454 $) still underperformed the QRNG, highlighting the fundamental advantage of quantum randomness.
• The dynamic critical exponent $ z $ extracted from QRNG-based simulations aligned closely with established theoretical and numerical values, validating the method’s sensitivity.
• The study estimates that QRNGs must achieve high generation rates and low access latency to outperform the best classical PRNGs in real-world quantum advantage scenarios.
• The benchmarking framework based on critical dynamics provides a scalable, physics-grounded method to distinguish high-quality randomness sources, with measurable impact on simulation outcomes.