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arXiv:2206.05328

Quantum Random Number Generators : Benchmarking and Challenges

David Cirauqui, Miguel Ángel García-March, Guillem Guigó i Corominas, Tobias Graß, Przemysław R. Grzybowski, Gorka Muñoz-Gil, J. R. M. Saavedra, Maciej Lewenstein

Published Jun 10, 2022• 5 citations
arXivHTMLPDF

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$\times$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.

DOI
10.48550/arxiv.2206.05328

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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×\times×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.
We study the importance of the quality of random numbers in Monte Carlo simulations of 2D Ising systems. Simulations are carried out at critical temperature to find the dynamic scaling law of the linear relaxation time. Our aim is to show that statistical correlations that appear in large Ising simulations performed with pseudorandom numbers can be corrected using a quantum random number generator (QRNG). To achieve high speeds and large systems, Ising lattices are simulated on a field programmable gate array (FPGA) with an optical QRNG.
Random Number Generators (RNGs) are used in various applications, including cryptography, scientific simulations, gaming, and virtual reality. The quality of these random numbers is crucial, especially for computational approaches that rely on unpredictability to produce accurate results. In this thesis, we perform a comprehensive assessment of the quality of a novel Quantum Random Number Generator (QRNG) based on single photon. QRNGs leverage quantum mechanical properties to produce truly random numbers. This ensures high entropy, unpredictability, and security, making QRNGs particularly useful in fields that require high-quality randomness.We evaluate the statistical properties of strings generated by our QRNG and then its practical application by comparing it to traditional Pseudo-Random Number Generators (PRNGs) in Monte Carlo Integration (MCI), a technique that estimates integrals using random sampling. In particular, we use two statistical randomness test suits, namely NIST and Dieharder, to assess the statistical properties of our QRNG. All tests within these tests were passed, confirming that the corresponding QRNG achieves true randomness with sufficient high entropy. Next, we use our QRNG-generated numbers to seed Monte Carlo Integration (MCI) and compare it against results obtained using classical PRNG. The QRNG-based MCI demonstrated more accurate and stable numerical estimates, showing lower error rates and improved convergence compared to PRNG-based simulations.These findings highlight the advantages of QRNGs in enhancing numerical accuracy and computational security. While QRNGs may have slower generation rates than PRNGs, their superior randomness quality allows for more reliable Monte Carlo-based simulations, suggesting that fewer samples may be needed to achieve the same level of accuracy compared to classical PRNGs. This research underscores the potential of QRNG-powered numerical methods, paving the way for their integration into more advanced applications, including scientific computing, financial modeling, and cryptographic security.
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.
ABSTRACT Quantum random number generator (QRNG) platforms use principles of quantum mechanics to create truly random numbers. Traditional pseudo-random number generators (PRNGs) generate numbers based on deterministic formulas. QRNG's use of the principles of superposition and measurement can provide numbers that cannot be predicted or replicated; therefore, they have been used as a source of randomness in various fields. In this research project, an experimental QRNG was designed and built using Qiskit simulations. Each experiment consisted of a series of two-qubit circuits. The circuits were created to place both qubits into an equal probability state. This was done by applying a pair of Hadamard gates (Hadamard gate applies a rotation operator of π/2 radians). Then each circuit was measured. For each measurement, there would be one output from each qubit. Since the Hadamard gate creates an equal-probability superposition, the combination of each qubit will either add up to 1 or subtract from -1. These combinations will be recorded and processed through several methods to evaluate their quality. Those methods include: Shannon Entropy Analysis, Frequency Distribution Analysis and Chi-Square Uniformity Testing. Keywords: Quantum Random Number Generator, Quantum Computing, Quantum Measurement, Cryptography, Secure Randomness, Qiskit Simulation
This paper explores the design of cryptographic algorithms leveraging the inherent randomness of quantum random number generators (QRNGs). Traditional cryptographic algorithms often rely on pseudo-random number generators (PRNGs), which are deterministic and therefore vulnerable to attacks if their internal state is compromised. QRNGs, on the other hand, derive their randomness from quantum mechanical phenomena, offering a fundamentally unpredictable source of numbers. This research investigates the application of QRNGs to enhance cryptographic security, focusing on constructing algorithms that exploit this unique property. The core claim is that utilizing QRNG characteristics allows for the design of more secure cryptographic algorithms. The proposed mechanism involves capitalizing on the non-deterministic nature of QRNGs to build algorithms with heightened security levels. This approach presents a novel security guarantee method by incorporating true randomness into cryptographic processes. We examine specific algorithm designs and analyze their security implications compared to traditional PRNG-based approaches. The paper concludes with a discussion on the challenges and future directions of utilizing QRNGs in cryptography.
Abstract The advantages of quantum random number generators (QRNGs) over pseudo-random number generators (PRNGs) are normally attributed to the nature of quantum measurements. This is often seen as implying the superiority of the sequences of bits themselves generated by QRNGs, despite the absence of empirical tests supporting this. Nonetheless, one may expect sequences of bits generated by QRNGs to have properties that pseudo-random sequences do not; indeed, pseudo-random sequences are necessarily computable, a highly nontypical property of sequences. In this paper, we discuss the differences between QRNGs and PRNGs and the challenges involved in certifying the quality of QRNGs theoretically and testing their output experimentally. While QRNGs are often tested with standard suites of statistical tests, such tests are designed for PRNGs and only verify statistical properties of a QRNG, but are insensitive to many supposed advantages of QRNGs. We discuss the ability to test the incomputability and algorithmic complexity of QRNGs. While such properties cannot be directly verified with certainty, we show how one can construct indirect tests that may provide evidence for the incomputability of QRNGs. We use these tests to compare various PRNGs to a QRNG, based on superconducting transmon qutrits and certified by the Kochen–Specker theorem, to see whether such evidence can be found in practice. While our tests fail to observe a strong advantage of the quantum random sequences due to algorithmic properties, the results are nonetheless informative: some of the test results are ambiguous and require further study, while others highlight difficulties that can guide the development of future tests of algorithmic randomness and incomputability.