This work presents a comparative study of pseudo-random (PRNG) and quantum-random (QRNG) number generators based on a combination of random-walk-based variance analysis and uniformity assessment. The analysis shows that the quantum source presents the expected variability patterns and exhibits closer agreement with an ideal uniform distribution, while pseudo-random shows wider dispersion and bias. These findings indicate that QRNG presents better performance for applications that require the highest levels of randomness integrity.
This work presents a comparative study of pseudo-random (PRNG) and quantum-random (QRNG) number generators based on a combination of random-walk-based variance analysis and uniformity assessment. The analysis shows that the quantum source presents the expected variability patterns and exhibits closer agreement with an ideal uniform distribution, while pseudo-random shows wider dispersion and bias. These findings indicate that QRNG presents better performance for applications that require the highest levels of randomness integrity.
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
Quantum random number generators (QRNGs) offer a fundamentally different approach to random number generation compared to classical methods, leveraging the inherent randomness of quantum processes. However, their practical implementation and analysis often face challenges, particularly concerning the accurate characterization of the underlying probability distribution and the optimization of generation algorithms. This paper presents a comprehensive probability analysis of QRNG output, focusing on identifying and quantifying sources of bias and uncertainty. We introduce a novel framework combining quantum information theory and statistical analysis to rigorously evaluate QRNG performance. Furthermore, we propose an optimization strategy based on adaptive sampling techniques and error correction, aiming to enhance both the security and efficiency of QRNGs. Our approach provides a detailed understanding of QRNG behavior and offers actionable insights for designing and deploying robust QRNG systems. The core of our analysis lies in the precise determination of the output probability distribution, denoted as P(s1, s2, ..., sK), where K represents the number of bits generated. We demonstrate how this distribution can be refined through iterative statistical estimation and how this information can be used to improve the generation process.
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.
Blockchain technology has grown rapidly and gained extensive adoption across various sectors due to its transparency and security benefits. Randomness plays crucial role in blockchain systems by ensuring fairness, security, and unpredictability in decentralized systems. This survey comprehensively analyzes randomness generation methods, particularly Pseudo-Random Number Generators (PRNGs) and Quantum Random Number Generators (QRNGs), in blockchain systems. PRNGs, while efficient, are vulnerable to predictability issues, whereas QRNGs offer higher security but require specialized hardware and have higher costs. The paper examines state-of-the-art randomness generation techniques, highlighting their strengths, limitations, and implications for blockchain security and efficiency. A novel taxonomy is proposed, categorizing randomness approaches into on-chain and off-chain mechanisms using PRNGs and QRNGs. By providing an in-depth exploration of existing methods and advancements, this survey enables readers to evaluate trade-offs and identify the most suitable approaches for specific blockchain applications. The survey also addresses gaps in current research and proposes future directions for secure and efficient randomness generation in decentralized systems. To the best of our knowledge, this paper is the first survey that analyses randomness techniques in blockchain using PRNG and QRNG.
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.
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.