A Critical Enquiry into Alleged Hidden Mathematical Structure in Quantum Random Number Generator Outputs: Absence of Substantiated 2024 Claims and the State of Quantum Randomness Research (2024–2026)
In late April 2026, a viral claim circulated on professional social media platforms asserting that researchers at the National University of Singapore's Centre for Quantum Technologies (CQT) had published a Physical Review X article demonstrating that outputs from superconducting-qubit-based quantum random number generators (QRNGs) exhibit Kolmogorov complexity approximately 7.3% below the theoretical maximum for truly random sequences. The reported analysis, purportedly performed on 10 billion bits and achieving 6.8σ statistical significance, was interpreted as evidence of "hidden mathematical structure" invisible to conventional statistical randomness tests, potentially supporting interpretations of quantum measurement such as pilot-wave theories or superdeterminism. A comprehensive search across peer-reviewed databases, arXiv, journal archives, and institutional repositories yields no trace of this paper, authors, DOI, or supporting data. This note presents the results of that enquiry, contextualises the claim within the broader literature on algorithmic versus statistical randomness, reviews genuine post-2024 advancements in QRNG technology and foundational studies of quantum randomness, and discusses epistemological, cryptographic, and philosophical implications. Also available on Academia.edu: https://www.academia.edu/attachments/132650936/download_file?s=portfolio
In late April 2026, a viral claim circulated on professional social media platforms asserting that researchers at the National University of Singapore's Centre for Quantum Technologies (CQT) had published a Physical Review X article demonstrating that outputs from superconducting-qubit-based quantum random number generators (QRNGs) exhibit Kolmogorov complexity approximately 7.3% below the theoretical maximum for truly random sequences. The reported analysis, purportedly performed on 10 billion bits and achieving 6.8σ statistical significance, was interpreted as evidence of "hidden mathematical structure" invisible to conventional statistical randomness tests, potentially supporting interpretations of quantum measurement such as pilot-wave theories or superdeterminism. A comprehensive search across peer-reviewed databases, arXiv, journal archives, and institutional repositories yields no trace of this paper, authors, DOI, or supporting data. This note presents the results of that enquiry, contextualises the claim within the broader literature on algorithmic versus statistical randomness, reviews genuine post-2024 advancements in QRNG technology and foundational studies of quantum randomness, and discusses epistemological, cryptographic, and philosophical implications. Also available on Academia.edu: https://www.academia.edu/attachments/132650936/download_file?s=portfolio
Quantum random number generation (QRNG) offers a fundamentally different approach to randomness compared to classical methods. This paper explores the design and principles of a QRNG based on harnessing the inherent uncertainty in quantum measurements. The core claim is the development of a system capable of generating truly random quantum bit sequences. This is achieved by exploiting the probabilistic nature of quantum measurement, specifically the collapse of the wave function upon observation, which yields unpredictable outcomes. The generated sequences are expected to exhibit statistical independence, a crucial property for various quantum computing applications. This work lays the groundwork for a detailed exploration of QRNG techniques, highlighting their potential impact on secure quantum communication and simulation. We will detail the theoretical underpinnings, focusing on the mathematical formulation of the process and the statistical properties of the generated random numbers.
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.
Random numbers are essential for cryptography and scientific simulation. Generating truly random numbers for cryptography can be a slow and expensive process. Quantum physics offers a variety of promising solutions to this challenge, proposing sources of entropy that may be genuinely unpredictable, based on the inherent randomness of certain physical phenomena. These properties have been employed to design Quantum Random Number Generators (QRNGs), some of which are commercially available. In this work, we present the first published analysis of the Quantis family of QRNGs (excluding AIS-31 models), designed and manufactured by ID Quantique (IDQ). Our study also includes Comscire’s PQ32MU QRNG, and two online services: the Australian National University’s (ANU) QRNG, and the Humboldt Physik generator. Each QRNG is analysed using five batteries of statistical tests: Dieharder, National Institute of Standards and Technology (NIST) SP800-22, Ent, Tuftests and TestU01, as part of our thorough examination of their output. Our analysis highlights issues with current certification schemes, which largely rely on NIST SP800-22 and Diehard tests of randomness. We find that more recent tests of randomness identify issues in the output of QRNG, highlighting the need for mandatory post-processing even for low-security usage of random numbers sourced from QRNGs.
In recent years, the advancement of quantum computing technology has posed potential security threats to RSA cryptography and elliptic curve cryptography. In response, the National Institute of Standards and Technology (NIST) published several Federal Information Processing Standards (FIPS) of post-quantum cryptography (PQC) in August 2024, including the Module-Lattice-Based Key-Encapsulation Mechanism (ML-KEM), Module-Lattice-Based Digital Signature Algorithm (ML-DSA), and Stateless Hash-Based Digital Signature Algorithm (SLH-DSA). Although these PQC algorithms are designed to resist quantum computing attacks, they may not provide adequate security in certain specialized application scenarios. To address this issue, this study proposes quantum random number generator (QRNG)-based PQC algorithms. These algorithms leverage quantum computing to generate random numbers, which serve as the foundation for key pair generation, key encapsulation, and digital signature generation. A generalized architecture of QRNG is proposed, along with the design of six QRNGs. Each generator is evaluated according to the statistical validation procedures outlined in NIST SP 800-90B, including tests for verification of entropy sources and independent and identically distributed (IID) outputs. Experimental results assess the computation time of the six QRNGs, as well as the performance of QRNG-based ML-KEM, QRNG-based ML-DSA, and QRNG-based SLH-DSA. These findings provide valuable reference data for future deployment of PQC-based Transport Layer Security in web systems.
This anatomical review critically dissects Igor Volovich's (2024) proposal for symplectic computers, a conceptual framework grounded in the quantum-symplectic duality. By reformulating the Schrödinger equation in real variables, Volovich reveals that unitary quantum evolution is embedded within the larger symplectic group Sp(2N, ℝ). The review evaluates the paper's mathematical structure, the introduction of symplectic bits (symbits), and the canonical embedding map γ : U(N) → Sp(2N, ℝ). While acknowledging the elegance of the duality, the analysis identifies significant gaps in the formal definition of a computational model, the absence of complexity-theoretic grounding for claimed superiority, and ambiguities in scaling from single symbits to multi-symbit registers. Comparative analysis situates the work within emerging geometric approaches to quantum and classical computation. Profound epistemological questions arise concerning the privileging of complex Hilbert spaces, alongside ontological implications for the quantum-classical boundary. This Volume I initiates a multi-volume research program aimed at rigorous formalization and exploration of symplectic computation as a potential post-quantum paradigm. K S C Also available on Academia.edu: https://www.academia.edu/attachments/133164750/download_file?s=portfolio
Even if the output of a Random Number Generator (RNG) is perfectly uniformly distributed, it may be correlated to pre-existing information and therefore be predictable. Statistical tests are thus not sufficient to guarantee that an RNG is usable for applications, e.g., in cryptography or gambling, where unpredictability is important. To enable such applications a stronger notion of randomness, termed "true randomness", is required, which includes independence from prior information. Quantum systems are particularly suitable for true randomness generation, as their unpredictability can be proved based on physical principles. Practical implementations of Quantum RNGs (QRNGs) are however always subject to noise, i.e., influences which are not fully controlled. This reduces the quality of the raw randomness generated by the device, making it necessary to post-process it. Here we provide a framework to analyse realistic QRNGs and to determine the post-processing that is necessary to turn their raw output into true randomness.