We present a scalable experimental framework for validating quantum-generated bitstreams using the NIST SP 800-22 statistical test suite. Quantum randomness was simulated using Qiskit’s aer_simulator, generating 10 independent sequences of 10,000,000 bits each. These bitstreams were evaluated across 15 statistical categories including Monobit, Block Frequency, FFT, Linear Complexity, and Excursion-based tests. All but one test passed the NIST-recommended thresholds for both pass rates and p-value distributions. Specifically, the Random Excursion (Standard) test narrowly missed the threshold with 52 out of 56 sequences passing. Despite this, the overall results confirm the high entropy and statistical randomness of the quantum-generated sequences. Our framework also incorporates a batch-based architecture that enforces streak continuity across sequence boundaries and uses SHA-256 hashing for integrity verification. This infrastructure supports reproducibility and lays the foundation for future exploration of probabilistic thresholds in ultra-large-scale quantum bitstreams. In particular, we plan to generate and analyze up to one trillion quantum bits to investigate whether there exists a natural limit to the length of repeated stochastic patterns (streaks) in true randomness.
We present a scalable experimental framework for validating quantum-generated bitstreams using the NIST SP 800-22 statistical test suite. Quantum randomness was simulated using Qiskit’s aer_simulator, generating 10 independent sequences of 10,000,000 bits each. These bitstreams were evaluated across 15 statistical categories including Monobit, Block Frequency, FFT, Linear Complexity, and Excursion-based tests. All but one test passed the NIST-recommended thresholds for both pass rates and p-value distributions. Specifically, the Random Excursion (Standard) test narrowly missed the threshold with 52 out of 56 sequences passing. Despite this, the overall results confirm the high entropy and statistical randomness of the quantum-generated sequences. Our framework also incorporates a batch-based architecture that enforces streak continuity across sequence boundaries and uses SHA-256 hashing for integrity verification. This infrastructure supports reproducibility and lays the foundation for future exploration of probabilistic thresholds in ultra-large-scale quantum bitstreams. In particular, we plan to generate and analyze up to one trillion quantum bits to investigate whether there exists a natural limit to the length of repeated stochastic patterns (streaks) in true randomness.
The rapid development of digital communications, cloud computing, the Internet of Things (IoT), and integrated data systems has raised concerns about securely and reliably protecting sensitive information transmitted over public and private networks.The security of cryptographic schemes such as Rivest-Shamir-Adleman (RSA) and Elliptic Curve Cryptography (ECC) relies mainly on the inherent hardness of the underlying mathematical problem.Yet the ABSTRACT: This paper evaluates a simulated quantum security pipeline integrating a Quantum Random Number Generator (QRNG), BB84 Quantum Key Distribution (QKD), and Quantum One-Time Pad (QOTP) bitwise XOR encryption.Developed using IBM Qiskit v0.45 within a controlled environment using a seed value of 12345, the proposed framework addresses the lack of multi-stage randomness testing across quantum cryptographic workflows.The execution follows a four-stage sequential workflow starting with QRNG bit generation and entropy verification, which provides the groundwork and measurement bases for BB84.Next, BB84 QKD handles qubit transmission, basis sifting, paritycheck error correction, and Toeplitz matrix hashing for privacy amplification to extract the secret key.The derived key is then used for bitwise QOTP encryption and decryption.Finally, the pipeline undergoes multi-stage statistical validation at the raw QRNG, privacy-amplified key, and ciphertext levels.Across 1,000 independent runs with 10 6 -bit systems, the framework achieved a 98.4% overall pass rate on selected NIST SP 800-22 tests at a 0.01 significance level.Under a depolarizing noise model, the Quantum Bit Error Rate (QBER) remained ≤ 4.2%.Using finite-key evaluation and composable security principles, the system maintained statistical integrity across all stages.The findings demonstrate a successful simulation-based proof-of-concept rather than a hardware-ready solution.Future research will focus on executing the pipeline on physical quantum hardware and evaluating performance under realistic channel loss models.
Quantum random number generators (QRNGs) play a crucial role in cryptography, secure communications, and stochastic simulations. This study presents the metrological characterization of a QRNG implemented on the Quandela photonic quantum computer, available via the cloud. The system generates random sequences using single photons and beam splitters, where quantum superposition ensures a fundamentally probabilistic outcome. A key aspect of this characterization involves defining the sample size and the number of qubits used. The Quandela quantum processor operates with up to six qubits, corresponding to six photons in twelve optical modes. However, the simultaneous use of multiple photons can introduce unintended correlations due to quantum interference, affecting the quality of randomness. To ensure independent bit generation, experiments were conducted with a single photon per measurement, producing one-bit outcomes per detection event. The analysis focuses on repeatability and reproducibility, examining the statistical properties of the generated sequences. Raw sequences underwent randomness testing using NIST SP800-22 and entropy assessment with NIST SP800-90B. Initial results indicate that raw sequences exhibit biases due to imperfections in single-photon sources and optical elements. The sequences generated by the Quandela photonic quantum processor failed most NIST SP800-22 tests, including Frequency (Global and Block), Runs, and Approximate Entropy, with six tests showing a 100% failure rate. Additionally, under the NIST SP800-90B evaluation, 100% of the raw sequences failed the independence and identically distributed (IID) test, highlighting strong correlations and statistical dependencies. To enhance randomness quality, post-processing techniques were applied, including Von Neumann and the combination Samuelson + Von Neumann extractors. These methods significantly improved bit balance and reduced statistical dependencies. After post-processing, all sequences passed the NIST SP800-90B IID test, and the entropy per bit increased to 0.771 ± 0.005 for the Ascella processor, ensuring improved randomness quality. The findings highlight the metrological challenges in QRNGs based on photonic quantum processors, emphasizing the need for rigorous statistical validation. Despite system-specific noise, the quantum origin of randomness remains preserved, ensuring that the extracted sequences retain their fundamental unpredictability. Additionally, limitations associated with photonic quantum systems, such as hardware imperfections, photon losses, and optical misalignment, are discussed in the context of their impact on randomness quality. Despite these limitations, rigorous statistical validation and post-processing enable the generation of high-quality random sequences suitable for cryptographic protocols, secure key distribution, and high-performance computing This study reinforces the importance of metrology in quantum technologies, providing a structured methodology for optimizing QRNG reliability and performance.
Quantum Random Number Generators (QRNGs) exploit intrinsic quantum mechanical randomness and are promising candidates for higher-quality randomness than classical RNGs. However, QRNGs on Noisy Intermediate-Scale Quantum (NISQ) platforms are constrained by decoherence, gate and measurement errors, and limited circuit depth, and the resulting impact on statistical randomness is not yet systematically characterized. This work introduces parameterized quantum random number generator (PQRNG) architectures built from parameterized quantum circuits (PQCs) to improve tunability and expressive power under realistic noise. We study three architectures, PQC-H-CH, H-PQC-CH, and H-CH-PQC, and evaluate their randomness under Transpiler optimization and circuit-level error mitigation as preprocessing steps, using NIST SP 800-22 for statistical validation. Utilizing default NIST settings, PQC-H-CH attains the largest number of fully passing preprocessing configurations (126 combinations passing all 15 tests), compared with 110 for H-PQC-CH and 69 for H-CH-PQC, indicating strong robustness across Transpiler optimization and mitigation settings, and we find that preprocessing choices influence randomness quality more strongly than adjusting NIST test parameters. Overall, these results demonstrate that the proposed approach provides a solid foundation for developing more reliable and practical QRNGs using PQCs in NISQ devices.
Generating random bit streams is required in various applications, most notably in cyber-security, which is essential for Internet of Everything applications to enable secure communication between interconnected devices. Ensuring high-quality and robust randomness is crucial to mitigate risks associated with predictability and system compromise. True random numbers provide the highest levels of unpredictability. However, known systematic biases that can emerge from physical imperfections, environmental variations, and device aging in the processes exploited for random number generation must be carefully monitored. This article reports the implementation and characterization of an online procedure for the detection of anomalies in a true random bit stream. It is based on the NIST adaptive proportion and repetition count tests, complemented by statistical analysis relying on the Monobit and RUNS tests. The procedure is implemented in firmware through dedicated hardware accelerators processing configurable-length sequences, with automated anomaly detection triggering alerts after three consecutive threshold violations. The implementation is performed simultaneously with bit stream generation and also provides an estimate of the entropy of the source. A statistical analysis of the results from the NIST procedure to evaluate the symbols of the bit-stream as independently and identically distributed is also performed, leading to a computation of the minimum entropy of the source that cross-checks the previously mentioned estimate. The experimental validation of the approach is performed up the bit streams generated by a quantum, silicon-based entropy source.
This chapter introduces a quantum phase-parameterized approach to true random number generation, utilizing a natural superposition of quantum gates. The method employs a scalable quantum circuit architecture, using the RY(π/2) gate followed by the S gate across multiple qubits to generate maximally unpredictable quantum states. The proposed circuit was implemented on the IBM Quantum platform, where it generates bitstrings from quantum measurements that form the basis of the QTRNG output. To validate the randomness and cryptographic strength, extensive statistical testing was performed. These include restart experiments to verify non-reproducibility, autocorrelation analysis for temporal independence, and evaluations using NIST SP 800-22, SP 800-90B, Dieharder, and ENT test suites. These tests evaluate frequency, runs, entropy, chi-square distribution, and serial correlation to ensure high entropy and strong randomness quality. Results confirm that the proposed QTRNG consistently passes all tests, generating unbiased, high-quality random numbers. The approach is suitable for applications in post-quantum cryptography, secure key generation, and communication protocols, establishing a robust framework for safe and scalable quantum-based randomness.
This study investigates the capability of a field-programmable gate array (FPGA)-based quantum bit (QUBIT) emulator to replicate the quantum superposition state with randomness evaluation serving as the primary verification method. The QUBIT device is built on the FPGA, an integrated circuit that is a massively parallel array of independent logic elements. Using two QUBIT devices, a simple random number generator is created and statistical tests are used to verify randomness. These tests provide a quantitative measure of randomness quality, reflecting the emulator effectiveness at mimicking quantum superposition. The results offer insights into the limitations and potential of using the emulator (QUBIT) as an alternative to a physical quantum system. Randomness of generated numbers (bit strings) was tested with the NIST Statistical Test Suite (SP 800-22), widely regarded as the standard for randomness evaluation. In total, 106 bits were generated and tested with different block lengths: 10 blocks of 105 bits and 100 blocks of 104 bits. The observed deviations indicate that while the emulator can serve as an educational tool, its statistical properties currently limit its applicability in cryptographic contexts.