Parameterized quantum random number generators for superconducting quantum hardware: novel architectures and NIST SP 800-22 evaluation under IBM noisy simulators
Ramin Salehi, Asad Waqar Malik, M. A. Novotny, Samee U. Khan
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.
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.
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.
Abstract Noisy Intermediate-Scale Quantum (NISQ) devices are near-term quantum computing devices that inherently suffer from imperfect gate implementation, decoherence, and measurement noise. The main type of variational quantum algorithms(VQAs) is based on Parameterized Quantum Circuits (PQCs), which, however, face practical challenges due to optimization instability of optimization caused by noise and reduced performance. In this paper, we suggest a comprehensive noise-resilient optimization framework for PQCs, which explicitly incorporates noise-resilient circuit architecture design, incorporating noise-aware training strategies into the variational optimization loop. The framework uses circuit structures that are efficient in depth and are hardware compatible in addition to adaptive optimizer choice, stochastic optimization, and averaging as a part of repeated measurement to reduce the impacts of realistic noise. Large-scale experiments are performed with different amounts of qubits, depths of the circuit and noise strengths with realistic noise models. The findings indicate that the convergence rate is faster, the stability is increased, the variability of run-to-run variability is minimized, and other robustness is better than the noise-unaware optimization techniques. Moreover, systematic studies determine optimal operating regions that optimally trade-off expressibility and noise tolerance to offer useful design advice on trusted implementation of VQAs with near-term quantum hardware.
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.
Abstract Designing novel circuits and models for generating truly random numbers is of great importance. Recent attention has been focused on the idea of using real quantum computers to generate random numbers. In order to generate purely random bits and numbers, one method relies on the natural superposition of quantum gates. Here, we design a Quantum Random Number Generator (QRNG) exploiting combinations of Hadamard and controlled-Hadamard gates in IBM Quantum Experience (QX). In order to verify that the generated bit sequences were truly random, the proposed circuit’s outputs were subjected to the National Institute of Standards and Technology (NIST) test suite. In comparison to previous works, we found that not only had the total number of passed tests increased, but the P-values had also improved in many cases. For example, in the simulation style of the IBM QX, the number of passed tests is 14 out of 15 standard NIST tests. For the experimental mood of the IBM 16Q Melbourne, the number of passed tests is six without using any extractions. Furthermore, one more test is passed by adding Barrier operations to the circuits, and the P-values have increased. As a result, we found that the proposed method had more passed tests than previous works. The average of P-values for the six passed tests in former research for the mood of using a combination of extractors is about 0.43 . However, the best result we can get with our circuits is around 0.60 (the average of P-values for 14 passed tests), which is an improvement of 0.17 compared to former works . Because of this, our circuits are getting ever closer to being a true QRNG.
Random numbers are the foundation for cryptographic protocols including encryption and key generation This work presents the design and evaluation of a Quantum Random Number Generator (QRNG) leveraging quantum phase gates in IBM Qiskit, specifically S†(S-dagger), Rx(θ) and S gates. These gates exploit quantum phenomena such as superposition and entanglement to generate high-quality random numbers. By optimizing resource utilization through qubit reuse by measurement operations, the generated binary outcomes form a random number sequence. The quality and unpredictability of the numbers are validated using statistical tests including NIST SP 800-90, SP 800-22 and other preliminary tests. The QRNG has significant potential for enhancing cryptographic protocols, secure data transmission and network authentication particularly in the context of emerging 6G communication systems.
Quantum computer (QC) can be used as a true random number generator (TRNG). However, various noise sources introduce a bias in the generated number which affects the randomness. In this work, we analyze the impact of noise sources e.g., gate error, decoherence, and readout error in QC-based TRNG by running a set of error calibration and quantum tomography experiments. We employ a hybrid quantum-classical gate parameter optimization routine to find an optimal gate parameter. The optimal parameter compensates for error-induced bias and improves the quality of the random number by exploiting even the worst quality qubits. However, searching the optimal parameter in a hybrid setup requires time-consuming iterations between classical and quantum machines. We propose a machine learning model to predict optimal quantum gate parameters based on the qubit error specifications. We validate our approach using experimental results from IBM's publicly accessible quantum computers and the NIST statistical test suite. The proposed method can correct bias in any worst-case qubit by up to 88.57% in real quantum hardware.