Parameterized quantum random number generators for superconducting quantum hardware: novel architectures and NIST SP 800-22 evaluation under IBM noisy simulators

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.