Sub-Shot-Noise Phase Estimation via Adaptive Bayesian Protocols in Noisy Intermediate-Scale Quantum Sensors
Uganda Uganda Uganda 
Abstract
Quantum sensing has emerged as a transformative technology for precision measurement, offering the potential to surpass the classical shot-noise limit through quantum-enhanced estimation strategies. Practical implementation within Noisy Intermediate-Scale Quantum (NISQ) platforms, however, remains constrained by decoherence, gate imperfections, measurement uncertainty, and limited quantum resources that reduce achievable sensing accuracy. This study aimed to evaluate the effectiveness of adaptive Bayesian protocols in achieving sub-shot-noise phase estimation under realistic NISQ operating conditions while examining the roles of adaptive feedback, posterior convergence, quantum coherence, and resource optimization. A mixed-methods sequential explanatory design was employed using 12,000 quantum sensing simulations complemented by experimental benchmark datasets, laboratory implementation records, and expert evaluations. Quantitative data were analyzed through Bayesian performance analysis, repeated-measures statistical testing, multivariate regression, and Monte Carlo uncertainty estimation, whereas qualitative evidence was interpreted using thematic analysis of experimental observations and implementation reports. Findings demonstrated that adaptive Bayesian estimation significantly improved phase estimation accuracy, accelerated posterior convergence, enhanced Fisher information, preserved quantum coherence, and consistently achieved sub-shot-noise precision across diverse NISQ sensing architectures despite realistic noise conditions. Results indicate that intelligent probabilistic inference functions as a critical component of practical quantum metrology by dynamically optimizing measurement strategies and compensating for hardware limitations. The proposed framework provides a robust foundation for developing scalable, resource-efficient, and experimentally feasible quantum sensing systems for future scientific and industrial precision measurement applications.
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Copyright (c) 2026 Helen Nabirye, Ronald Muwanguzi, Deborah Wanyama
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