Measurement-Driven Diagnostics and Uncertainty Evaluation of NISQ Hardware: A Metrological Framework for NMR Quantum Nodes

The transition from isolated quantum demonstrations to deployable hybrid quantum-classical infrastructures requires quantum nodes that are not only functional, but also experimentally characterized, diagnostically understood, and metrologically validated. In this work, a desktop NMR quantum computer is investigated as a physical node of a hybrid architecture rather than as a mere abstract backend for algorithm execution. A variational quantum circuit is adopted as a representative workload to probe the practical execution limits of the platform, with particular attention to runtime feasibility, RF compilation overhead, and stability of the measured probabilistic outputs. The experimental analysis shows that the main bottleneck is not only circuit depth, but also the analog compilation burden associated with arbitrary continuous-angle rotations, which can drive the total execution time beyond the effective coherence-compatible operating regime of the node. To address this issue, a hardware-aware redesign is introduced by constraining both trainable parameters and encoded inputs to LUT-compatible discrete angular values and by remapping negative angles through 2π module equivalence. This strategy substantially reduces execution overhead and enables operation within a regime compatible with stable on-hardware execution. On top of this diagnostic analysis, the output of the node is interpreted as an experimentally estimated probability and is characterized through a metrological uncertainty framework combining finite-shot variability and repeatability contributions. The obtained results show that, under nominally stable operating conditions within the optimized regime, the repeatability contribution remains smaller than the intrinsic finite-shot uncertainty, indicating that the node can provide stable and traceable probabilistic outputs despite current NISQ limitations. The proposed approach provides a practical methodology for diagnosing, constraining, and validating compact quantum nodes intended for future hybrid quantum-classical infrastructures.