Adaptive Fidelity Estimation for Quantum Programs with Graph-Guided Noise Awareness

Fidelity estimation is a critical yet resource-intensive step in testing quantum programs on noisy intermediate-scale quantum (NISQ) devices, where the required number of measurements is difficult to predefine due to hardware noise, device heterogeneity, and transpilation-induced circuit transformations. We present QuFid, an adaptive and noise-aware framework that determines measurement budgets online by leveraging circuit structure and runtime statistical feedback. QuFid models a quantum program as a directed acyclic graph (DAG) and employs a control-flow-aware random walk to characterize noise propagation along gate dependencies. Backend-specific effects are captured via transpilation-induced structural deformation metrics, which are integrated into the random-walk formulation to induce a noise-propagation operator. Circuit complexity is then quantified through the spectral characteristics of this operator, providing a principled and lightweight basis for adaptive measurement planning. Experiments on 18 quantum benchmarks executed on IBM Quantum backends show that QuFid significantly reduces measurement cost compared to fixed-shot and learning-based baselines, while consistently maintaining acceptable fidelity bias.