Calibration-Aware Graph Neural Networks for Robust and Scalable Quantum Error Mitigation

Noisy Intermediate-Scale Quantum (NISQ) computing is fundamentally constrained by hardware noise that is not only large but also temporally drifting and structurally complex. Traditional quantum error mitigation (QEM) techniques, such as Zero-Noise Extrapolation (ZNE), often rely on simplified noise assumptions that degrade under coherent errors and deep circuit structures. Conversely, existing machine learning-based QEM approaches typically treat device noise as a static background, leading to poor generalization when hardware calibration shifts. In this work, we propose \textbf{Calib-GNN}, a novel framework that explicitly integrates real-time hardware calibration data into a Graph Neural Network (GNN) architecture. By embedding gate-specific error rates directly into the graph representation, our model learns a dynamic mapping from noisy measurements to ideal expectation values. Through extensive simulations based on real noise profiles from the IBM Quantum \texttt{ibm\_fez} backend, we demonstrate that Calib-GNN significantly outperforms standard baselines. Specifically, it reduces the Root Mean Square Error (RMSE) by approximately 14\% compared to ZNE on random circuits and exhibits superior robustness against severe noise drift where traditional models fail. Furthermore, we show that Calib-GNN effectively scales to deeper circuits and recovers the ground state energy of the $H_2$ molecule in Variational Quantum Eigensolver (VQE) tasks with high fidelity, overcoming the limitations of ZNE in the presence of coherent noise.