HaQGNN: Hardware-Aware Quantum Kernel Design Based on Graph Neural Networks

Designing effective quantum kernels is a central challenge in Quantum Machine Learning (QML), particularly under the limitations of Noisy Intermediate-Scale Quantum (NISQ) devices with a limited number of qubits, error-prone gate operations, and restricted qubit connectivity. To address this, we propose HaQGNN, a hardware-aware quantum kernel design method that integrates quantum device topology, noise characteristics, and Graph Neural Networks (GNNs) to evaluate and select task-relevant quantum circuits that define quantum kernels. First, each quantum circuit is represented as a directed acyclic graph that encodes hardware-specific features, including gate types, target qubits, and noise characteristics. Next, two GNNs are trained to predict surrogate metrics, Probability of Successful Trials (PST) and Kernel-Target Alignment (KTA), for fast and accurate fidelity and performance estimation. Additionally, feature selection is further incorporated to reduce input dimensionality and improve compatibility with limited-qubit devices. Finally, extensive experiments on three benchmark datasets, Credit Card (CC), MNIST-5, and FMNIST-4, demonstrate that HaQGNN outperforms existing baselines in terms of classification accuracy. Our results highlight the potential of learning-based and hardware-aware strategies for advancing practical quantum kernel design on near-term quantum hardware.