This paper pioneers the use of quantum machine learning (QML) for modeling the Ohmic contact process in GaN high-electron-mobility transistors (HEMTs) for the first time. Utilizing data from 159 devices and variational auto-encoder-based augmentation, we developed a quantum kernel-based regressor (QKR) with a 2-level ZZ-feature map. Benchmarking against six classical machine learning (CML) models, our QKR consistently demonstrated the lowest mean absolute error (MAE), mean squared error (MSE), and root mean squared error (RMSE). Repeated statistical analysis confirmed its robustness. Additionally, experiments verified an MAE of 0.314 ohm-mm, underscoring the QKR's superior performance and potential for semiconductor applications, and demonstrating significant advancements over traditional CML methods.