Strong generalization in quantum neural networks

Generalization is an important feature of neural networks (Nns) as it indicates their ability to predict new and unknown data. However, classical Nns face the challenge of overcoming overfitting in applications due to their nonlinear characteristics, which represents poor generalization. By combining quantum computing with Nns, quantum neural networks (Qnns) have more potential than classical Nns. In this work, we study the generalization of Qnns and compare it with classical Nns. We prove that Qnns have a generalization error bound and propose its theoretical value. We also show that Qnns perform almost the same on the training dataset and test dataset without the overfitting phenomenon. To validate our proposal, we simulate three Qnn models on two public datasets and compare them with a traditional network model. The results demonstrate that Qnns have ideal generalization, much better than classical Nns. Finally, we implement the experiment on a quantum processor to prove the simulation's results.