Parallel Hybrid Networks: an interplay between quantum and classical neural networks

The use of quantum neural networks for machine learning is a paradigm that has recently attracted considerable interest. Under certain conditions, these models approximate the distributions of their datasets using truncated Fourier series. Owing to the trigonometric nature of this fit, angle-embedded quantum neural networks may have difficulty fitting nonharmonic features in a given dataset. Moreover, the interpretability of hybrid neural networks remains a challenge. In this study, we introduce an interpretable class of hybrid quantum neural networks that pass the inputs of the dataset in parallel to (a) a classical multi-layered perceptron and (b) a variational quantum circuit, after which the 2 outputs are linearly combined. The quantum neural network creates a smooth sinusoidal foundation based on the training set, and the classical perceptrons fill the nonharmonic gaps in the landscape. We demonstrate this claim using 2 synthetic datasets sampled from periodic distributions with added protrusions as noise. The training results indicate that parallel hybrid network architecture can improve solution optimality on periodic datasets with additional noise.