Quantum neural networks represent a new machine learning paradigm that has recently attracted much attention due to its potential promise. Under certain conditions, these models approximate the distribution of their dataset with a truncated Fourier series. The trigonometric nature of this fit could result in angle-embedded quantum neural networks struggling to fit the non-harmonic features in a given dataset. Moreover, the interpretability of neural networks remains a challenge. In this work, we introduce a new, interpretable class of hybrid quantum neural networks that pass the inputs of the dataset in parallel to 1) a classical multi-layered perceptron and 2) a variational quantum circuit, and then the outputs of the two are linearly combined. We observe that the quantum neural network creates a smooth sinusoidal foundation base on the training set, and then the classical perceptrons fill the non-harmonic gaps in the landscape. We demonstrate this claim on two synthetic datasets sampled from periodic distributions with added protrusions as noise. The training results indicate that the parallel hybrid network architecture could improve the solution optimality on periodic datasets with additional noise.

翻译：量子神经网络是一种新兴的机器学习范式，因其潜在前景近期备受关注。在某些条件下，这些模型通过截断傅里叶级数逼近其数据集的分布。这种拟合的三角特性可能导致角度嵌入量子神经网络难以拟合给定数据集中的非谐波特征。此外，神经网络的解释性仍然是一个挑战。本文提出一种可解释的新型混合量子神经网络架构，该架构将数据集的输入并行传输至：1）经典多层感知器，2）变分量子电路，然后将两者的输出进行线性组合。我们观察到，量子神经网络基于训练集构建平滑的正弦基函数，而经典感知器则填补该地貌中的非谐波缺口。我们在两个从周期分布中采样并加入凸起噪声的合成数据集上验证了这一论断。训练结果表明，并行混合网络架构能提升带额外噪声周期数据集上的解最优性。