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：量子神经网络代表了一种新的机器学习范式，因其潜在前景近期备受关注。在特定条件下，这些模型通过截断傅里叶级数逼近其数据集的分布。这种拟合的三角函数特性可能导致角度嵌入型量子神经网络在拟合给定数据集中的非谐波特征时面临困难。此外，神经网络的解释性仍是一个挑战。本文提出一类新型可解释的混合量子神经网络，该网络将数据集输入并行传递给：1）经典多层感知器，2）变分量子电路，而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形成平滑的正弦基函数，而经典感知器则填补了该地形中的非谐波间隙。我们在两个从周期性分布中采样并叠加突起噪声的合成数据集上验证了这一论断。训练结果表明，这种并行混合网络架构能够提升含噪周期性数据集上的解最优性。