In this paper, we propose a novel Hadamard Transform (HT)-based neural network layer for hybrid quantum-classical computing. It implements the regular convolutional layers in the Hadamard transform domain. The idea is based on the HT convolution theorem which states that the dyadic convolution between two vectors is equivalent to the element-wise multiplication of their HT representation. Computing the HT is simply the application of a Hadamard gate to each qubit individually, so the HT computations of our proposed layer can be implemented on a quantum computer. Compared to the regular Conv2D layer, the proposed HT-perceptron layer is computationally more efficient. Compared to a CNN with the same number of trainable parameters and 99.26\% test accuracy, our HT network reaches 99.31\% test accuracy with 57.1\% MACs reduced in the MNIST dataset; and in our ImageNet-1K experiments, our HT-based ResNet-50 exceeds the accuracy of the baseline ResNet-50 by 0.59\% center-crop top-1 accuracy using 11.5\% fewer parameters with 12.6\% fewer MACs.

翻译：本文提出一种基于哈达玛变换（Hadamard Transform, HT）的新型神经网络层，适用于混合量子-经典计算。该层在哈达玛变换域中实现常规卷积层功能。其核心思想基于HT卷积定理：两个向量的二元卷积等价于二者HT表示逐元素相乘的结果。由于计算HT只需对每个量子比特单独施加哈达玛门，因此所提层的HT计算可在量子计算机上实现。与常规Conv2D层相比，该HT感知机层计算效率更高。在与具有相同可训练参数数量、测试准确率为99.26%的CNN对比中，我们的HT网络在MNIST数据集上达到99.31%的测试准确率，同时减少57.1%的MAC运算量；而在ImageNet-1K实验中，基于HT的ResNet-50相比基线ResNet-50，在中心裁剪Top-1准确率上提升0.59%，参数减少11.5%，MAC运算量降低12.6%。