  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.
