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In this paper, we propose a novel Hadamard Transform (HT)-based neuralnetwork layer for hybrid quantum-classical computing. It implements the regularconvolutional layers in the Hadamard transform domain. The idea is based on theHT convolution theorem which states that the dyadic convolution between twovectors is equivalent to the element-wise multiplication of their HTrepresentation. Computing the HT is simply the application of a Hadamard gateto each qubit individually, so the HT computations of our proposed layer can beimplemented on a quantum computer. Compared to the regular Conv2D layer, theproposed HT-perceptron layer is computationally more efficient. Compared to aCNN with the same number of trainable parameters and 99.26\% test accuracy, ourHT network reaches 99.31\% test accuracy with 57.1\% MACs reduced in the MNISTdataset; and in our ImageNet-1K experiments, our HT-based ResNet-50 exceeds theaccuracy of the baseline ResNet-50 by 0.59\% center-crop top-1 accuracy using11.5\% fewer parameters with 12.6\% fewer MACs.

A Hybrid Quantum-Classical Approach based on the Hadamard Transform for the Convolutional Layer