A Hybrid Quantum-Classical Approach based on the Hadamard Transform for the Convolutional Layer
This work addresses efficiency challenges in deep learning for computer vision applications, offering a hybrid quantum-classical method that is incremental but provides measurable gains.
The paper tackles the computational inefficiency of convolutional neural networks by proposing a Hadamard Transform-based layer for hybrid quantum-classical computing, achieving improved accuracy and reduced computational costs, such as 99.31% test accuracy with 57.1% fewer MACs on MNIST and 0.59% higher accuracy with 12.6% fewer MACs on ImageNet-1K.
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.