WTHaar-Net: a Hybrid Quantum-Classical Approach

TL;DR

WTHaar-Net introduces a hybrid quantum-classical convolutional neural network utilizing the Haar Wavelet Transform, which offers localized multi-resolution features, leading to parameter efficiency and competitive accuracy on image classification benchmarks.

Contribution

The paper proposes replacing the Hadamard Transform with the Haar Wavelet Transform in hybrid quantum-classical CNNs, enabling spatially localized features and quantum circuit implementation.

Findings

Achieves parameter reduction while maintaining accuracy.

Outperforms ResNet and Hadamard-based models on Tiny-ImageNet.

Successfully implements quantum realization on IBM Quantum hardware.

Abstract

Convolutional neural networks rely on linear filtering operations that can be reformulated efficiently in suitable transform domains. At the same time, advances in quantum computing have shown that certain structured linear transforms can be implemented with shallow quantum circuits, opening the door to hybrid quantum-classical approaches for enhancing deep learning models. In this work, we introduce WTHaar-Net, a convolutional neural network that replaces the Hadamard Transform used in prior hybrid architectures with the Haar Wavelet Transform (HWT). Unlike the Hadamard Transform, the Haar transform provides spatially localized, multi-resolution representations that align more closely with the inductive biases of vision tasks. We show that the HWT admits a quantum realization using structured Hadamard gates, enabling its decomposition into unitary operations suitable for quantum circuits. Experiments on CIFAR-10 and Tiny-ImageNet demonstrate that WTHaar-Net achieves substantial parameter reduction while maintaining competitive accuracy. On Tiny-ImageNet, our approach outperforms both ResNet and Hadamard-based baselines. We validate the quantum implementation on IBM Quantum cloud hardware, demonstrating compatibility with near-term quantum devices.