# WTHaar-Net: a Hybrid Quantum-Classical Approach

arXiv: https://arxiv.org/abs/2603.02497 · HTML: https://mlsanity.com/paper/2603.02497/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 25 references that are in the map.
- First posted on arXiv 3 Mar 2026.

## Builds on (most cited first, 12 of 12)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [Multi-level Wavelet-CNN for Image Restoration](https://mlsanity.com/paper/1805.07071/) (2018)
- [Wavelet Convolutional Neural Networks](https://mlsanity.com/paper/1805.08620/) (2018)
- [Fast Walsh-Hadamard Transform and Smooth-Thresholding Based Binary Layers in Deep Neural Networks](https://mlsanity.com/paper/2104.07085/) (2021)
- [Block Walsh-Hadamard Transform Based Binary Layers in Deep Neural Networks](https://mlsanity.com/paper/2201.02711/) (2022)
- [Energy Efficient Hadamard Neural Networks](https://mlsanity.com/paper/1805.05421/) (2018)
- [A Hybrid Quantum-Classical Approach based on the Hadamard Transform for the Convolutional Layer](https://mlsanity.com/paper/2305.17510/) (2023)
- [A hybrid classical-quantum algorithm for digital image processing](https://mlsanity.com/paper/2208.09714/) (2022)
- [Partitioned Hybrid Quantum Fourier Neural Operators for Scientific Quantum Machine Learning](https://mlsanity.com/paper/2507.08746/) (2025)

## Abstract (arXiv)

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.