cs.CVMar 3, 2026

WTHaar-Net: a Hybrid Quantum-Classical Approach

Authors: Vittorio Palladino, Tsai Idden, Ahmet Enis Cetin

Organizations: University of Illinois Chicago (UIC), Chicago, IL, USA · Politecnico di Milano, Department of Electronics, Information and Bioengineering, Milano, Italy

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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.

Figures & tables

Figure 1: Illustration of the Haar wavelet filter bank. Approximation and detail coefficients are obtained by successive low-pass and high-pass filtering followed by downsampling.
Figure 2: A 4-dimensional input vector processed through the decomposed Haar circuit. Each coefficient x0,x1x_{0},x_{1} corresponds to the amplitude of the quantum state in the computational basis, allowing the Hadamard gates to compute the wavelet transform directly on the quantum state.
Layer (Operation)MACs
K×KK\times K Conv2DK2N2C2K^{2}N^{2}C^{2}
3×33\times 3 Conv2D9N2C29N^{2}C^{2}
Scaling, Soft-thresholdingN2CN^{2}C
Channel-wise ProcessingN2C2N^{2}C^{2}
PP -path HT-perceptronPN2C+PN2C2PN^{2}C+PN^{2}C^{2}
1-path HT-perceptronN2C+N2C2N^{2}C+N^{2}C^{2}
Table 1: Multiply-Accumulates (MACs) of a Conv2D layer versus an HT-perceptron layer for a CC -channel N×NN\times N image. NN is a power of 2.
Figure 3: Architecture of the Haar wavelet transform Conv Layer
ModelParams (M)Single-Crop10-Crop
LossAcc@1Acc@5LossAcc@1Acc@5
ResNet (our trial, baseline) [ 11 ]23.721.40963.2886.371.28865.6887.83
Hadamard Transform (HT, 3-path) [ 22 ]20.78 (-12.4%)1.39066.6587.431.22869.0689.29
Haar Wavelet (HWT, 3-path)20.78 (-12.4%)1.17570.8490.151.02073.2491.48
Table 2: Tiny-ImageNet comparison between Haar wavelet, Hadamard transforms, and ResNet baseline. Haar and Hadamard models use a 3-path design. All models are trained for 60 epochs with learning rate 0.1 with schedule rate decrementing of 10 every 30 epochs.
MethodParamsTest Acc (%)
Prior work
ResNet-20 (He et al., 2016) [ 11 ]272,47491.25
WHT-based ResNet-20 [ 22 ]133,082 (51.26% ↓\downarrow )90.12
LDW-ResNet-20 [ 26 ]274,47491.80
ResNet-20 (our trial)272,47491.66
HT-ResNet-20 (1-path)151,514 (44.39% ↓\downarrow )91.25
Table 3: Comparison of HT-ResNet-20 and HWT-ResNet-20 variants on CIFAR-10 (200 epochs). Parameter reduction is reported relative to ResNet-20 [ 11 ] . Baseline HT results are from Pan et al. [ 22 ] . LDW-ResNet-20 [ 26 ] is included for comparison with other wavelet-based methods.
Figure 4: Image corruptions used for robustness evaluation in the comparison between Haar (HWT) and Hadamard (WHT) architectures on Tiny-ImageNet.
Figure 5: Quantum circuit for the decomposition of the wavelet transform into Hadamard gates for a 4×44\times 4 patch.

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