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
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,x1 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×K Conv2D
K2N2C2
3×3 Conv2D
9N2C2
Scaling, Soft-thresholding
N2C
Channel-wise Processing
N2C2
P -path HT-perceptron
PN2C+PN2C2
1-path HT-perceptron
N2C+N2C2
Table 1: Multiply-Accumulates (MACs) of a Conv2D layer versus an HT-perceptron layer for a C -channel N×N image. N is a power of 2.
Figure 3: Architecture of the Haar wavelet transform Conv Layer
Model
Params (M)
Single-Crop
10-Crop
Loss
Acc@1
Acc@5
Loss
Acc@1
Acc@5
ResNet (our trial, baseline) [ 11 ]
23.72
1.409
63.28
86.37
1.288
65.68
87.83
Hadamard Transform (HT, 3-path) [ 22 ]
20.78 (-12.4%)
1.390
66.65
87.43
1.228
69.06
89.29
Haar Wavelet (HWT, 3-path)
20.78 (-12.4%)
1.175
70.84
90.15
1.020
73.24
91.48
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.
Method
Params
Test Acc (%)
Prior work
ResNet-20 (He et al., 2016) [ 11 ]
272,474
91.25
WHT-based ResNet-20 [ 22 ]
133,082 (51.26% ↓ )
90.12
LDW-ResNet-20 [ 26 ]
274,474
91.80
ResNet-20 (our trial)
272,474
91.66
HT-ResNet-20 (1-path)
151,514 (44.39% ↓ )
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 4×4 patch.
Hybrid quantum classical neural networks integrate parameterized quantum circuits (PQCs) with established deep learning architectures, but their performance depends strongly on the choice of quantum circuit architecture, a choice that remains largely manual. Most existing approaches rely on hand-designed or fixed circuit ansätze, requiring circuit structure, gate composition, and qubit connectivity to be specified in advance with no guarantee that they suit the task. This limitation is especially acute in image classification, where quantum circuits must transform features extracted by classical networks while remaining compact enough for practical training, requirements that generic, task-agnostic ansätze are unlikely to satisfy simultaneously. We extend EXAQC, an evolutionary framework for automated quantum circuit discovery, to image classification. EXAQC evolves PQCs as intermediate processing modules while retaining classical feature-extraction and prediction layers. On MNIST, Fashion-MNIST, and CIFAR-10, EXAQC achieves 98.42%, 90.62%, and 85.47% accuracy, respectively, while using comparable gate counts to other quantum architecture-search methods. Against classical networks, evolved hybrid models maintain comparable accuracy with substantially fewer trainable parameters, reaching 85.68% on CIFAR-10 with over 25× fewer parameters than a 10-layer CNN. Encoding choice also matters: rotation-based encodings (RX, RY, U3) outperform amplitude encoding by 22-25 points on CIFAR-10. These results demonstrate that automated circuit discovery yields compact quantum modules that can replace larger classical components in vision architectures while retaining competitive accuracy.
Devroop Kar, Daniel Krutz, Travis Desell
Rochester Institute of Technology Rochester, NY 14623, USA
Hybrid quantum-classical neural networks have emerged as a promising approach for leveraging quantum computing in machine learning while mitigating current hardware limitations. This paper presents Sim-HVQC, a hybrid Deep Quantum Neural Network that couples an adaptive, parameter-free SimAM weighting module with classical feature extraction to preserve class-discriminative information prior to encoding into a Variational Quantum Circuit (VQC). Previous studies are restricted to binary classification [1] [2] [3] [4] [5]. In contrast, the proposed framework is trained and evaluated on various multi-class datasets(MNIST, KMNIST, Fashion-MNIST, and EMNIST). The framework further demonstrates reproducibility, parameter efficiency, and interpretability through multi-seed evaluation, parameter analysis, and latent/quantum feature inspection. The source code is publicly available at https://github.com/Dilli822/ SimAM-HVQC
Dilli Hang Rai
Institute of Science and Technology Tribhuvan University, Kritipur, Nepal
While Quantum Convolutional Neural Networks (QCNNs) offer a theoretical paradigm for quantum machine learning, their practical implementation is severely bottlenecked by barren plateaus -- the exponential vanishing of gradients -- and poor empirical accuracy compared to classical counterparts. In this work, we propose a novel QCNN architecture utilizing localized cost functions and a hardware-efficient tensor-network initialization strategy to provably mitigate barren plateaus. We evaluate our scalable QCNN on the MNIST dataset, demonstrating a significant performance leap. By resolving the gradient vanishing issue, our optimized QCNN achieves a classification accuracy of 98.7%, a substantial improvement over the baseline QCNN accuracy of 52.32% found in unmitigated models. Furthermore, we provide empirical evidence of a parameter-efficiency advantage, requiring O(logN) fewer trainable parameters than equivalent classical CNNs to achieve >95% convergence. This work bridges the gap between theoretical quantum utility and practical application, providing a scalable framework for quantum computer vision tasks without succumbing to loss landscape concentration.
Radhakrishnan Delhibabu
School of Computing Science and Engineering (SCOPE), Vellore Institute of Technology, Vellore, 632014, India.