mlsanityData to 14 Oct 2026

A Hybrid Quantum-Classical Approach based on the Hadamard Transform for the Convolutional Layer

arXiv 2305.17510 ↗First posted 27 May 2023cs.CV eess.SPcited by 12

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Abstract (arXiv)

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.

Key facts. Cited by 12 papers in the map (data through 14 Oct 2026). Builds on 11 of its 45 references that are in the map. First posted on arXiv 27 May 2023.

Builds on

11 of 45 references.

References · 11

  1. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  2. 2020Harmonic Convolutional Networks based on Discrete Cosine Transformcited by 14
  3. 2021Fast Walsh-Hadamard Transform and Smooth-Thresholding Based Binary Layers in Deep Neural Networkscited by 14
  4. 2022Block Walsh-Hadamard Transform Based Binary Layers in Deep Neural Networkscited by 13
  5. 2018Energy Efficient Hadamard Neural Networkscited by 12
  6. 2021Less is More: Accelerating Faster Neural Networks Straight from JPEGcited by 7
  7. 2020Discrete Cosine Transform Based Causal Convolutional Neural Network for Drift Compensation in Chemical Sensorscited by 5
  8. 2020A Simulation Study to Evaluate the Performance of the Cauchy Proximal Operator in Despeckling SAR Images of the Sea Surfacecited by 4
  9. 2022Real-time Wireless ECG-derived Respiration Rate Estimation Using an Autoencoder with a DCT Layercited by 4
  10. 2019HadaNets: Flexible Quantization Strategies for Neural Networkscited by 3
  11. 2022A hybrid classical-quantum algorithm for digital image processingcited by 3

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 3; 2024: 5; 2025: 1; 2026: 3.

12 papers.

  1. 2023Domain Generalization with Fourier Transform and Soft Thresholdingcited by 4
  2. 2024A Probabilistic Hadamard U-Net for MRI Bias Field Correctioncited by 4
  3. 2023ADC/DAC-Free Analog Acceleration of Deep Neural Networks with Frequency Transformationcited by 3
  4. 2023A novel asymmetrical autoencoder with a sparsifying discrete cosine Stockwell transform layer for gearbox sensor data compressioncited by 3
  5. 2024Discrete Cosine Transform Based Decorrelated Attention for Vision Transformerscited by 2
  6. 2024Qsco: A Quantum Scoring Module for Open-set Supervised Anomaly Detectioncited by 1
  7. 2025HTMA-Net: Towards Multiplication-Avoiding Neural Networks via Hadamard Transform and In-Memory Computingcited by 1
  8. 2024The Blind Normalized Stein Variational Gradient Descent-Based Detection for Intelligent Random Access in Cellular IoTcited by 0
  9. 2024Enhancing Microgrid Performance Prediction with Attention-based Deep Learning Modelscited by 0
  10. 2026WTHaar-Net: a Hybrid Quantum-Classical Approachcited by 0
  11. 2026Structure of the Circular-Dyadic Convolution Errorcited by 0
  12. 2026Learned Queries and Keys Are All You Need: Replacing the Value Projection with Structured Transformscited by 0