# QFCNN: Quantum Fourier Convolutional Neural Network

arXiv: https://arxiv.org/abs/2106.10421 · HTML: https://mlsanity.com/paper/2106.10421/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 61 references that are in the map.
- First posted on arXiv 19 Jun 2021.

## Builds on (most cited first, 26 of 26)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [You Only Look Once: Unified, Real-Time Object Detection](https://mlsanity.com/paper/1506.02640/) (2015)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [YOLOv4: Optimal Speed and Accuracy of Object Detection](https://mlsanity.com/paper/2004.10934/) (2020)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Adversarial Attacks on Neural Networks for Graph Data](https://mlsanity.com/paper/1805.07984/) (2018)
- [Adversarial Attack on Graph Structured Data](https://mlsanity.com/paper/1806.02371/) (2018)
- [Structured Sequence Modeling with Graph Convolutional Recurrent Networks](https://mlsanity.com/paper/1612.07659/) (2016)
- [Image to Image Translation for Domain Adaptation](https://mlsanity.com/paper/1712.00479/) (2017)
- [Quantum generative adversarial networks](https://mlsanity.com/paper/1804.08641/) (2018)
- [Layerwise learning for quantum neural networks](https://mlsanity.com/paper/2006.14904/) (2020)
- [Spectral Representations for Convolutional Neural Networks](https://mlsanity.com/paper/1506.03767/) (2015)
- [Quantum Recommendation Systems](https://mlsanity.com/paper/1603.08675/) (2016)
- [Quantum Graph Neural Networks](https://mlsanity.com/paper/1909.12264/) (2019)
- [q-means: A quantum algorithm for unsupervised machine learning](https://mlsanity.com/paper/1812.03584/) (2018)
- [Machine learning & artificial intelligence in the quantum domain](https://mlsanity.com/paper/1709.02779/) (2017)
- [Stacked Spatio-Temporal Graph Convolutional Networks for Action Segmentation](https://mlsanity.com/paper/1811.10575/) (2018)
- [FALCON: A Fourier Transform Based Approach for Fast and Secure Convolutional Neural Network Predictions](https://mlsanity.com/paper/1811.08257/) (2018)
- [Universal discriminative quantum neural networks](https://mlsanity.com/paper/1805.08654/) (2018)
- [QDNN: DNN with Quantum Neural Network Layers](https://mlsanity.com/paper/1912.12660/) (2019)
- [Acceleration of Convolutional Neural Network Using FFT-Based Split Convolutions](https://mlsanity.com/paper/2003.12621/) (2020)

## Built on by (most cited first, 2 of 2)

- [Fast Quantum Convolutional Neural Networks for Low-Complexity Object Detection in Autonomous Driving Applications](https://mlsanity.com/paper/2401.01370/) (2023)
- [Compton Form Factor Extraction using Quantum Deep Neural Networks](https://mlsanity.com/paper/2504.15458/) (2025)

## Abstract (arXiv)

The neural network and quantum computing are both significant and appealing fields, with their interactive disciplines promising for large-scale computing tasks that are untackled by conventional computers. However, both developments are restricted by the scope of the hardware development. Nevertheless, many neural network algorithms had been proposed before GPUs become powerful enough for running very deep models. Similarly, quantum algorithms can also be proposed as knowledge reserves before real quantum computers are easily accessible. Specifically, taking advantage of both the neural networks and quantum computation and designing quantum deep neural networks (QDNNs) for acceleration on Noisy Intermediate-Scale Quantum (NISQ) processors is also an important research problem. As one of the most widely used neural network architectures, convolutional neural network (CNN) remains to be accelerated by quantum mechanisms, with only a few attempts have been demonstrated. In this paper, we propose a new hybrid quantum-classical circuit, namely Quantum Fourier Convolutional Network (QFCN). Our model achieves exponential speed-up compared with classical CNN theoretically and improves over the existing best result of quantum CNN. We demonstrate the potential of this architecture by applying it to different deep learning tasks, including traffic prediction and image classification.