skip to main content
research-article

Quantum Fourier Convolutional Network

Published:05 January 2023Publication History
Skip Abstract Section

Abstract

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 became powerful enough for running very deep models. Similarly, quantum algorithms can also be proposed as knowledge reserve 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 the 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 having been demonstrated. In this article, we propose a new hybrid quantum-classical circuit, namely, Quantum Fourier Convolutional Network (QFCN). Our model achieves exponential speedup 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 on different deep learning tasks, including traffic prediction and image classification.

REFERENCES

  1. [1] Biamonte Jacob, Wittek Peter, Pancotti Nicola, Rebentrost Patrick, Wiebe Nathan, and Lloyd Seth. 2017. Quantum machine learning. Nature 549, 7671 (2017), 195202.Google ScholarGoogle ScholarCross RefCross Ref
  2. [2] Bochkovskiy Alexey, Wang Chien-Yao, and Liao Hong-Yuan Mark. 2020. YOLOv4: Optimal speed and accuracy of object detection. arXiv preprint arXiv:2004.10934 (2020).Google ScholarGoogle Scholar
  3. [3] Chen Hongxiang, Wossnig Leonard, Severini Simone, Neven Hartmut, and Mohseni Masoud. 2018. Universal discriminative quantum neural networks. arXiv preprint arXiv:1805.08654 (2018).Google ScholarGoogle Scholar
  4. [4] Chitsaz Kamran, Hajabdollahi Mohsen, Karimi Nader, Samavi Shadrokh, and Shirani Shahram. 2020. Acceleration of convolutional neural network using FFT-based split convolutions. arXiv preprint arXiv:2003.12621 (2020).Google ScholarGoogle Scholar
  5. [5] Cong Iris, Choi Soonwon, and Lukin Mikhail D.. 2019. Quantum convolutional neural networks. Nat. Phys. 15, 12 (2019), 12731278.Google ScholarGoogle ScholarCross RefCross Ref
  6. [6] Dai Hanjun, Li Hui, Tian Tian, Huang Xin, Wang Lin, Zhu Jun, and Song Le. 2018. Adversarial attack on graph structured data. arXiv preprint arXiv:1806.02371 (2018).Google ScholarGoogle Scholar
  7. [7] Dallaire-Demers Pierre-Luc and Killoran Nathan. 2018. Quantum generative adversarial networks. Phys. Rev. A 98, 1 (2018), 012324.Google ScholarGoogle ScholarCross RefCross Ref
  8. [8] Devlin Jacob, Chang Ming-Wei, Lee Kenton, and Toutanova Kristina. 2018. BERT: Pre-training of deep bidirectional transformers for language understanding. arXiv preprint arXiv:1810.04805 (2018).Google ScholarGoogle Scholar
  9. [9] Dunjko Vedran and Briegel Hans J.. 2018. Machine learning & artificial intelligence in the quantum domain: A review of recent progress. Rep. Progr. Phys. 81, 7 (2018), 074001.Google ScholarGoogle ScholarCross RefCross Ref
  10. [10] Farhi Edward, Goldstone Jeffrey, and Gutmann Sam. 2014. A quantum approximate optimization algorithm. arXiv preprint arXiv:1411.4028 (2014).Google ScholarGoogle Scholar
  11. [11] Ghosh Pallabi, Yao Yi, Davis Larry, and Divakaran Ajay. 2020. Stacked spatio-temporal graph convolutional networks for action segmentation. In IEEE Winter Conference on Applications of Computer Vision. 576585.Google ScholarGoogle Scholar
  12. [12] Hadfield Stuart, Wang Zhihui, O’Gorman Bryan, Rieffel Eleanor G., Venturelli Davide, and Biswas Rupak. 2019. From the quantum approximate optimization algorithm to a quantum alternating operator Ansatz. Algorithms 12, 2 (2019), 34.Google ScholarGoogle ScholarCross RefCross Ref
  13. [13] Hales Lisa and Hallgren Sean. 2000. An improved quantum Fourier transform algorithm and applications. In 41st Annual Symposium on Foundations of Computer Science. IEEE, 515525.Google ScholarGoogle Scholar
  14. [14] He Kaiming, Zhang Xiangyu, Ren Shaoqing, and Sun Jian. 2016. Deep residual learning for image recognition. In IEEE Conference on Computer Vision and Pattern Recognition. 770778.Google ScholarGoogle ScholarCross RefCross Ref
  15. [15] Hibat-Allah Mohamed, Ganahl Martin, Hayward Lauren E., Melko Roger G., and Carrasquilla Juan. 2020. Recurrent neural network wave functions. Phys. Rev. Res. 2, 2 (2020), 023358.Google ScholarGoogle ScholarCross RefCross Ref
  16. [16] Huang Gao, Liu Zhuang, Maaten Laurens Van Der, and Weinberger Kilian Q.. 2017. Densely connected convolutional networks. In IEEE Conference on Computer Vision and Pattern Recognition. 47004708.Google ScholarGoogle ScholarCross RefCross Ref
  17. [17] Jaffe Arthur, Jiang Chunlan, Liu Zhengwei, Ren Yunxiang, and Wu Jinsong. 2020. Quantum Fourier analysis. Proc. Nat. Acad. Sci. 117, 20 (2020), 1071510720.Google ScholarGoogle ScholarCross RefCross Ref
  18. [18] Karras Tero, Laine Samuli, and Aila Timo. 2019. A style-based generator architecture for generative adversarial networks. In IEEE Conference on Computer Vision and Pattern Recognition. 44014410.Google ScholarGoogle ScholarCross RefCross Ref
  19. [19] Kerenidis Iordanis, Landman Jonas, Luongo Alessandro, and Prakash Anupam. 2019. q-means: A quantum algorithm for unsupervised machine learning. In International Conference on Advances in Neural Information Processing Systems. 41344144.Google ScholarGoogle Scholar
  20. [20] Kerenidis Iordanis, Landman Jonas, and Prakash Anupam. 2019. Quantum algorithms for deep convolutional neural networks. In International Conference on Learning Representations.Google ScholarGoogle Scholar
  21. [21] Kerenidis Iordanis and Prakash Anupam. 2016. Quantum recommendation systems. arXiv preprint arXiv:1603.08675 (2016).Google ScholarGoogle Scholar
  22. [22] Kerenidis Iordanis and Prakash Anupam. 2020. Quantum gradient descent for linear systems and least squares. Phys. Rev. A 101, 2 (2020), 022316.Google ScholarGoogle ScholarCross RefCross Ref
  23. [23] Kipf Thomas N. and Welling Max. 2017. Semi-supervised classification with graph convolutional networks. In International Conference on Learning Representations.Google ScholarGoogle Scholar
  24. [24] Li Shaohua, Xue Kaiping, Zhu Bin, Ding Chenkai, Gao Xindi, Wei David, and Wan Tao. 2020. FALCON: A Fourier transform based approach for fast and secure convolutional neural network predictions. In IEEE/CVF Conference on Computer Vision and Pattern Recognition. 87058714.Google ScholarGoogle ScholarCross RefCross Ref
  25. [25] Li Yaguang, Yu Rose, Shahabi Cyrus, and Liu Yan. 2017. Diffusion convolutional recurrent neural network: Data-driven traffic forecasting. arXiv preprint arXiv:1707.01926 (2017).Google ScholarGoogle Scholar
  26. [26] Lloyd Seth, Mohseni Masoud, and Rebentrost Patrick. 2013. Quantum algorithms for supervised and unsupervised machine learning. arXiv preprint arXiv:1307.0411 (2013).Google ScholarGoogle Scholar
  27. [27] Lloyd Seth, Mohseni Masoud, and Rebentrost Patrick. 2014. Quantum principal component analysis. Nat. Phys. 10, 9 (2014), 631633.Google ScholarGoogle ScholarCross RefCross Ref
  28. [28] Lloyd Seth and Weedbrook Christian. 2018. Quantum generative adversarial learning. Phys. Rev. Lett. 121, 4 (2018), 040502.Google ScholarGoogle ScholarCross RefCross Ref
  29. [29] Lomont Chris. 2003. Quantum convolution and quantum correlation algorithms are physically impossible. arXiv preprint quant-ph/0309070 (2003).Google ScholarGoogle Scholar
  30. [30] Ma Guangsheng, Li Hongbo, and Zhao Jiman. 2019. Windowed Fourier transform and general wavelet algorithms in quantum computation. Quant. Inf. Computat. 19, 3–4 (2019), 237251.Google ScholarGoogle ScholarDigital LibraryDigital Library
  31. [31] McClean Jarrod R., Boixo Sergio, Smelyanskiy Vadim N., Babbush Ryan, and Neven Hartmut. 2018. Barren plateaus in quantum neural network training landscapes. Nat. Commun. 9, 1 (2018), 16.Google ScholarGoogle ScholarCross RefCross Ref
  32. [32] McClean Jarrod R., Romero Jonathan, Babbush Ryan, and Aspuru-Guzik Alán. 2016. The theory of variational hybrid quantum-classical algorithms. New J. Phys. 18, 2 (2016), 023023.Google ScholarGoogle ScholarCross RefCross Ref
  33. [33] Melnikov Alexey A., Fedichkin Leonid E., and Alodjants Alexander. 2019. Predicting quantum advantage by quantum walk with convolutional neural networks. New J. Phys. 21, 12 (2019), 125002.Google ScholarGoogle ScholarCross RefCross Ref
  34. [34] Moore Cristopher, Rockmore Daniel, and Russell Alexander. 2006. Generic quantum Fourier transforms. ACM Trans. Algor. 2, 4 (2006), 707723.Google ScholarGoogle ScholarDigital LibraryDigital Library
  35. [35] Casares Pablo Antonio Moreno. 2020. Circuit implementation of bucket brigade qRAM for quantum state preparation. arXiv e-prints (2020), arXiv–2006.Google ScholarGoogle Scholar
  36. [36] Murez Zak, Kolouri Soheil, Kriegman David, Ramamoorthi Ravi, and Kim Kyungnam. 2018. Image to image translation for domain adaptation. In IEEE Conference on Computer Vision and Pattern Recognition. 45004509.Google ScholarGoogle ScholarCross RefCross Ref
  37. [37] Nielsen Michael A. and Chuang Isaac. 2002. Quantum Computation and Quantum Information. Cambridge University Press.Google ScholarGoogle Scholar
  38. [38] Nussbaumer Henri J.. 1981. The fast Fourier transform. In Fast Fourier Transform and Convolution Algorithms. Springer, 80111.Google ScholarGoogle ScholarCross RefCross Ref
  39. [39] Park Daniel K., Petruccione Francesco, and Rhee June-Koo Kevin. 2019. Circuit-based quantum random access memory for classical data. Sci. Rep. 9, 1 (2019), 18.Google ScholarGoogle Scholar
  40. [40] Peruzzo Alberto, McClean Jarrod, Shadbolt Peter, Yung Man-Hong, Zhou Xiao-Qi, Love Peter J., Aspuru-Guzik Alán, and O’Brien Jeremy L.. 2014. A variational eigenvalue solver on a photonic quantum processor. Nat. Comm. 5 (2014), 4213.Google ScholarGoogle ScholarCross RefCross Ref
  41. [41] Pratt Harry, Williams Bryan, Coenen Frans, and Zheng Yalin. 2017. FCNN: Fourier convolutional neural networks. In Joint European Conference on Machine Learning and Knowledge Discovery in Databases. Springer, 786798.Google ScholarGoogle ScholarCross RefCross Ref
  42. [42] Preskill John. 2018. Quantum computing in the NISQ era and beyond. Quantum 2 (2018), 79.Google ScholarGoogle Scholar
  43. [43] Rebentrost Patrick, Mohseni Masoud, and Lloyd Seth. 2014. Quantum support vector machine for big data classification. Phys. Rev. Lett. 113, 13 (2014), 130503.Google ScholarGoogle ScholarCross RefCross Ref
  44. [44] Redmon Joseph, Divvala Santosh, Girshick Ross, and Farhadi Ali. 2016. You only look once: Unified, real-time object detection. In IEEE Conference on Computer Vision and Pattern Recognition. 779788.Google ScholarGoogle ScholarCross RefCross Ref
  45. [45] Reed M. A., Chen J., Rawlett A. M., Price D. W., and Tour J. M.. 2001. Molecular random access memory cell. Appl. Phys. Lett. 78, 23 (2001), 37353737.Google ScholarGoogle ScholarCross RefCross Ref
  46. [46] Rippel Oren, Snoek Jasper, and Adams Ryan P.. 2015. Spectral representations for convolutional neural networks. In International Conference on Advances in Neural Information Processing Systems. 24492457.Google ScholarGoogle Scholar
  47. [47] Rumelhart David E., Hinton Geoffrey E., and Williams Ronald J.. 1986. Learning representations by back-propagating errors. Nature 323, 6088 (1986), 533536.Google ScholarGoogle ScholarCross RefCross Ref
  48. [48] Skolik Andrea, McClean Jarrod R., Mohseni Masoud, Smagt Patrick van der, and Leib Martin. 2020. Layerwise learning for quantum neural networks. arXiv preprint arXiv:2006.14904 (2020).Google ScholarGoogle Scholar
  49. [49] Tannu Swamit S. and Qureshi Moinuddin K.. 2018. A case for variability-aware policies for NISQ-era quantum computers. arXiv preprint arXiv:1805.10224 (2018).Google ScholarGoogle Scholar
  50. [50] Verdon Guillaume, McCourt Trevor, Luzhnica Enxhell, Singh Vikash, Leichenauer Stefan, and Hidary Jack. 2019. Quantum graph neural networks. arXiv preprint arXiv:1909.12264 (2019).Google ScholarGoogle Scholar
  51. [51] Wiebe Nathan, Kapoor Ashish, and Svore Krysta. 2014. Quantum algorithms for nearest-neighbor methods for supervised and unsupervised learning. arXiv preprint arXiv:1401.2142 (2014).Google ScholarGoogle Scholar
  52. [52] Winograd Shmuel. 1978. On computing the discrete Fourier transform. Math. Computat. 32, 141 (1978), 175199.Google ScholarGoogle ScholarCross RefCross Ref
  53. [53] Wu Zonghan, Pan Shirui, Chen Fengwen, Long Guodong, Zhang Chengqi, and Philip S. Yu. 2020. A comprehensive survey on graph neural networks. IEEE Trans. Neural Netw. Learn. Syst. 32, 1 (2020).Google ScholarGoogle Scholar
  54. [54] Yang Chao-Han Huck, Qi Jun, Chen Samuel Yen-Chi, Chen Pin-Yu, Siniscalchi Sabato Marco, Ma Xiaoli, and Lee Chin-Hui. 2021. Decentralizing feature extraction with quantum convolutional neural network for automatic speech recognition. In IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP’21). IEEE, 65236527.Google ScholarGoogle ScholarCross RefCross Ref
  55. [55] Yu Bing, Yin Haoteng, and Zhu Zhanxing. 2017. Spatio-temporal graph convolutional networks: A deep learning framework for traffic forecasting. arXiv preprint arXiv:1709.04875 (2017).Google ScholarGoogle Scholar
  56. [56] Zhao Chen and Gao Xiao-Shan. 2019. QDNN: DNN with quantum neural network layers. arXiv preprint arXiv:1912.12660 (2019).Google ScholarGoogle Scholar
  57. [57] Zhao Pengpeng, Luo Anjing, Liu Yanchi, Zhuang Fuzhen, Xu Jiajie, Li Zhixu, Sheng Victor S., and Zhou Xiaofang. 2020. Where to go next: A spatio-temporal gated network for next PoI recommendation. IEEE Trans. Knowl. Data Eng. 34, 5 (2020).Google ScholarGoogle ScholarCross RefCross Ref

Index Terms

  1. Quantum Fourier Convolutional Network

      Recommendations

      Comments

      Login options

      Check if you have access through your login credentials or your institution to get full access on this article.

      Sign in

      Full Access

      • Published in

        cover image ACM Transactions on Multimedia Computing, Communications, and Applications
        ACM Transactions on Multimedia Computing, Communications, and Applications  Volume 19, Issue 1
        January 2023
        505 pages
        ISSN:1551-6857
        EISSN:1551-6865
        DOI:10.1145/3572858
        • Editor:
        • Abdulmotaleb El Saddik
        Issue’s Table of Contents

        Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

        Publisher

        Association for Computing Machinery

        New York, NY, United States

        Publication History

        • Published: 5 January 2023
        • Online AM: 5 July 2022
        • Accepted: 28 January 2022
        • Revised: 2 January 2022
        • Received: 10 August 2021
        Published in tomm Volume 19, Issue 1

        Permissions

        Request permissions about this article.

        Request Permissions

        Check for updates

        Qualifiers

        • research-article
        • Refereed
      • Article Metrics

        • Downloads (Last 12 months)431
        • Downloads (Last 6 weeks)32

        Other Metrics

      PDF Format

      View or Download as a PDF file.

      PDF

      eReader

      View online with eReader.

      eReader

      Full Text

      View this article in Full Text.

      View Full Text

      HTML Format

      View this article in HTML Format .

      View HTML Format
      About Cookies On This Site

      We use cookies to ensure that we give you the best experience on our website.

      Learn more

      Got it!