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Training deep quantum neural networks

Author

Listed:
  • Kerstin Beer

    (Institut für Theoretische Physik, Leibniz Universität Hannover)

  • Dmytro Bondarenko

    (Institut für Theoretische Physik, Leibniz Universität Hannover)

  • Terry Farrelly

    (Institut für Theoretische Physik, Leibniz Universität Hannover
    ARC Centre for Engineered Quantum Systems, School of Mathematics and Physics, University of Queensland)

  • Tobias J. Osborne

    (Institut für Theoretische Physik, Leibniz Universität Hannover)

  • Robert Salzmann

    (Institut für Theoretische Physik, Leibniz Universität Hannover
    University of Cambridge)

  • Daniel Scheiermann

    (Institut für Theoretische Physik, Leibniz Universität Hannover)

  • Ramona Wolf

    (Institut für Theoretische Physik, Leibniz Universität Hannover)

Abstract

Neural networks enjoy widespread success in both research and industry and, with the advent of quantum technology, it is a crucial challenge to design quantum neural networks for fully quantum learning tasks. Here we propose a truly quantum analogue of classical neurons, which form quantum feedforward neural networks capable of universal quantum computation. We describe the efficient training of these networks using the fidelity as a cost function, providing both classical and efficient quantum implementations. Our method allows for fast optimisation with reduced memory requirements: the number of qudits required scales with only the width, allowing deep-network optimisation. We benchmark our proposal for the quantum task of learning an unknown unitary and find remarkable generalisation behaviour and a striking robustness to noisy training data.

Suggested Citation

  • Kerstin Beer & Dmytro Bondarenko & Terry Farrelly & Tobias J. Osborne & Robert Salzmann & Daniel Scheiermann & Ramona Wolf, 2020. "Training deep quantum neural networks," Nature Communications, Nature, vol. 11(1), pages 1-6, December.
    • Handle: RePEc:nat:natcom:v:11:y:2020:i:1:d:10.1038_s41467-020-14454-2
    DOI: 10.1038/s41467-020-14454-2
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    Cited by:

    1. Samson Wang & Enrico Fontana & M. Cerezo & Kunal Sharma & Akira Sone & Lukasz Cincio & Patrick J. Coles, 2021. "Noise-induced barren plateaus in variational quantum algorithms," Nature Communications, Nature, vol. 12(1), pages 1-11, December.
    2. Eric R. Anschuetz & Bobak T. Kiani, 2022. "Quantum variational algorithms are swamped with traps," Nature Communications, Nature, vol. 13(1), pages 1-10, December.
    3. Xue, Gang & Liu, Shifeng & Ren, Long & Gong, Daqing, 2024. "Risk assessment of utility tunnels through risk interaction-based deep learning," Reliability Engineering and System Safety, Elsevier, vol. 241(C).
    4. Wei-Ming Li & Shi-Ju Ran, 2022. "Non-Parametric Semi-Supervised Learning in Many-Body Hilbert Space with Rescaled Logarithmic Fidelity," Mathematics, MDPI, vol. 10(6), pages 1-15, March.
    5. Huang, Fangyu & Tan, Xiaoqing & Huang, Rui & Xu, Qingshan, 2022. "Variational convolutional neural networks classifiers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 605(C).
    6. Xiaoxuan Pan & Zhide Lu & Weiting Wang & Ziyue Hua & Yifang Xu & Weikang Li & Weizhou Cai & Xuegang Li & Haiyan Wang & Yi-Pu Song & Chang-Ling Zou & Dong-Ling Deng & Luyan Sun, 2023. "Deep quantum neural networks on a superconducting processor," Nature Communications, Nature, vol. 14(1), pages 1-7, December.
    7. Johannes Herrmann & Sergi Masot Llima & Ants Remm & Petr Zapletal & Nathan A. McMahon & Colin Scarato & François Swiadek & Christian Kraglund Andersen & Christoph Hellings & Sebastian Krinner & Nathan, 2022. "Realizing quantum convolutional neural networks on a superconducting quantum processor to recognize quantum phases," Nature Communications, Nature, vol. 13(1), pages 1-7, December.
    8. He, Zhimin & Deng, Maijie & Zheng, Shenggen & Li, Lvzhou & Situ, Haozhen, 2023. "GSQAS: Graph Self-supervised Quantum Architecture Search," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 630(C).
    9. Takayuki Sakuma, 2020. "Application of deep quantum neural networks to finance," Papers 2011.07319, arXiv.org, revised May 2022.
    10. Francesco Piccialli & Vincenzo Schiano Cola & Fabio Giampaolo & Salvatore Cuomo, 2021. "The Role of Artificial Intelligence in Fighting the COVID-19 Pandemic," Information Systems Frontiers, Springer, vol. 23(6), pages 1467-1497, December.
    11. Su Fong Chien & Heng Siong Lim & Michail Alexandros Kourtis & Qiang Ni & Alessio Zappone & Charilaos C. Zarakovitis, 2021. "Quantum-Driven Energy-Efficiency Optimization for Next-Generation Communications Systems," Energies, MDPI, vol. 14(14), pages 1-15, July.
    12. Zhang, Yanbing & Song, Tingting & Wu, Zhihao, 2022. "An improved algorithm for computing hitting probabilities of quantum walks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 594(C).

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