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Efficient representation of quantum many-body states with deep neural networks

Author

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  • Xun Gao

    (Tsinghua University)

  • Lu-Ming Duan

    (Tsinghua University
    University of Michigan)

Abstract

Part of the challenge for quantum many-body problems comes from the difficulty of representing large-scale quantum states, which in general requires an exponentially large number of parameters. Neural networks provide a powerful tool to represent quantum many-body states. An important open question is what characterizes the representational power of deep and shallow neural networks, which is of fundamental interest due to the popularity of deep learning methods. Here, we give a proof that, assuming a widely believed computational complexity conjecture, a deep neural network can efficiently represent most physical states, including the ground states of many-body Hamiltonians and states generated by quantum dynamics, while a shallow network representation with a restricted Boltzmann machine cannot efficiently represent some of those states.

Suggested Citation

  • Xun Gao & Lu-Ming Duan, 2017. "Efficient representation of quantum many-body states with deep neural networks," Nature Communications, Nature, vol. 8(1), pages 1-6, December.
    • Handle: RePEc:nat:natcom:v:8:y:2017:i:1:d:10.1038_s41467-017-00705-2
    DOI: 10.1038/s41467-017-00705-2
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    Cited by:

    1. Lennart Dabelow & Masahito Ueda, 2022. "Three learning stages and accuracy–efficiency tradeoff of restricted Boltzmann machines," Nature Communications, Nature, vol. 13(1), pages 1-11, December.
    2. Jiequn Han & Ruimeng Hu, 2019. "Deep Fictitious Play for Finding Markovian Nash Equilibrium in Multi-Agent Games," Papers 1912.01809, arXiv.org, revised Jun 2020.

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