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Information Scrambling in Quantum Neural Networks

Shen, Huitao and Zhang, Pengfei and You, Yi-Zhuang and Zhai, Hui (2020) Information Scrambling in Quantum Neural Networks. Physical Review Letters, 124 (20). Art. No. 200504. ISSN 0031-9007. doi:10.1103/physrevlett.124.200504.

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The quantum neural network is one of the promising applications for near-term noisy intermediate-scale quantum computers. A quantum neural network distills the information from the input wave function into the output qubits. In this Letter, we show that this process can also be viewed from the opposite direction: the quantum information in the output qubits is scrambled into the input. This observation motivates us to use the tripartite information—a quantity recently developed to characterize information scrambling—to diagnose the training dynamics of quantum neural networks. We empirically find strong correlation between the dynamical behavior of the tripartite information and the loss function in the training process, from which we identify that the training process has two stages for randomly initialized networks. In the early stage, the network performance improves rapidly and the tripartite information increases linearly with a universal slope, meaning that the neural network becomes less scrambled than the random unitary. In the latter stage, the network performance improves slowly while the tripartite information decreases. We present evidences that the network constructs local correlations in the early stage and learns large-scale structures in the latter stage. We believe this two-stage training dynamics is universal and is applicable to a wide range of problems. Our work builds bridges between two research subjects of quantum neural networks and information scrambling, which opens up a new perspective to understand quantum neural networks.

Item Type:Article
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URLURL TypeDescription Paper
Shen, Huitao0000-0003-1667-8011
Additional Information:© 2020 American Physical Society. Received 3 November 2019; revised manuscript received 19 April 2020; accepted 1 May 2020; published 21 May 2020. We thank Yingfei Gu for discussions and an anonymous referee for the suggestion to average results from different initializations. H. S. thanks IASTU for hosting his visit to Beijing, where key parts of this work were done. H. S. thanks Guangyu Du for suggestions on the data presentation. P. Z. acknowledges support from the Walter Burke Institute for Theoretical Physics at Caltech. This work is supported by Beijing Outstanding Young Scientist Program (H. Z.), MOST under Grant No. 2016YFA0301600 (H. Z.), and NSFC Grant No. 11734010 (H. Z.).
Group:Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Beijing Outstanding Young Scientist ProgramUNSPECIFIED
Ministry of Science and Technology (Taipei)2016YFA0301600
National Natural Science Foundation of China11734010
Issue or Number:20
Record Number:CaltechAUTHORS:20200521-154830923
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:103386
Deposited By: Tony Diaz
Deposited On:21 May 2020 23:00
Last Modified:16 Nov 2021 18:21

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