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Scrambling ability of quantum neural network architectures

Wu, Yadong and Zhang, Pengfei and Zhai, Hui (2021) Scrambling ability of quantum neural network architectures. Physical Review Research, 3 (3). Art. No. L032057. ISSN 2643-1564. doi:10.1103/physrevresearch.3.L032057.

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In this Letter, we propose a guiding principle for how to design the architecture of a quantum neural network in order to achieve a high learning efficiency. This principle is inspired by the equivalence between extracting information from the input state to the readout qubit and scrambling information from the readout qubit to input qubits. We characterize the quantum information scrambling by operator size growth. By Haar random averaging over operator sizes, we propose an averaged operator size to describe the information scrambling ability of a given quantum neural network architecture. The key conjecture of this Letter is that this quantity is positively correlated with the learning efficiency of this architecture. To support this conjecture, we consider several different architectures, and we also consider two typical learning tasks. One is a regression task of a quantum problem, and the other is a classification task on classical images. In both cases, we find that, for the architecture with a larger averaged operator size, the loss function decreases faster or the prediction accuracy increases faster as the training epoch increases, which means higher learning efficiency. Our results can be generalized to more complicated quantum versions of machine learning algorithms.

Item Type:Article
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URLURL TypeDescription Paper
Zhang, Pengfei0000-0002-7408-0918
Zhai, Hui0000-0001-8118-6027
Additional Information:© 2021 The Author(s). Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. (Received 30 November 2020; revised 1 March 2021; accepted 23 August 2021; published 3 September 2021) This work was supported by the Beijing Outstanding Young Scientist Program, NSFC Grant No. 11734010, MOST under Grant No. 2016YFA0301600.
Group:Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Beijing Outstanding Young Scientist ProgramUNSPECIFIED
National Natural Science Foundation of China11734010
Ministry of Science and Technology (China)2016YFA0301600
Issue or Number:3
Record Number:CaltechAUTHORS:20210927-213255436
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:111054
Deposited By: George Porter
Deposited On:28 Sep 2021 14:05
Last Modified:28 Sep 2021 14:05

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