• Open Access

Interpretable Quantum Advantage in Neural Sequence Learning

Eric R. Anschuetz, Hong-Ye Hu, Jin-Long Huang, and Xun Gao
PRX Quantum 4, 020338 – Published 8 June 2023

Abstract

Quantum neural networks have been widely studied in recent years, given their potential practical utility and recent results regarding their ability to efficiently express certain classical data. However, analytic results to date rely on assumptions and arguments from complexity theory. Because of this, there is little intuition as to the source of the expressive power of quantum neural networks or for which classes of classical data any advantage can be reasonably expected to hold. Here, we study the relative expressive power between a broad class of neural network sequence models and a class of recurrent models based on Gaussian operations with non-Gaussian measurements. We explicitly show that quantum contextuality is the source of an unconditional memory separation in the expressivity of the two model classes. We use this intuition to study the relative performance of our introduced model on a standard translation data set exhibiting linguistic contextuality. In doing so, we demonstrate that our introduced quantum models are able to outperform state-of-the-art classical models even in practice.

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  • Received 7 November 2022
  • Accepted 6 March 2023

DOI:https://doi.org/10.1103/PRXQuantum.4.020338

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.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Eric R. Anschuetz1,*, Hong-Ye Hu2,3,4, Jin-Long Huang2, and Xun Gao4,†

  • 1MIT Center for Theoretical Physics, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
  • 2Department of Physics, University of California San Diego, 9500 Gilman Drive, La Jolla, California 92093, USA
  • 3Harvard Quantum Initiative, Harvard University, 17 Oxford Street, Cambridge, Massachusetts 02138, USA
  • 4Department of Physics, Harvard University, 17 Oxford Street, Cambridge, Massachusetts 02138, USA

  • *eans@mit.edu
  • xungao@g.harvard.edu

Popular Summary

Many concepts and models in the field of machine learning are inspired by physical systems. With the recent flurry of research on the use of quantum mechanics for computation, there has been growing interest in how quantum physics might enhance the power of neural networks. Though there have been heuristic constructions of quantum neural networks (QNNs) capable of learning classical data, any proof of their power has thus far relied on complexity theoretic assumptions. We prove, without relying on any assumptions, that a certain class of QNNs are more powerful than a large class of classical neural networks in performing certain translation tasks.

This separation is very general and holds even over the state-of-the-art neural networks in use today. This is surprising, given the quantum model requires only a simple subclass of quantum operations to implement using continuous variable quantum systems. We achieve this separation by studying the effects of quantum contextuality in these systems. Intuitively, we show that QNNs can “store” extra memory in the measurement context of the system. Though our separation is shown on a constructed translation task, we also demonstrate through numerical simulations that this separation persists on real translation data sets.

This work introduces techniques to further study the use of restricted classes of quantum systems for difficult machine-learning tasks. Our work demonstrates that such systems are capable of not only yielding rigorous performance guarantees, but also of being more amenable to experimental implementation than other QNN models, motivating future experiments.

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Vol. 4, Iss. 2 — June - August 2023

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It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

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