Quantum Entanglement in Deep Learning Architectures
Open accessAbstract
Modern deep learning has enabled unprecedented achievements in various domains. Nonetheless, employment of machine learning for wave function representations is focused on more traditional architectures such as restricted Boltzmann machines (RBMs) and fully connected neural networks. In this Letter, we establish that contemporary deep learning architectures, in the form of deep convolutional and recurrent networks, can efficiently represent highly entangled quantum systems. By constructing tensor network equivalents of these architectures, we identify an inherent reuse of information in the network operation as a key trait which distinguishes them from standard tensor network-based representations, and which enhances their entanglement capacity. Our results show that such architectures can support volume-law entanglement scaling, polynomially more efficiently than presently employed RBMs. Thus, beyond a quantification of the entanglement capacity of leading deep learning architectures, our analysis formally motivates a shift of trending neural-network-based wave function representations closer to the state-of-the-art in machine learning.
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Tensor networks can encode long-range dependencies, nonlinear relationships, and the integration of distributed features into unified percepts-core challenges that classical models tend to address only through ad hoc architectural modifications.
“Tensor networks can encode long-range dependencies, nonlinear relationships, and the integration of distributed features into unified percepts—core challenges that classical models tend to address only through ad hoc architectural modifications.”
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A Linear Frequency Principle Model to Understand the Absence of Overfitting in Neural Networks
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- Authors
- Levine, Y., Sharir, O., Cohen, N., & Shashua, A.
- Affiliations
- Hebrew University of Jerusalem (IL)
- Institute for Advanced Study (US)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2019-02-12
- Volume
- 122
- Issue
- 6
- Pages
- 065301-065301
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2912516940
- Cited by
- 206
- References
- 63
- Citations by year
- 2026: 16 · 2025: 24 · 2024: 22 · 2023: 27 · 2022: 32 · 2021: 39 · 2020: 33 · 2019: 10 · 2018: 3
- FWCI
- 12.55
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Israel Science Foundation (1790/12)
- H2020 European Research Council
- Israel Academy of Sciences and Humanities
- Schmidt Foundation
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Keywords
- quantum entanglement, deep convolutional neural networks, recurrent neural networks, tensor networks, wave function representation, restricted Boltzmann machine, entanglement capacity, information reuse
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