Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1803.09780 · Physical Review Letters

Quantum Entanglement in Deep Learning Architectures

Yoav Levine, Or Sharir, Nadav Cohen, Amnon Shashua

Published Feb 12, 2019• 206 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.122.065301

Related papers

Bridging Many-Body Quantum Physics and Deep Learning via Tensor Networks

Yoav Levine, Or Sharir, Nadav Cohen +1 more

In this chapter, we describe a tensor network (TN) based common language established between machine learning and many-body physics, which allows for bidirectional contributions. By showing that many-body wave functions are structurally equivalent to mappings of convolutional and recurrent networks, we bring forth quantum entanglement measures as natural quantifiers of dependencies modeled by such networks. Accordingly, we propose a novel entanglement-based deep learning design scheme that sheds light on the success of popular architectural choices made by deep learning practitioners and suggests new practical prescriptions. In the other direction, we construct TNs corresponding to deep recurrent and convolutional networks. This allows us to theoretically demonstrate that these architectures are powerful enough to represent highly entangled quantum systems polynomially more efficiently than previously employed architectures. We thus provide theoretical motivation to shift neural-network-based wave function representations closer to state-of-the-art deep learning architectures.

Cambridge University Press eBooks•Nov 29, 2022•4 citations

Deep Learning and Quantum Entanglement: Fundamental Connections with Implications to Network Design

Yoav Levine, David Yakira, Nadav Cohen +1 more

Deep convolutional networks have witnessed unprecedented success in various machine learning applications. Formal understanding on what makes these networks so successful is gradually unfolding, but for the most part there are still significant mysteries to unravel. The inductive bias, which reflects prior knowledge embedded in the network architecture, is one of them. In this work, we establish a fundamental connection between the fields of quantum physics and deep learning. We use this connection for asserting novel theoretical observations regarding the role that the number of channels in each layer of the convolutional network fulfills in the overall inductive bias. Specifically, we show an equivalence between the function realized by a deep convolutional arithmetic circuit (ConvAC) and a quantum many-body wave function, which relies on their common underlying tensorial structure. This facilitates the use of quantum entanglement measures as well-defined quantifiers of a deep network's expressive ability to model intricate correlation structures of its inputs. Most importantly, the construction of a deep ConvAC in terms of a Tensor Network is made available. This description enables us to carry a graph-theoretic analysis of a convolutional network, with which we demonstrate a direct control over the inductive bias of the deep network via its channel numbers, that are related to the min-cut in the underlying graph. This result is relevant to any practitioner designing a network for a specific task. We theoretically analyze ConvACs, and empirically validate our findings on more common ConvNets which involve ReLU activations and max pooling. Beyond the results described above, the description of a deep convolutional network in well-defined graph-theoretic tools and the formal connection to quantum entanglement, are two interdisciplinary bridges that are brought forth by this work.

arXiv:1704.01552•Apr 5, 2017•61 citations

Entanglement transition in deep neural quantum states

Giacomo Passetti, Dante Marvin Kennes

Despite the huge theoretical potential of neural quantum states, their use in describing generic, highly-correlated quantum many-body systems still often poses practical difficulties. Customized network architectures are under active investigation to address these issues. For a guided search of suited network architectures a deepened understanding of the link between neural network properties and attributes of the physical system one is trying to describe, is imperative. Drawing inspiration from the field of machine learning, in this work we show how information propagation in deep neural networks impacts the physical entanglement properties of deep neural quantum states. In fact, we link a previously identified information propagation phase transition of a neural network to a similar transition of entanglement in neural quantum states. With this bridge we can identify optimal neural quantum state hyperparameter regimes for representing area as well as volume law entangled states. The former are easily accessed by alternative methods, such as tensor network representations, at least in low physical dimensions, while the latter are challenging to describe generally due to their extensive quantum entanglement. This advance of our understanding of network configurations for accurate quantum state representation helps to develop effective representations to deal with volume-law quantum states, and we apply these findings to describe the ground state (area law state) vs. the excited state (volume law state) properties of the prototypical next-nearest neighbor spin-1/2 Heisenberg model.

arXiv:2312.11941•Jan 1, 2023•0 citations

Quantum Entanglement-Based Non-Local Data Dependency Learning

Jincheng Zhang

This paper proposes a novel approach to deep learning leveraging the phenomenon of quantum entanglement for enhanced training efficiency and generalization capabilities. The core idea is to construct a neural network architecture where neurons are interconnected via entangled quantum states, enabling non-local data dependency learning. We introduce a framework where input data is encoded into quantum states, subjected to quantum gate transformations, and utilizes entanglement for information propagation. This fundamentally shifts the paradigm from classical, locally-connected networks to a system exploiting inherent quantum parallelism. The theoretical underpinning of this approach suggests potential advantages in terms of computational speed and model performance, offering a new direction for deep learning research. We explore the mathematical formalization of this process, emphasizing the key components and their relationships. The primary goal is to demonstrate the feasibility and potential benefits of integrating quantum mechanics into the architecture and training of deep neural networks. The exploration focuses on the design principles and initial mathematical framework for this entanglement-based learning system. ---

•Sep 2, 2026•0 citations

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

Xun Gao, Lu-Ming Duan

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.One of the challenges in studies of quantum many-body physics is finding an efficient way to record the large system wavefunctions. Here the authors present an analysis of the capabilities of recently-proposed neural network representations for storing physically accessible quantum states.

arXiv:1701.05039•Nature Communications•Sep 18, 2017•345 citations

Quantum-inspired tensor networks in machine learning models

Guillermo Valverde, Igor García-Olaizola, Giannicola Scarpa +1 more

Tensor networks were developed in the context of many-body physics as compressed representations of multiparticle quantum states. These representations mitigate the exponential complexity of many-body systems by capturing only the most relevant dependencies. Due to the formal similarity between quantum entanglement and statistical correlations, tensor networks have recently been integrated in machine learning, operating both as alternative learning architectures and as decompositions of components of neural networks. The expectation is that the theoretical understanding of tensor networks developed within quantum many-body physics leads to novel methods that offer advantages in terms of computational efficiency, explainability, or privacy. Here we review the use of tensor networks in the context of machine learning, providing a critical assessment of the state of the art, the potential advantages, and the challenges that must be overcome.

cs.LGCross-listedarXiv:2604.14287•Apr 17, 2026•0 citations
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.
In this chapter, we describe a tensor network (TN) based common language established between machine learning and many-body physics, which allows for bidirectional contributions. By showing that many-body wave functions are structurally equivalent to mappings of convolutional and recurrent networks, we bring forth quantum entanglement measures as natural quantifiers of dependencies modeled by such networks. Accordingly, we propose a novel entanglement-based deep learning design scheme that sheds light on the success of popular architectural choices made by deep learning practitioners and suggests new practical prescriptions. In the other direction, we construct TNs corresponding to deep recurrent and convolutional networks. This allows us to theoretically demonstrate that these architectures are powerful enough to represent highly entangled quantum systems polynomially more efficiently than previously employed architectures. We thus provide theoretical motivation to shift neural-network-based wave function representations closer to state-of-the-art deep learning architectures.
Deep convolutional networks have witnessed unprecedented success in various machine learning applications. Formal understanding on what makes these networks so successful is gradually unfolding, but for the most part there are still significant mysteries to unravel. The inductive bias, which reflects prior knowledge embedded in the network architecture, is one of them. In this work, we establish a fundamental connection between the fields of quantum physics and deep learning. We use this connection for asserting novel theoretical observations regarding the role that the number of channels in each layer of the convolutional network fulfills in the overall inductive bias. Specifically, we show an equivalence between the function realized by a deep convolutional arithmetic circuit (ConvAC) and a quantum many-body wave function, which relies on their common underlying tensorial structure. This facilitates the use of quantum entanglement measures as well-defined quantifiers of a deep network's expressive ability to model intricate correlation structures of its inputs. Most importantly, the construction of a deep ConvAC in terms of a Tensor Network is made available. This description enables us to carry a graph-theoretic analysis of a convolutional network, with which we demonstrate a direct control over the inductive bias of the deep network via its channel numbers, that are related to the min-cut in the underlying graph. This result is relevant to any practitioner designing a network for a specific task. We theoretically analyze ConvACs, and empirically validate our findings on more common ConvNets which involve ReLU activations and max pooling. Beyond the results described above, the description of a deep convolutional network in well-defined graph-theoretic tools and the formal connection to quantum entanglement, are two interdisciplinary bridges that are brought forth by this work.
Despite the huge theoretical potential of neural quantum states, their use in describing generic, highly-correlated quantum many-body systems still often poses practical difficulties. Customized network architectures are under active investigation to address these issues. For a guided search of suited network architectures a deepened understanding of the link between neural network properties and attributes of the physical system one is trying to describe, is imperative. Drawing inspiration from the field of machine learning, in this work we show how information propagation in deep neural networks impacts the physical entanglement properties of deep neural quantum states. In fact, we link a previously identified information propagation phase transition of a neural network to a similar transition of entanglement in neural quantum states. With this bridge we can identify optimal neural quantum state hyperparameter regimes for representing area as well as volume law entangled states. The former are easily accessed by alternative methods, such as tensor network representations, at least in low physical dimensions, while the latter are challenging to describe generally due to their extensive quantum entanglement. This advance of our understanding of network configurations for accurate quantum state representation helps to develop effective representations to deal with volume-law quantum states, and we apply these findings to describe the ground state (area law state) vs. the excited state (volume law state) properties of the prototypical next-nearest neighbor spin-1/2 Heisenberg model.
This paper proposes a novel approach to deep learning leveraging the phenomenon of quantum entanglement for enhanced training efficiency and generalization capabilities. The core idea is to construct a neural network architecture where neurons are interconnected via entangled quantum states, enabling non-local data dependency learning. We introduce a framework where input data is encoded into quantum states, subjected to quantum gate transformations, and utilizes entanglement for information propagation. This fundamentally shifts the paradigm from classical, locally-connected networks to a system exploiting inherent quantum parallelism. The theoretical underpinning of this approach suggests potential advantages in terms of computational speed and model performance, offering a new direction for deep learning research. We explore the mathematical formalization of this process, emphasizing the key components and their relationships. The primary goal is to demonstrate the feasibility and potential benefits of integrating quantum mechanics into the architecture and training of deep neural networks. The exploration focuses on the design principles and initial mathematical framework for this entanglement-based learning system. ---
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.One of the challenges in studies of quantum many-body physics is finding an efficient way to record the large system wavefunctions. Here the authors present an analysis of the capabilities of recently-proposed neural network representations for storing physically accessible quantum states.
Tensor networks were developed in the context of many-body physics as compressed representations of multiparticle quantum states. These representations mitigate the exponential complexity of many-body systems by capturing only the most relevant dependencies. Due to the formal similarity between quantum entanglement and statistical correlations, tensor networks have recently been integrated in machine learning, operating both as alternative learning architectures and as decompositions of components of neural networks. The expectation is that the theoretical understanding of tensor networks developed within quantum many-body physics leads to novel methods that offer advantages in terms of computational efficiency, explainability, or privacy. Here we review the use of tensor networks in the context of machine learning, providing a critical assessment of the state of the art, the potential advantages, and the challenges that must be overcome.