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:2608.05293

Entangling power of neural networks

Taige Wang, Nisarga Paul, Liang Fu

cond-mat.dis-nnquant-phSubmitted Aug 5, 2026• Announced Aug 7, 2026• 0 citations
arXivHTMLPDF

Abstract

Characterizing the complexity of correlations between subsystems is a fundamental task across information theory, machine learning, and science. In quantum physics, neural networks have found increasing application in learning wavefunctions. Here we introduce the entangling power of an encoder-decoder neural network, which quantifies its ability to generate entanglement between subsystems, dependent on a latent space dimension $K$ and the complexity class of the decoder. We exactly calculate this quantity for polynomial decoders of degree $p$ acting on a $K$-dimensional latent space. Our results establish the exponential entangling power of neural networks with modest resources. More broadly, our work provides a framework for analyzing correlations in machine learning that generalizes the notion of the Schmidt rank in entanglement theory.

Comments
5+2 pages

Related papers

Quantum-Inspired Entanglement-Based Neural Networks

Jincheng Zhang

This paper proposes a novel neural network architecture, termed Entanglement-Based Neural Networks (EBNNs), inspired by the principles of quantum entanglement. Conventional classical neural networks often face challenges in effectively capturing and representing intricate correlations within data, particularly when dealing with high-dimensional or complex datasets. The core idea behind EBNNs is to construct networks where nodes are interconnected in a manner that mirrors the correlated states observed in quantum entanglement, even across spatial separation. This is achieved through a specifically designed network topology that introduces dependencies between nodes, allowing for a more efficient representation of complex relationships. The network's structure is defined by a set of interconnected nodes, each possessing a state (s_i) represented by a real number. The connections between nodes are characterized by a correlation function (C_{ij}), which dictates the degree to which the state of node *j* is influenced by the state of node *i*. The architecture utilizes a layered approach, where layers are composed of interconnected nodes. The propagation of information through the network is governed by a modified version of the Hebbian learning rule, adapted to incorporate the entanglement-like correlation functions. This approach aims to improve the network's ability to learn and represent complex patterns by leveraging inherent correlations rather than relying solely on independent node activations. The key contributions of this work are the conceptual design of EBNNs and the formulation of the core mathematical framework for their implementation. We present a detailed description of the network architecture, the correlation function definition, and the learning rule, offering a foundation for further research and development in this area. Finally, we demonstrate the potential advantages of EBNNs in terms of improved learning efficiency and representation capacity.

•Aug 29, 2026•0 citations

Detecting quantum entanglement with unsupervised learning

Yiwei Chen, Yu Pan, Guofeng Zhang +1 more

Abstract Quantum properties, such as entanglement and coherence, are indispensable resources in various quantum information processing tasks. However, there still lacks an efficient and scalable way to detecting these useful features especially for high-dimensional and multipartite quantum systems. In this work, we exploit the convexity of samples without the desired quantum features and design an unsupervised machine learning method to detect the presence of such features as anomalies. Particularly, in the context of entanglement detection, we propose a complex-valued neural network composed of pseudo-siamese network and generative adversarial net, and then train it with only separable states to construct non-linear witnesses for entanglement. It is shown via numerical examples, ranging from two-qubit to ten-qubit systems, that our network is able to achieve high detection accuracy which is above 97.5% on average. Moreover, it is capable of revealing rich structures of entanglement, such as partial entanglement among subsystems. Our results are readily applicable to the detection of other quantum resources such as Bell nonlocality and steerability, and thus our work could provide a powerful tool to extract quantum features hidden in multipartite quantum data.

arXiv:2103.04804•Quantum Science and Technology•Oct 19, 2021•61 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

Arbitrary Polynomial Separations in Trainable Quantum Machine Learning

Eric R. Anschuetz, Xun Gao

Recent theoretical results in quantum machine learning have demonstrated a general trade-off between the expressive power of quantum neural networks (QNNs) and their trainability; as a corollary of these results, practical exponential separations in expressive power over classical machine learning models are believed to be infeasible as such QNNs take a time to train that is exponential in the model size. We here circumvent these negative results by constructing a hierarchy of efficiently trainable QNNs that exhibit unconditionally provable, polynomial memory separations of arbitrary constant degree over classical neural networks—including state-of-the-art models, such as Transformers—in performing a classical sequence modeling task. This construction is also computationally efficient, as each unit cell of the introduced class of QNNs only has constant gate complexity. We show that contextuality—informally, a quantitative notion of semantic ambiguity—is the source of the expressivity separation, suggesting that other learning tasks with this property may be a natural setting for the use of quantum learning algorithms.

arXiv:2402.08606•Quantum•Jan 20, 2026•3 citations

Quantum Entanglement in Neural Network States

Dong-Ling Deng, Xiaopeng Li, S. Das Sarma

Machine learning has recently gained attention as a possible way to understand phase transitions in many-body quantum systems. A new entanglement analysis reveals crucial properties of the data structures that encode quantum states in a neural network, opening new inroads in applying machine learning to quantum many-body physics.

arXiv:1701.04844•Physical Review X•May 11, 2017•424 citations

Unsupervised generalization of correlated quantum dynamics on disordered lattices

Miri Kenig, Yoav Lahini

The application of unsupervised machine learning to the study of physical problems is an emerging field aimed at leveraging their outstanding capabilities to distill essential information from complex data sets. Here we use Generative Adversarial Networks (GANs), deep learning algorithms mainly used to synthesize realistic images, for the analysis of a physical problem: the propagation of interacting quantum particles on disordered chains, characterized by the emergence of complex quantum correlations. We find that GANs can learn these correlations and identify the physical control parameters in a completely unsupervised manner. After training on a data set of unlabeled examples, the algorithm can generate, without further calculations, a much larger number of unseen yet physically correct new instances. Most notably, the knowledge distilled in the algorithm's latent space identifies the relevant control parameter, the level of disorder in our case, even though this was not highlighted in the training set. This allows tuning the disorder level in the generated samples to values the algorithm was not explicitly trained on, thereby uncovering a fundamental physical phenomenon---the crossover from nearly free propagation to localization. These results demonstrate the ability of deep neural networks to learn and generalize physical rules by scanning examples and suggest their use in physical analysis and discovery.

Physical Review A•Jan 26, 2023•0 citations
Characterizing the complexity of correlations between subsystems is a fundamental task across information theory, machine learning, and science. In quantum physics, neural networks have found increasing application in learning wavefunctions. Here we introduce the entangling power of an encoder-decoder neural network, which quantifies its ability to generate entanglement between subsystems, dependent on a latent space dimension KKK and the complexity class of the decoder. We exactly calculate this quantity for polynomial decoders of degree ppp acting on a KKK-dimensional latent space. Our results establish the exponential entangling power of neural networks with modest resources. More broadly, our work provides a framework for analyzing correlations in machine learning that generalizes the notion of the Schmidt rank in entanglement theory.
This paper proposes a novel neural network architecture, termed Entanglement-Based Neural Networks (EBNNs), inspired by the principles of quantum entanglement. Conventional classical neural networks often face challenges in effectively capturing and representing intricate correlations within data, particularly when dealing with high-dimensional or complex datasets. The core idea behind EBNNs is to construct networks where nodes are interconnected in a manner that mirrors the correlated states observed in quantum entanglement, even across spatial separation. This is achieved through a specifically designed network topology that introduces dependencies between nodes, allowing for a more efficient representation of complex relationships. The network's structure is defined by a set of interconnected nodes, each possessing a state (s_i) represented by a real number. The connections between nodes are characterized by a correlation function (C_{ij}), which dictates the degree to which the state of node *j* is influenced by the state of node *i*. The architecture utilizes a layered approach, where layers are composed of interconnected nodes. The propagation of information through the network is governed by a modified version of the Hebbian learning rule, adapted to incorporate the entanglement-like correlation functions. This approach aims to improve the network's ability to learn and represent complex patterns by leveraging inherent correlations rather than relying solely on independent node activations. The key contributions of this work are the conceptual design of EBNNs and the formulation of the core mathematical framework for their implementation. We present a detailed description of the network architecture, the correlation function definition, and the learning rule, offering a foundation for further research and development in this area. Finally, we demonstrate the potential advantages of EBNNs in terms of improved learning efficiency and representation capacity.
Abstract Quantum properties, such as entanglement and coherence, are indispensable resources in various quantum information processing tasks. However, there still lacks an efficient and scalable way to detecting these useful features especially for high-dimensional and multipartite quantum systems. In this work, we exploit the convexity of samples without the desired quantum features and design an unsupervised machine learning method to detect the presence of such features as anomalies. Particularly, in the context of entanglement detection, we propose a complex-valued neural network composed of pseudo-siamese network and generative adversarial net, and then train it with only separable states to construct non-linear witnesses for entanglement. It is shown via numerical examples, ranging from two-qubit to ten-qubit systems, that our network is able to achieve high detection accuracy which is above 97.5% on average. Moreover, it is capable of revealing rich structures of entanglement, such as partial entanglement among subsystems. Our results are readily applicable to the detection of other quantum resources such as Bell nonlocality and steerability, and thus our work could provide a powerful tool to extract quantum features hidden in multipartite quantum data.
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.
Recent theoretical results in quantum machine learning have demonstrated a general trade-off between the expressive power of quantum neural networks (QNNs) and their trainability; as a corollary of these results, practical exponential separations in expressive power over classical machine learning models are believed to be infeasible as such QNNs take a time to train that is exponential in the model size. We here circumvent these negative results by constructing a hierarchy of efficiently trainable QNNs that exhibit unconditionally provable, polynomial memory separations of arbitrary constant degree over classical neural networks—including state-of-the-art models, such as Transformers—in performing a classical sequence modeling task. This construction is also computationally efficient, as each unit cell of the introduced class of QNNs only has constant gate complexity. We show that contextuality—informally, a quantitative notion of semantic ambiguity—is the source of the expressivity separation, suggesting that other learning tasks with this property may be a natural setting for the use of quantum learning algorithms.
The application of unsupervised machine learning to the study of physical problems is an emerging field aimed at leveraging their outstanding capabilities to distill essential information from complex data sets. Here we use Generative Adversarial Networks (GANs), deep learning algorithms mainly used to synthesize realistic images, for the analysis of a physical problem: the propagation of interacting quantum particles on disordered chains, characterized by the emergence of complex quantum correlations. We find that GANs can learn these correlations and identify the physical control parameters in a completely unsupervised manner. After training on a data set of unlabeled examples, the algorithm can generate, without further calculations, a much larger number of unseen yet physically correct new instances. Most notably, the knowledge distilled in the algorithm's latent space identifies the relevant control parameter, the level of disorder in our case, even though this was not highlighted in the training set. This allows tuning the disorder level in the generated samples to values the algorithm was not explicitly trained on, thereby uncovering a fundamental physical phenomenon---the crossover from nearly free propagation to localization. These results demonstrate the ability of deep neural networks to learn and generalize physical rules by scanning examples and suggest their use in physical analysis and discovery.