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:2103.04804 · Quantum Science and Technology

Detecting quantum entanglement with unsupervised learning

Yiwei Chen, Yu Pan, Guofeng Zhang, Shuming Cheng

Published Oct 19, 2021• 61 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/2058-9565/ac310f

Related papers

Entanglement verification with deep semisupervised machine learning

Lifeng Zhang, Zhihua Chen, Shao-Ming Fei

Quantum entanglement lies at the heart of quantum information-processing tasks. Although many criteria have been proposed, efficient and scalable methods to detect the entanglement of generally given quantum states are still not available yet, particularly for high-dimensional and multipartite quantum systems. Based on FixMatch and Pseudo-Label methods, we propose a deep semisupervised learning model with a small portion of labeled data and a large portion of unlabeled data. The data-augmentation strategies are applied in this model by using the convexity of separable states and performing local unitary operations on the training data. We verify that our model has good generalization ability and gives rise to better accuracies than traditional supervised learning models with detailed examples.

arXiv:2308.15391•Physical Review A•Aug 28, 2023•17 citations

Entanglement structure detection via computer vision

Rui Li, Junling Du, Zheng Qin +4 more

Quantum entanglement plays a pivotal role in various quantum information processing tasks. However, a universal and effective way to detect entanglement structures is still lacking, especially for high-dimensional and multipartite quantum systems. Noticing the mathematical similarities between the common representations of many-body quantum states and the data structures of images, we are inspired to employ advanced computer vision technologies for data analysis. In this work, we propose a hybrid convolutional neural network--transformer model for both the classification of Greenberger-Horne-Zeilinger and $W$ states and the detection of various entanglement structures. By leveraging the feature-extraction capabilities of convolutional neural networks and the powerful modeling abilities of transformers, we not only can effectively reduce the time and computational resources required for the training process but can also obtain high detection accuracies. Through numerical simulation and physical verification, it is confirmed that our hybrid model is more effective than traditional techniques and thus offers a powerful tool for characterizing multipartite entanglement structures.

arXiv:2401.03400•Physical Review A•Jul 19, 2024•9 citations

Identification of quantum entanglement with Siamese convolutional neural networks and semisupervised learning

Jarosław Pawłowski, Mateusz Krawczyk

Quantum entanglement is a fundamental property commonly used in various quantum information protocols and algorithms. Nonetheless, the problem of identifying entanglement has still not reached a general solution for systems larger than $2\ifmmode\times\else\texttimes\fi{}3$. In this study, we use deep convolutional NNs, a type of supervised machine learning, to identify quantum entanglement for any bipartition in a three-qubit system. We demonstrate that training the model on synthetically generated datasets of random density matrices excluding challenging positive-under-partial-transposition entangled states (PPTES), which cannot be identified (and correctly labeled) in general, leads to good model accuracy even for PPTES states, that were outside the training data. Our aim is to enhance the model's generalization on PPTES. By applying entanglement-preserving symmetry operations through a triple Siamese network trained in a semisupervised manner, we improve the model's accuracy and ability to recognize PPTES. Moreover, by constructing an ensemble of Siamese models, even better generalization is observed, in analogy with the idea of finding separate types of entanglement witnesses for different classes of states.

arXiv:2210.07410•Physical Review Applied•Jul 26, 2024•9 citations

Towards efficient and generic entanglement detection by machine learning

Jue Xu, Qi Zhao

Detection of entanglement is an indispensable step to practical quantum computation and communication. Compared with the conventional entanglement witness method based on fidelity, we propose a flexible, machine learning assisted entanglement detection protocol that is robust to different types of noises and sample efficient. In this protocol, an entanglement classifier for a generic entangled state is obtained by training a classical machine learning model with a synthetic dataset. The dataset contains classical features of two types of states and their labels (either entangled or separable). The classical features of a state, which are expectation values of a set of k-local Pauli observables, are estimated sample-efficiently by the classical shadow method. In the numerical simulation, our classifier can detect the entanglement of 4-qubit GHZ states with coherent noise and W states mixed with large white noise, with high accuracy.

arXiv:2211.05592•Nov 10, 2022•0 citations

Separability-entanglement classifier via machine learning

Sirui Lu, Shilin Huang, Keren Li +7 more

The problem of determining whether a given quantum state is entangled lies at the heart of quantum information processing. Despite the many methods---such as the positive partial transpose criterion and the $k$-symmetric extendibility criterion---to tackle this problem, none of them enables a general, practical solution due to the problem's NP-hard complexity. Explicitly, separable states form a high-dimensional convex set of vastly complicated structures. In this work, we build a different separability-entanglement classifier underpinned by machine learning techniques. We use standard tools from machine learning to learn the entanglement feature of arbitrary given quantum states. We perform substantial numerical tests on two-qubit and two-qutrit systems, and the results indicate that our method can outperform the existing methods in generic cases in terms of both speed and accuracy. This opens up avenues to explore quantum entanglement via the machine learning approach.

arXiv:1705.01523•Physical Review A•Jul 13, 2018•117 citations

Entanglement detection with artificial neural networks

Naema Asif, Uman Khalid, Awais Khan +2 more

Quantum entanglement is one of the essential resources involved in quantum information processing tasks. However, its detection for usage remains a challenge. The Bell-type inequality for relative entropy of coherence serves as an entanglement witness for pure entangled states. However, it does not perform reliably for mixed entangled states. This paper constructs a classifier by employing the relationship between coherence and entanglement for supervised machine learning methods. This method encodes multiple Bell-type inequalities for the relative entropy of coherence into an artificial neural network to detect the entangled and separable states in a quantum dataset.

Scientific Reports•Jan 28, 2023•47 citations
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.
Quantum entanglement lies at the heart of quantum information-processing tasks. Although many criteria have been proposed, efficient and scalable methods to detect the entanglement of generally given quantum states are still not available yet, particularly for high-dimensional and multipartite quantum systems. Based on FixMatch and Pseudo-Label methods, we propose a deep semisupervised learning model with a small portion of labeled data and a large portion of unlabeled data. The data-augmentation strategies are applied in this model by using the convexity of separable states and performing local unitary operations on the training data. We verify that our model has good generalization ability and gives rise to better accuracies than traditional supervised learning models with detailed examples.
Quantum entanglement plays a pivotal role in various quantum information processing tasks. However, a universal and effective way to detect entanglement structures is still lacking, especially for high-dimensional and multipartite quantum systems. Noticing the mathematical similarities between the common representations of many-body quantum states and the data structures of images, we are inspired to employ advanced computer vision technologies for data analysis. In this work, we propose a hybrid convolutional neural network--transformer model for both the classification of Greenberger-Horne-Zeilinger and WWW states and the detection of various entanglement structures. By leveraging the feature-extraction capabilities of convolutional neural networks and the powerful modeling abilities of transformers, we not only can effectively reduce the time and computational resources required for the training process but can also obtain high detection accuracies. Through numerical simulation and physical verification, it is confirmed that our hybrid model is more effective than traditional techniques and thus offers a powerful tool for characterizing multipartite entanglement structures.
Quantum entanglement is a fundamental property commonly used in various quantum information protocols and algorithms. Nonetheless, the problem of identifying entanglement has still not reached a general solution for systems larger than $2\ifmmode\times\else\texttimes\fi{}3$. In this study, we use deep convolutional NNs, a type of supervised machine learning, to identify quantum entanglement for any bipartition in a three-qubit system. We demonstrate that training the model on synthetically generated datasets of random density matrices excluding challenging positive-under-partial-transposition entangled states (PPTES), which cannot be identified (and correctly labeled) in general, leads to good model accuracy even for PPTES states, that were outside the training data. Our aim is to enhance the model's generalization on PPTES. By applying entanglement-preserving symmetry operations through a triple Siamese network trained in a semisupervised manner, we improve the model's accuracy and ability to recognize PPTES. Moreover, by constructing an ensemble of Siamese models, even better generalization is observed, in analogy with the idea of finding separate types of entanglement witnesses for different classes of states.
Detection of entanglement is an indispensable step to practical quantum computation and communication. Compared with the conventional entanglement witness method based on fidelity, we propose a flexible, machine learning assisted entanglement detection protocol that is robust to different types of noises and sample efficient. In this protocol, an entanglement classifier for a generic entangled state is obtained by training a classical machine learning model with a synthetic dataset. The dataset contains classical features of two types of states and their labels (either entangled or separable). The classical features of a state, which are expectation values of a set of k-local Pauli observables, are estimated sample-efficiently by the classical shadow method. In the numerical simulation, our classifier can detect the entanglement of 4-qubit GHZ states with coherent noise and W states mixed with large white noise, with high accuracy.
The problem of determining whether a given quantum state is entangled lies at the heart of quantum information processing. Despite the many methods---such as the positive partial transpose criterion and the kkk-symmetric extendibility criterion---to tackle this problem, none of them enables a general, practical solution due to the problem's NP-hard complexity. Explicitly, separable states form a high-dimensional convex set of vastly complicated structures. In this work, we build a different separability-entanglement classifier underpinned by machine learning techniques. We use standard tools from machine learning to learn the entanglement feature of arbitrary given quantum states. We perform substantial numerical tests on two-qubit and two-qutrit systems, and the results indicate that our method can outperform the existing methods in generic cases in terms of both speed and accuracy. This opens up avenues to explore quantum entanglement via the machine learning approach.
Quantum entanglement is one of the essential resources involved in quantum information processing tasks. However, its detection for usage remains a challenge. The Bell-type inequality for relative entropy of coherence serves as an entanglement witness for pure entangled states. However, it does not perform reliably for mixed entangled states. This paper constructs a classifier by employing the relationship between coherence and entanglement for supervised machine learning methods. This method encodes multiple Bell-type inequalities for the relative entropy of coherence into an artificial neural network to detect the entangled and separable states in a quantum dataset.