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:2509.03233

Scalable Entanglement Detection in Quantum Systems via Fisher Linear Discriminant Analysis

M. Mahdian, Zahra Beygom Mousavi

Published Oct 17, 2025• 0 citations
arXivHTMLPDF

Abstract

Abstract Quantum entanglement is the cornerstone of quantum technology and enables quantum devices to outperform classical systems in terms of performance. However, detecting entanglement in high-dimensional systems remains a significant challenge due to the exponential growth of the Hilbert space with the number of particles. In this work, we use machine learning to classify entangled states and separable states, focusing on the application of classical Fisher Linear Discriminant Analysis (FLDA). By adapting classical statistical learning techniques to quantum state discriminant analysis, we present the theoretical foundations, a practical implementation strategy, and the advantages of FLDA in this context. We systematically evaluate the performance of this method on different quantum states and demonstrate its effectiveness as a tool for efficient quantum state classification. Finally, we investigate multi-qubit quantum states with high accuracy and classify these states.

DOI
10.21203/rs.3.rs-7726040/v1

Related papers

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 quantum-inspired kernels and SVMs

Ana Martínez-Sabiote, Michalis Skotiniotis, Jara J. Bermejo-Vega +2 more

Abstract This work presents a machine learning approach based on support vector machines (SVMs) for quantum entanglement detection. Particularly, we focus on bipartite systems of dimensions $$3\times 3$$ 3 × 3 , $$4\times 4$$ 4 × 4 , and $$5\times 5$$ 5 × 5 , where the positive partial transpose criterion (PPT) provides only partial characterization. Using SVMs with quantum-inspired kernels, we develop a classification scheme that distinguishes between separable and entangled states, including PPT-detectable entangled states, and entangled states that evade PPT detection. Our method achieves increasing accuracy with system dimension, reaching $$80\%$$ 80 % , $$90\%$$ 90 % , and nearly $$100\%$$ 100 % for $$3\times 3$$ 3 × 3 , $$4\times 4$$ 4 × 4 , and $$5\times 5$$ 5 × 5 systems, respectively. Our results show that principal component analysis significantly enhances performance for small training sets. The study reveals important practical considerations regarding purity biases in the generation of data for this problem and examines the challenges of implementing these techniques on near-term quantum hardware. Our results demonstrate that machine learning can be an effective alternative to entanglement detection of higher-dimensional systems where conventional entanglement detection methods struggle. Our approach provides improved data generation protocols and can be readily implemented in hybrid classical-quantum architectures, overcoming current limitations.

arXiv:2508.17909•The Journal of Supercomputing•Jan 27, 2026•4 citations

Machine Learning Based Detection of Quantum Entanglement in Two-Qubit Systems

Shanidev Ambadas Sontakke

This paper explores the use of machine learning techniques for detecting quantum entanglement in two-qubit systems. A dataset of randomly generated quantum states was constructed and labeled using the Positive Partial Transpose (PPT) criterion. Several supervised learning models, including Random Forest and Multi-Layer Perceptron neural networks, were trained to classify quantum states as entangled or separable. The results show that machine learning models can effectively learn patterns from quantum state data, while also highlighting the impact of dataset imbalance on classification performance. This study demonstrates the potential of machine learning as a complementary tool for quantum entanglement detection and provides insights into the challenges and opportunities of integrating artificial intelligence with quantum physics.

•Jan 24, 2026•0 citations

AI-Driven Quantum Entanglement Classification: A Novel Noise-Robust Approach

Tahmina Akter Anondi

This paper introduces a new method to identify quantum entanglement in diverse quantum states by leveraging artificial intelligence. We establish a robust classifier by training a machine learning model on a synthetically generated dataset, enabling accurate differentiation of entangled states even amidst significant noise. The technique employs classical features derived from quantum state measurements, optimizing for sample efficiency. Numerical evaluations demonstrate this approach achieves high accuracy in classifying entangled multi-qubit states under various noisy environments.

International Conference on AI Innovations and Industry (ICAIII)•Apr 6, 2026•1 citation

Variational quantum entanglement classification discrimination

Shaoxuan Wang, Yingtong Shen, Xinjian Liu +2 more

With the rapid development of quantum technology, understanding the properties of entanglement states has become an urgent task.Various classifications of entanglement states have been proposed to cater to distinct quantum applications, highlighting the significance of entanglement classification. This paper presents a variational quantum classifier for entanglement classification discrimination which can effectively reduce the measurement resources, specifically for four-qubit entanglement equivalence classifications under SLOCC (Stochastic Local Operations and Classical Communication). Through training one-to-one and one-to-many models, our proposed method achieves excellent performance in the entanglement classification. We further investigate the impact of parameterized quantum circuit layers and various measurement settings on the classifier’s performance. Considering the inherent noise present in near-term quantum computers, we also analyze how noise affects the model’s performance. Moreover, we explore the classifier’s capabilities in the context of multi-qubit entanglement systems. Numerical simulations demonstrate that high-precision entanglement classification tasks can be accomplished with shallow circuit depths, and the model exhibits resilience to noise. Additionally, the results reveal the versatility and potential application of our proposed model in larger-scale quantum systems by effectively handling entanglement classification tasks involving an increased number of qubits.

Physica A Statistical Mechanics and its Applications•Jan 18, 2024•2 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
Abstract Quantum entanglement is the cornerstone of quantum technology and enables quantum devices to outperform classical systems in terms of performance. However, detecting entanglement in high-dimensional systems remains a significant challenge due to the exponential growth of the Hilbert space with the number of particles. In this work, we use machine learning to classify entangled states and separable states, focusing on the application of classical Fisher Linear Discriminant Analysis (FLDA). By adapting classical statistical learning techniques to quantum state discriminant analysis, we present the theoretical foundations, a practical implementation strategy, and the advantages of FLDA in this context. We systematically evaluate the performance of this method on different quantum states and demonstrate its effectiveness as a tool for efficient quantum state classification. Finally, we investigate multi-qubit quantum states with high accuracy and classify these states.
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.
Abstract This work presents a machine learning approach based on support vector machines (SVMs) for quantum entanglement detection. Particularly, we focus on bipartite systems of dimensions 3×33\times 33×3 3 × 3 , 4×44\times 44×4 4 × 4 , and 5×55\times 55×5 5 × 5 , where the positive partial transpose criterion (PPT) provides only partial characterization. Using SVMs with quantum-inspired kernels, we develop a classification scheme that distinguishes between separable and entangled states, including PPT-detectable entangled states, and entangled states that evade PPT detection. Our method achieves increasing accuracy with system dimension, reaching 80%80\%80% 80 % , 90%90\%90% 90 % , and nearly 100%100\%100% 100 % for 3×33\times 33×3 3 × 3 , 4×44\times 44×4 4 × 4 , and 5×55\times 55×5 5 × 5 systems, respectively. Our results show that principal component analysis significantly enhances performance for small training sets. The study reveals important practical considerations regarding purity biases in the generation of data for this problem and examines the challenges of implementing these techniques on near-term quantum hardware. Our results demonstrate that machine learning can be an effective alternative to entanglement detection of higher-dimensional systems where conventional entanglement detection methods struggle. Our approach provides improved data generation protocols and can be readily implemented in hybrid classical-quantum architectures, overcoming current limitations.
This paper explores the use of machine learning techniques for detecting quantum entanglement in two-qubit systems. A dataset of randomly generated quantum states was constructed and labeled using the Positive Partial Transpose (PPT) criterion. Several supervised learning models, including Random Forest and Multi-Layer Perceptron neural networks, were trained to classify quantum states as entangled or separable. The results show that machine learning models can effectively learn patterns from quantum state data, while also highlighting the impact of dataset imbalance on classification performance. This study demonstrates the potential of machine learning as a complementary tool for quantum entanglement detection and provides insights into the challenges and opportunities of integrating artificial intelligence with quantum physics.
This paper introduces a new method to identify quantum entanglement in diverse quantum states by leveraging artificial intelligence. We establish a robust classifier by training a machine learning model on a synthetically generated dataset, enabling accurate differentiation of entangled states even amidst significant noise. The technique employs classical features derived from quantum state measurements, optimizing for sample efficiency. Numerical evaluations demonstrate this approach achieves high accuracy in classifying entangled multi-qubit states under various noisy environments.
With the rapid development of quantum technology, understanding the properties of entanglement states has become an urgent task.Various classifications of entanglement states have been proposed to cater to distinct quantum applications, highlighting the significance of entanglement classification. This paper presents a variational quantum classifier for entanglement classification discrimination which can effectively reduce the measurement resources, specifically for four-qubit entanglement equivalence classifications under SLOCC (Stochastic Local Operations and Classical Communication). Through training one-to-one and one-to-many models, our proposed method achieves excellent performance in the entanglement classification. We further investigate the impact of parameterized quantum circuit layers and various measurement settings on the classifier’s performance. Considering the inherent noise present in near-term quantum computers, we also analyze how noise affects the model’s performance. Moreover, we explore the classifier’s capabilities in the context of multi-qubit entanglement systems. Numerical simulations demonstrate that high-precision entanglement classification tasks can be accomplished with shallow circuit depths, and the model exhibits resilience to noise. Additionally, the results reveal the versatility and potential application of our proposed model in larger-scale quantum systems by effectively handling entanglement classification tasks involving an increased number of qubits.
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.