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Advanced Quantum Technologies

Quantum State Separability Identification via Neural Networks

Zhenhua Zhu, Chong‐Qiang Ye, Guo-Lin Lv, Xiaoke Wang, Ling-Hui Zhu, Tuo Huang, Xiaoyu Chen

Published Mar 1, 2026• 0 citations
Publisher

Abstract

ABSTRACT Quantum entanglement is a fundamental resource in quantum information science. In recent years, many researchers have explored the use of machine learning techniques to detect entanglement. However, most existing models still suffer from limited classification and generalization capability. To address these issues, we construct a randomly generated dataset of three‐qubit quantum states covering fully separable, bi‐separable, and genuine entangled states, and train a complex‐valued convolutional neural network to classify these three classes. Numerical results demonstrate that the proposed model accurately identifies all separability classes and exhibits strong generalization performance not only on the constructed dataset but also on various noisy quantum states, including noisy GHZ, W, GHZ‐W mixed, and hypergraph states, achieving an overall accuracy of 98.6%. In addition, we test the ability of the proposed model to identify certain positive‐partial‐transpose entangled states (PPTES), as well as quantum states that undergo local unitary (LU) operations. All of these results indicate that the proposed model can accurately identify the separability of most three‐qubit quantum states and can also serve as a reliable tool, providing highly probable and accurate predictions when theoretical methods fail.

DOI
10.1002/qute.202500951

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ABSTRACT Quantum entanglement is a fundamental resource in quantum information science. In recent years, many researchers have explored the use of machine learning techniques to detect entanglement. However, most existing models still suffer from limited classification and generalization capability. To address these issues, we construct a randomly generated dataset of three‐qubit quantum states covering fully separable, bi‐separable, and genuine entangled states, and train a complex‐valued convolutional neural network to classify these three classes. Numerical results demonstrate that the proposed model accurately identifies all separability classes and exhibits strong generalization performance not only on the constructed dataset but also on various noisy quantum states, including noisy GHZ, W, GHZ‐W mixed, and hypergraph states, achieving an overall accuracy of 98.6%. In addition, we test the ability of the proposed model to identify certain positive‐partial‐transpose entangled states (PPTES), as well as quantum states that undergo local unitary (LU) operations. All of these results indicate that the proposed model can accurately identify the separability of most three‐qubit quantum states and can also serve as a reliable tool, providing highly probable and accurate predictions when theoretical methods fail.
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.
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.
We design and successfully implement artificial neural networks (ANNs) to detect and classify entanglement for three-qubit systems using limited state features. The overall design principle is a feed forward neural network (FFNN), with the output layer consisting of a single neuron for the detection of genuine multipartite entanglement (GME) and six neurons for the classification problem corresponding to six entanglement classes under stochastic local operations and classical communication (SLOCC). The models are trained and validated on a simulated dataset of randomly generated states. We achieve high accuracy, around 98%, for detecting GME as well as for SLOCC classification. Remarkably, we find that feeding only 7 diagonal elements of the density matrix into the ANN results in an accuracy greater than 94% for both the tasks, showcasing the strength of the method in reducing the required input data while maintaining efficient performance. Reducing the feature set makes it easier to apply ANN models for entanglement classification, particularly in resource-constrained environments, without sacrificing accuracy. The performance of the ANN models was further evaluated by introducing white noise into the data set, and the results indicate that the models are robust and are able to well tolerate noise.
Entanglement is a central resource in quantum information and quantum technologies, yet its characterization remains challenging due to both theoretical complexity and measurement requirements. Machine learning has emerged as a promising alternative, enabling entanglement characterization from incomplete measurement data, however model interpretability remains a challenge. In this work, we introduce a unified and interpretable framework for SLOCC entanglement classification of two- and three-qubit states, encompassing both pure and mixed states. We train dense and convolutional neural networks on Pauli-measurement outcomes, provide design guidelines for each architecture, and systematically compare their performance across types of states. To interpret the models, we compute Shapley values to quantify the contribution of each measurement, analyze measurement-importance patterns across different systems, and use these insights to guide a measurement-reduction scheme. Accuracy-versus-measurement curves and comparisons with analytical entanglement criteria demonstrate the minimal resources required for reliable classification and highlight both the capabilities and limitations of Shapley-based interpretability when using machine learning models for entanglement detection and classification.
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 detection is one of the fundamental tasks in quantum information science. Conventional methods for quantum state tomography exhibit limitations in scalability as the number of qubits increases, leading to exponential growth in the number of unknown parameters and required measurements. Consequently, the accuracy enhancement achieved by these methods is constrained. In response to this challenge, we developed a tailored convolutional neural network (CNN) model capable of effectively detecting entanglement in two-qubit quantum states, achieving an accuracy exceeding 97.5%. Notably, even in the presence of noise, this model retains its robust performance, displaying resilience against a tolerable level of noise contamination. Furthermore, the inherent generalization power of CNNs allows our model, which was initially trained on a specific spectrum of quantum states, to extend its applicability to wider states, positioning it as an outstanding tool for the further application of machine learning in the field of quantum computing, opening up new pathways for solving entanglement detection problems in quantum information.