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Classifying multipartite continuous-variable entanglement structures through data-augmented neural networks
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DOI：10.1038/s42256-026-01284-y.png)
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Abstract
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Neural networks have emerged as a promising paradigm for quantum information processing, yet they confront the challenge of generating training datasets with sufficient size and rich diversity, which is particularly acute when dealing with multipartite quantum systems. For instance, in the task of classifying different structures of multipartite entanglement in continuous-variable systems, it is necessary to simulate a large number of infinite-dimensional state data that can cover as many types of non-Gaussian states as possible. Here we develop a data-augmented neural network to address this task with homodyne measurement data. A quantum data augmentation method based on classical data processing techniques and quantum physical principles is proposed to efficiently enhance network performance. By testing on randomly generated tripartite and quadripartite states, we demonstrate that the network can infer the entanglement structure among the various partitions, and the accuracies are substantially improved with data augmentation. Our approach allows us to further extend the use of data-driven machine learning techniques to more complex tasks of learning quantum systems encoded in a large Hilbert space. Gao et al. introduce a quantum data augmentation method to enable neural networks to classify multipartite entanglement structures in infinite-dimensional systems, substantially improving accuracy and reducing the data acquisition costs that typically limit training.
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