Guo Jie, Yan Taotao, Hou Jinchuan, Qi Xiaofei, He Kan
College of Mathematics, Taiyuan University of Technology, Taiyuan, 030024, China.
School of Mathematics and Statistics, Shanxi University, Taiyuan, 030006, China.
Sci Rep. 2025 Jul 1;15(1):21376. doi: 10.1038/s41598-025-06409-8.
Gaussian steering in continuousvariable (CV) systems, as a quantum correlation between nonlocality and entanglement, is an important quantum resource. Rapid detection of Gaussian steering is a significant challenge in quantum information process. In this paper, we employ a combination of machine learning methods, including Support Vector Machine (SVM), Backpropagation Neural Network (BPNN) and Meta-Weight-Net Neural Network (MWN) to speed up the detection. An ensemble learning approach that integrates these methods is also utilized to increase the accuracy of detection. A computable Gaussian steering quantification [Formula: see text] introduced recently in [Phys. Rev. A 110, 052427] serves as a pivotal tool for labeling the samples. A key observation is that steerable Gaussian states are vastly outnumbered by unsteerable ones, particularly in configurations where the untrusted party possesses significantly more modes than the trusted party. This leads to a highly skewed distribution of sample states in the dataset. In response to this phenomenon and to make comparison, we propose the imbalance factor ξ and prepare three types of datasets to be trained: balanced datasets, naturally generated datasets and augmented datasets with [Formula: see text] via a data augmentation strategy. Numerical experiments for seven low modes scenarios reveal that the classifiers obtained by utilizing the ensemble learning method training on augmented dataset have the best overall performance, significantly improving generalization capabilities with low cost and high test accuracy, achieving detection times as fast as [Formula: see text] seconds, at least 100 times faster than calculating [Formula: see text]. The speed advantage of machine learning detection will be more obvious in the case of higher modes. Thus the approach is both efficient and reliable, offering valuable insights into the broader potential of machine learning applications in quantum information science and providing a robust framework for machine learning utilized to classification tasks, especially in data-imbalanced scenarios.
连续变量（CV）系统中的高斯导引作为非局域性与纠缠之间的一种量子关联，是一种重要的量子资源。快速检测高斯导引是量子信息处理中的一项重大挑战。在本文中，我们采用了包括支持向量机（SVM）、反向传播神经网络（BPNN）和元权重网络神经网络（MWN）在内的机器学习方法组合来加速检测。还利用了一种整合这些方法的集成学习方法来提高检测精度。最近在[《物理评论A》110, 052427]中引入的一种可计算的高斯导引量化[公式：见原文]作为标记样本的关键工具。一个关键观察结果是，可导引的高斯态数量远远少于不可导引的高斯态，特别是在不可信方拥有比可信方多得多的模式的配置中。这导致数据集中样本态的分布高度不均衡。针对这一现象并为了进行比较，我们提出了不平衡因子ξ，并准备了三种类型的数据集进行训练：平衡数据集、自然生成数据集以及通过数据增强策略生成的具有[公式：见原文]的增强数据集。针对七种低模式场景的数值实验表明，通过在增强数据集上使用集成学习方法训练得到的分类器具有最佳的整体性能，以低成本和高测试精度显著提高了泛化能力，实现了快至[公式：见原文]秒的检测时间，比计算[公式：见原文]至少快100倍。在更高模式的情况下，机器学习检测的速度优势将更加明显。因此，该方法既高效又可靠，为机器学习在量子信息科学中的更广泛潜力提供了有价值的见解，并为用于分类任务的机器学习提供了一个强大的框架，特别是在数据不平衡的场景中。
