The quantum separability problem consists in deciding whether a bipartite density matrix is entangled or separable. In this work, we propose a machine learning pipeline for finding approximate solutions for this NP-hard problem in large-scale scenarios. We provide an efficient Frank-Wolfe-based algorithm to approximately seek the nearest separable density matrix and derive a systematic way for labeling density matrices as separable or entangled, allowing us to treat quantum separability as a classification problem. Our method is applicable to any two-qudit mixed states. Numerical experiments with quantum states of 3- and 7-dimensional qudits validate the efficiency of the proposed procedure, and demonstrate that it scales up to thousands of density matrices with a high quantum entanglement detection accuracy. This takes a step towards benchmarking quantum separability to support the development of more powerful entanglement detection techniques.

翻译：量子可分离性问题旨在判定二分密度矩阵是纠缠态还是可分离态。本文提出了一种机器学习流程，用于在规模场景下近似求解这一NP难问题。我们提供了一种基于Frank-Wolfe的高效算法，以近似寻找最近的可分离密度矩阵，并推导出一种系统化方法标记密度矩阵为可分离或纠缠态，从而将量子可分离性转化为分类问题。该方法适用于任意两qudit混合态。通过3维和7维qudit量子态的数值实验，验证了所提流程的高效性，并展示了其可扩展至数千个密度矩阵，且具有高量子纠缠检测准确率。这为基准测试量子可分离性以支持更强大纠缠检测技术的发展迈出了关键一步。