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。本研究提出一种机器学习流水线方法，用于在大规模场景下为该NP难问题寻求近似解。我们开发了一种基于Frank-Wolfe的高效算法，以近似求解最近的可分离密度矩阵，并推导出将密度矩阵标记为可分离或纠缠的系统化方法，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量子比特混合态。针对3维和7维量子比特量子态的数值实验验证了所提流程的有效性，证明该方法可处理数千个密度矩阵且具备高精度纠缠检测能力。这项工作为基准化量子可分离性迈出重要一步，有助于推动更强大纠缠检测技术的发展。