Scalable Entanglement Detection in Quantum Systems via Fisher Linear Discriminant Analysis

Quantum entanglement is the cornerstone of quantum technology and enables quantum devices to outperform classical systems in terms of performance. However, detecting entanglement in high-dimensional systems remains a significant challenge due to the exponential growth of the Hilbert space with the number of particles. In this work, we use machine learning to classify entangled states and separable states, focusing on the application of classical Fisher Linear Discriminant Analysis (FLDA). By adapting classical statistical learning techniques to quantum state discriminant analysis, we present the theoretical foundations, a practical implementation strategy, and the advantages of FLDA in this context. We systematically evaluate the performance of this method on different quantum states and demonstrate its effectiveness as a tool for efficient quantum state classification. Finally, we investigate multi-qubit quantum states with high accuracy and classify these states.