Entanglement detection with quantum-inspired kernels and SVMs

Abstract This work presents a machine learning approach based on support vector machines (SVMs) for quantum entanglement detection. Particularly, we focus on bipartite systems of dimensions 3 3 3 × 3, 4 4 4 × 4, and 5 5 5 × 5, where the positive partial transpose criterion (PPT) provides only partial characterization. Using SVMs with quantum-inspired kernels, we develop a classification scheme that distinguishes between separable and entangled states, including PPT-detectable entangled states, and entangled states that evade PPT detection. Our method achieves increasing accuracy with system dimension, reaching 80\% 80 %, 90\% 90 %, and nearly 100\% 100 % for 3 3 3 × 3, 4 4 4 × 4, and 5 5 5 × 5 systems, respectively. Our results show that principal component analysis significantly enhances performance for small training sets. The study reveals important practical considerations regarding purity biases in the generation of data for this problem and examines the challenges of implementing these techniques on near-term quantum hardware. Our results demonstrate that machine learning can be an effective alternative to entanglement detection of higher-dimensional systems where conventional entanglement detection methods struggle. Our approach provides improved data generation protocols and can be readily implemented in hybrid classical-quantum architectures, overcoming current limitations.