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Entanglement Detection with Quantum-inspired Kernels and SVMs

This work presents a machine learning approach based on support vector machines (SVMs) for quantum entanglement detection. Particularly, we focus in bipartite systems of dimensions 3x3, 4x4, and 5x5, 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 states, PPT-detectable entangled states, and entangled states that evade PPT detection. Our method achieves increasing accuracy with system dimension, reaching 80%, 90%, and nearly 100% for 3x3, 4x4, and 5x5 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 establish machine learning as a powerful complement to traditional entanglement detection methods, particularly for higher-dimensional systems where conventional approaches become inadequate. The findings highlight key directions for future research, including hybrid quantum-classical implementations and improved data generation protocols to overcome current limitations.

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