Optimal Classification of Three-Qubit Entanglement with Cascaded Support Vector Machine

TL;DR

This paper presents a cascaded SVM framework for classifying three-qubit entanglement with high accuracy, robustness, and an optimized feature set, advancing quantum state analysis methods.

Contribution

The study introduces a systematic, optimized SVM-based framework for three-qubit entanglement classification, improving accuracy and reducing feature complexity.

Findings

Achieved 95% classification accuracy on mixed states.

Maintained high performance against noise and out-of-distribution states.

Developed a feature importance-based optimization protocol.

Abstract

We introduce a systematic framework for three-qubit entanglement classification using a cascaded architecture of Support Vector Machine (SVM) classifiers. Leveraging the well defined three-qubit structure with the four nested entanglement classes (S, B, W, and GHZ), we construct three distinct witness models ($\mathcal{M}_{B}$, $\mathcal{M}_{W}$, and $\mathcal{M}_{GHZ}$) that sequentially discriminate between these classes. The proposed Cascaded model achieves an overall classification accuracy of $95\%$ on a comprehensive dataset of mixed states. The framework's robustness and generalization capabilities are confirmed through rigorous testing against out-of-distribution (OOD) entangled states and various quantum noise channels, where the model maintains high performance. A key contribution of this research is an optimization protocol based on systematic feature importance analysis. This approach yields a tunable framework that significantly reduces the number of required features, while maintaining reliable model accuracy.