Classification of four-qubit entangled states via Machine Learning

TL;DR

This paper demonstrates that support vector machines can effectively classify four-qubit entangled states and identify entanglement patterns using entanglement witnesses, especially when combined with nonlinear kernels.

Contribution

The study introduces a machine learning approach using SVMs to classify four-qubit entangled states based on SLOCC classification and Werner states, enhancing entanglement detection methods.

Findings

SVM effectively identifies entanglement patterns in four-qubit states.

Nonlinear kernel SVM improves classification accuracy.

Method applicable to coarse-grained state descriptions.

Abstract

We apply the support vector machine (SVM) algorithm to derive a set of entanglement witnesses (EW) to identify entanglement patterns in families of four-qubit states. The effectiveness of SVM for practical EW implementations stems from the coarse-grained description of families of equivalent entangled quantum states. The equivalence criteria in our work is based on the stochastic local operations and classical communication (SLOCC) classification and the description of the four-qubit entangled Werner states. We numerically verify that the SVM approach provides an effective tool to address the entanglement witness problem when the coarse-grained description of a given family state is available. We also discuss and demonstrate the efficiency of nonlinear kernel SVM methods as applied to four-qubit entangled state classification.