Detecting Entanglement in High-Spin Quantum Systems via a Stacking Ensemble of Machine Learning Models

TL;DR

This paper presents a stacking ensemble machine learning approach that reliably detects and quantifies entanglement in high-spin quantum systems, overcoming computational challenges of traditional methods.

Contribution

It introduces a novel ensemble model combining neural networks and gradient boosting techniques, demonstrating improved accuracy and consistency in estimating quantum entanglement.

Findings

Ensemble model outperforms individual learners in predictive accuracy.

Stacking ensemble exhibits lower deviation and higher reliability.

Empirical formula for data requirement estimation is derived.

Abstract

Reliable detection and quantification of quantum entanglement, particularly in high-spin or many-body systems, present significant computational challenges for traditional methods. This study examines the effectiveness of ensemble machine learning models as a reliable and scalable approach for estimating entanglement, measured by negativity, in quantum systems. We construct an ensemble regressor integrating Neural Networks (NNs), XGBoost (XGB), and Extra Trees (ET), trained on datasets of pure states and mixed Werner states for various spin dimensions. The ensemble model with stacking meta-learner demonstrates robust performance by CatBoost (CB), accurately predicting negativity across different dimensionalities and state types. Crucially, visual analysis of prediction scatter plots reveals that the ensemble model exhibits superior predictive consistency and lower deviation from true entanglement values compared to individual strong learners like NNs, even when aggregate metrics are comparable. This enhanced reliability, attributed to error cancellation and variance reduction inherent in ensembling, underscores the potential of this approach to bypass computational bottlenecks and provide a trustworthy tool for characterizing entanglement in high-dimensional quantum physics. An empirical formula for estimating data requirements based on system dimensionality and desired accuracy is also derived.