Evaluating Supervised Learning Approaches for Quantification of Quantum Entanglement

TL;DR

The paper addresses the challenge of quantifying quantum entanglement from accessible measurements without full state tomography by training supervised regression models to map measurement-derived features to entanglement measures. It introduces datasets of 2-qubit and 3-qubit states with targets given by $C$ and $C_{\mathrm{GME}}$, respectively, and uses Pauli-correlation and Svetlichny features to train five regression models, with cross-validation. The results show that LS-Boost-based Ensemble (LS-ENS) achieves the best overall accuracy, with SVM-R and GAM also competitive, and DT-R often underperforming for some tasks; the approach remains robust as the number of qubits increases. The work demonstrates a scalable, measurement-based framework for entanglement quantification that can be extended to higher dimensions and integrated with real-device data, offering a practical alternative to full tomography. $$C(|\psi_{AB}\rangle)=\sqrt{2\left(1-\mathrm{Tr}\rho_A^2\right)},$$ $$C_{\mathrm{GME}}(|\psi\rangle)=\min_{\gamma}\sqrt{2\left(1-\mathrm{Tr}\rho_{\gamma}^2\right)},$$ and related constructs are central to the targets used in learning.

Abstract

Quantum entanglement is a key resource in quantum computing and quantum information processing tasks. However, its quantification remains a major challenge since it cannot be directly extracted from physical observables. To address this issue, we study a few machine-learning based models to estimate the amount of entanglement in two-qubit as well as three-qubit systems. We use measurement outcomes as the input features and entanglement measures as the training labels. Our models predict entanglement without requiring the full state information. This demonstrates the potential of machine learning as an effcient and powerful tool for characterizing quantum entanglement

Figures (2)

• Figure 1: Comparison between the analytically calculated concurrence and the concurrence predicted by different ML models for two-qubit system. Target value on $x$-axis represents the true concurrence, and the output on $y$-axis represents the predicted concurrence. The pink dots represent the sampled data, the dotted line represents the theoretical line where the predicted results are exactly equal to the true results, the sold blue line represents the fitting line, and R is the correlation coefficient.
• Figure 2: Comparison between the analytically calculated GME concurrence and the concurrence predicted by different ML models for three-qubit system. Target value on $x$-axis represents the true GME concurrence, and the output on $y$-axis represents the predicted GME concurrence. The pink dots represent the sampled data, the dotted line represents the theoretical line where the predicted results are exactly equal to the true results, the sold blue line represents the fitting line, and R is the correlation coefficient.