ANN-Enhanced Detection of Multipartite Entanglement in a Three-Qubit NMR Quantum Processor

TL;DR

This paper presents an ANN-based method for identifying and classifying multipartite entanglement in three-qubit states generated on an NMR quantum processor, achieving high accuracy with limited data.

Contribution

It introduces a neural network approach that efficiently detects GME and classifies entanglement classes using minimal density matrix information, validated on experimental NMR data.

Findings

ANN accurately detects GME in noisy experimental states

Reduced density matrix elements suffice for classification

Outperforms traditional classification schemes in limited-data scenarios

Abstract

We use an artificial neural network (ANN) model to identify the entanglement class of an experimentally generated three-qubit pure state drawn from one of the six inequivalent classes under stochastic local operations and classical communication (SLOCC). The ANN model is also able to detect the presence of genuinely multipartite entanglement (GME) in the state. We apply data science techniques to reduce the dimensionality of the problem, which corresponds to a reduction in the number of required density matrix elements to be computed. The ANN model is first trained on a simulated dataset containing randomly generated states, and is later tested and validated on noisy experimental three-qubit states cast in the canonical form and generated on a nuclear magnetic resonance (NMR) quantum processor. We benchmark the ANN model via Support Vector Machines (SVMs) and K-Nearest Neighbor (KNN) algorithms and compare the results of our ANN-based entanglement classification with existing three-qubit SLOCC entanglement classification schemes such as 3-tangle and correlation tensors. Our results demonstrate that the ANN model can perform GME detection and SLOCC class identification with high accuracy, using a priori knowledge of only a few density matrix elements as inputs. Since the ANN model works well with a reduced input dataset, it is an attractive method for entanglement classification in real-life situations with limited experimental data sets.