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arXiv:2311.17548 · Physical Review A

Detecting genuine multipartite entanglement via machine learning

Yi-Jun Luo, Jin‐Ming Liu, Chengjie Zhang

Published Nov 21, 2023• 18 citations
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Abstract

In recent years, supervised and semisupervised machine learning methods such as neural networks, support vector machines (SVMs), and semisupervised support vector machines (S4VMs) have been widely used in quantum entanglement and quantum steering verification problems. However, few studies have focused on detecting genuine multipartite entanglement based on machine learning. Here, we investigate supervised and semisupervised machine learning for detecting genuine multipartite entanglement of three-qubit states. We randomly generate three-qubit density matrices and train an SVM for the detection of genuine multipartite entangled states. Moreover, we improve the S4VM training method, which optimizes the grouping of prediction samples and then performs iterative predictions. Through numerical simulation, it is confirmed that this method can significantly improve the prediction accuracy.

DOI
10.1103/physreva.108.052424

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In recent years, supervised and semisupervised machine learning methods such as neural networks, support vector machines (SVMs), and semisupervised support vector machines (S4VMs) have been widely used in quantum entanglement and quantum steering verification problems. However, few studies have focused on detecting genuine multipartite entanglement based on machine learning. Here, we investigate supervised and semisupervised machine learning for detecting genuine multipartite entanglement of three-qubit states. We randomly generate three-qubit density matrices and train an SVM for the detection of genuine multipartite entangled states. Moreover, we improve the S4VM training method, which optimizes the grouping of prediction samples and then performs iterative predictions. Through numerical simulation, it is confirmed that this method can significantly improve the prediction accuracy.
In recent years, the detection of genuine multipartite entanglement (GME) via machine learning has received scant attention. Here, we employ convolutional neural networks (CNNs), as well as CNNs enhanced with squeeze and excitation (SE) to detect GME. We randomly generated GME states with 4 to 6 qubits and GHZ-diagonal states ranging from 4 to 20 qubits using the semidefinite programming approach. Subsequently, we assessed their classification accuracy. Our results demonstrate that the integration of the SE module significantly improved training performance. Additionally, we conducted an analysis of false positive and false negative occurrences. Utilizing our training data, we have substantially reduced the likelihood of incorrectly classifying nonentangled states as entangled.
Quantum entanglement lies at the heart of quantum information-processing tasks. Although many criteria have been proposed, efficient and scalable methods to detect the entanglement of generally given quantum states are still not available yet, particularly for high-dimensional and multipartite quantum systems. Based on FixMatch and Pseudo-Label methods, we propose a deep semisupervised learning model with a small portion of labeled data and a large portion of unlabeled data. The data-augmentation strategies are applied in this model by using the convexity of separable states and performing local unitary operations on the training data. We verify that our model has good generalization ability and gives rise to better accuracies than traditional supervised learning models with detailed examples.
Quantum entanglement is a fundamental property commonly used in various quantum information protocols and algorithms. Nonetheless, the problem of identifying entanglement has still not reached a general solution for systems larger than $2\ifmmode\times\else\texttimes\fi{}3$. In this study, we use deep convolutional NNs, a type of supervised machine learning, to identify quantum entanglement for any bipartition in a three-qubit system. We demonstrate that training the model on synthetically generated datasets of random density matrices excluding challenging positive-under-partial-transposition entangled states (PPTES), which cannot be identified (and correctly labeled) in general, leads to good model accuracy even for PPTES states, that were outside the training data. Our aim is to enhance the model's generalization on PPTES. By applying entanglement-preserving symmetry operations through a triple Siamese network trained in a semisupervised manner, we improve the model's accuracy and ability to recognize PPTES. Moreover, by constructing an ensemble of Siamese models, even better generalization is observed, in analogy with the idea of finding separate types of entanglement witnesses for different classes of states.
Abstract This work presents a machine learning approach based on support vector machines (SVMs) for quantum entanglement detection. Particularly, we focus on bipartite systems of dimensions 3×33\times 33×3 3 × 3 , 4×44\times 44×4 4 × 4 , and 5×55\times 55×5 5 × 5 , where the positive partial transpose criterion (PPT) provides only partial characterization. Using SVMs with quantum-inspired kernels, we develop a classification scheme that distinguishes between separable and entangled states, including PPT-detectable entangled states, and entangled states that evade PPT detection. Our method achieves increasing accuracy with system dimension, reaching 80%80\%80% 80 % , 90%90\%90% 90 % , and nearly 100%100\%100% 100 % for 3×33\times 33×3 3 × 3 , 4×44\times 44×4 4 × 4 , and 5×55\times 55×5 5 × 5 systems, respectively. Our results show that principal component analysis significantly enhances performance for small training sets. The study reveals important practical considerations regarding purity biases in the generation of data for this problem and examines the challenges of implementing these techniques on near-term quantum hardware. Our results demonstrate that machine learning can be an effective alternative to entanglement detection of higher-dimensional systems where conventional entanglement detection methods struggle. Our approach provides improved data generation protocols and can be readily implemented in hybrid classical-quantum architectures, overcoming current limitations.
Abstract Recently, machine learning has been widely applied in the field of quantum information, notably in tasks such as entanglement detection, steering characterization, and nonlocality verification. However, few studies have focused on utilizing machine learning to detect quantum information masking (QIM). In this work, we investigate supervised machine learning for detecting QIM in both pure and mixed qubit states. For pure qubit states, we randomly generate the corresponding density matrices and train an XGBoost model to detect QIM. For mixed qubit states, we improve the XGBoost method by optimizing the selection of training samples. The experimental results demonstrate that our approach achieves higher classification accuracy. Furthermore, we analyze the area under the curve of the receiver operating characteristic curve for this method, which further confirms its classification performance.
Abstract An entanglement witness (EW) is a Hermitian operator that can distinguish an entangled state from all separable states. We developed and implemented a numerical method based on machine learning to create multipartite EW. Using a Support Vector Machine (SVM) algorithm, we construct EW's based on local orthogonal observables in the form of a hyperplane that separates the separable region from the entangled state for two, three, and four qubits Bell-diagonal mixed states which can be generalized to a multipartite mixed state. One of the important features of this method is that the EW s are optimal and are completely tangent to the separable region. Also, we generate non-decomposable EW's that can detect positive partial transpose entangled states (PPTES).