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Quantum Machine Intelligence

Positive-unlabeled learning for training an entanglement detector

Taisei Nohara, Itsuki Noda, Satoshi Oyama

Published Feb 5, 2026• 0 citations
Publisher

Abstract

Abstract Entanglement detection, the process of verifying quantum entanglement is a fundamental challenge in quantum information processing. Various approaches have been proposed to address this challenge, with many recent studies applying supervised machine learning methods. While these methods have demonstrated high accuracy in entanglement detection, it is reasonable to assume that the entangled states themselves are not definitively known. To address this limitation, we have devised a machine learning method for entanglement detection based on positive-unlabeled learning, a classical machine learning framework that does not use label information from negative data. Using a deep neural network model to synthetic dataset under the assumption of mixed states, we conducted experiments on a classical computer to valid the effectiveness and characteristics of the proposed method. Our approach introduces a novel framework that accounts for the data generation constraints in the training process of entanglement detector, thereby advancing machine learning techniques in quantum information science.

DOI
10.1007/s42484-026-00343-2

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Abstract Entanglement detection, the process of verifying quantum entanglement is a fundamental challenge in quantum information processing. Various approaches have been proposed to address this challenge, with many recent studies applying supervised machine learning methods. While these methods have demonstrated high accuracy in entanglement detection, it is reasonable to assume that the entangled states themselves are not definitively known. To address this limitation, we have devised a machine learning method for entanglement detection based on positive-unlabeled learning, a classical machine learning framework that does not use label information from negative data. Using a deep neural network model to synthetic dataset under the assumption of mixed states, we conducted experiments on a classical computer to valid the effectiveness and characteristics of the proposed method. Our approach introduces a novel framework that accounts for the data generation constraints in the training process of entanglement detector, thereby advancing machine learning techniques in quantum information science.
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.
This paper explores the use of machine learning techniques for detecting quantum entanglement in two-qubit systems. A dataset of randomly generated quantum states was constructed and labeled using the Positive Partial Transpose (PPT) criterion. Several supervised learning models, including Random Forest and Multi-Layer Perceptron neural networks, were trained to classify quantum states as entangled or separable. The results show that machine learning models can effectively learn patterns from quantum state data, while also highlighting the impact of dataset imbalance on classification performance. This study demonstrates the potential of machine learning as a complementary tool for quantum entanglement detection and provides insights into the challenges and opportunities of integrating artificial intelligence with quantum physics.
Detection of entanglement is an indispensable step to practical quantum computation and communication. Compared with the conventional entanglement witness method based on fidelity, we propose a flexible, machine learning assisted entanglement detection protocol that is robust to different types of noises and sample efficient. In this protocol, an entanglement classifier for a generic entangled state is obtained by training a classical machine learning model with a synthetic dataset. The dataset contains classical features of two types of states and their labels (either entangled or separable). The classical features of a state, which are expectation values of a set of k-local Pauli observables, are estimated sample-efficiently by the classical shadow method. In the numerical simulation, our classifier can detect the entanglement of 4-qubit GHZ states with coherent noise and W states mixed with large white noise, with high accuracy.
Abstract Learning from only positive and unlabeled (PU) data has broad applications in fields such as web data mining, product recommendations and medical diagnosis, which aims to train a binary classifier in the absence of negative labeled data. However, due to the lack of negative label information, prevailing PU learning methods usually rely on prior knowledge of unknown class distributions heavily. In fact, without additional constraints imposed by the prior knowledge, a direct learning strategy to coordinate the underlying clustering information in unlabeled data with the label information from positive training data is often considered challenging. To tackle this challenge, we propose a direct PU learning strategy using quantum formalization. By employing neural networks as backends, the samples are mapped into two-qubit composite systems, which should be understood here as mathematical entities encapsulating various classical distributions of two classical bits. Subsequently, the two qubits within the systems are trained to be as independent as possible from each other, capturing patterns of different classes. At the same time, their measurement results serving as the model outputs are encouraged to be maximally dissimilar. These characteristics enable effective training of classifiers on PU data. After formulating an appropriate discriminant rule, we introduce a quantum-inspired PU method named qPU using the direct learning strategy. This method not only has the potential to alleviate parameter sensitivity issues caused by prior estimation in other methods but is also straightforward to implement. Finally, experiments conducted on 13 classical datasets validate the effectiveness of qPU.
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 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.