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 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.
Abstract Quantum properties, such as entanglement and coherence, are indispensable resources in various quantum information processing tasks. However, there still lacks an efficient and scalable way to detecting these useful features especially for high-dimensional and multipartite quantum systems. In this work, we exploit the convexity of samples without the desired quantum features and design an unsupervised machine learning method to detect the presence of such features as anomalies. Particularly, in the context of entanglement detection, we propose a complex-valued neural network composed of pseudo-siamese network and generative adversarial net, and then train it with only separable states to construct non-linear witnesses for entanglement. It is shown via numerical examples, ranging from two-qubit to ten-qubit systems, that our network is able to achieve high detection accuracy which is above 97.5% on average. Moreover, it is capable of revealing rich structures of entanglement, such as partial entanglement among subsystems. Our results are readily applicable to the detection of other quantum resources such as Bell nonlocality and steerability, and thus our work could provide a powerful tool to extract quantum features hidden in multipartite quantum data.
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.
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.
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.
Multipartite entanglement is one of the crucial resources in quantum information processing tasks such as quantum metrology, quantum computing and quantum communications. It is essential to verify not only the multipartite entanglement, but also the entanglement structure in both fundamental theories and the applications of quantum information technologies. However, it is proved to be challenging to detect the entanglement structures, including entanglement depth, entanglement intactness and entanglement stretchability, especially for general states and large-scale quantum systems. By using the partitions of the tensor product space we propose a systematic method to construct powerful entanglement witnesses which identify better the multipartite entanglement structures. Besides, an efficient algorithm using semi-definite programming and a gradient descent algorithm are designed to detect entanglement structure from the inner polytope of the convex set containing all the states with the same entanglement structure. We demonstrate by detailed examples that our criteria perform better than other known ones. Our results may be applied to many quantum information processing tasks.
The problem of determining whether a given quantum state is entangled lies at the heart of quantum information processing. Despite the many methods---such as the positive partial transpose criterion and the k-symmetric extendibility criterion---to tackle this problem, none of them enables a general, practical solution due to the problem's NP-hard complexity. Explicitly, separable states form a high-dimensional convex set of vastly complicated structures. In this work, we build a different separability-entanglement classifier underpinned by machine learning techniques. We use standard tools from machine learning to learn the entanglement feature of arbitrary given quantum states. We perform substantial numerical tests on two-qubit and two-qutrit systems, and the results indicate that our method can outperform the existing methods in generic cases in terms of both speed and accuracy. This opens up avenues to explore quantum entanglement via the machine learning approach.