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.
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.
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.
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 3×3 3 × 3 , 4×4 4 × 4 , and 5×5 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 % , 90% 90 % , and nearly 100% 100 % for 3×3 3 × 3 , 4×4 4 × 4 , and 5×5 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 Quantum entanglement is a fundamental resource in quantum information science. In recent years, many researchers have explored the use of machine learning techniques to detect entanglement. However, most existing models still suffer from limited classification and generalization capability. To address these issues, we construct a randomly generated dataset of three‐qubit quantum states covering fully separable, bi‐separable, and genuine entangled states, and train a complex‐valued convolutional neural network to classify these three classes. Numerical results demonstrate that the proposed model accurately identifies all separability classes and exhibits strong generalization performance not only on the constructed dataset but also on various noisy quantum states, including noisy GHZ, W, GHZ‐W mixed, and hypergraph states, achieving an overall accuracy of 98.6%. In addition, we test the ability of the proposed model to identify certain positive‐partial‐transpose entangled states (PPTES), as well as quantum states that undergo local unitary (LU) operations. All of these results indicate that the proposed model can accurately identify the separability of most three‐qubit quantum states and can also serve as a reliable tool, providing highly probable and accurate predictions when theoretical methods fail.
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.
Quantum entanglement is one of the essential resources involved in quantum information processing tasks. However, its detection for usage remains a challenge. The Bell-type inequality for relative entropy of coherence serves as an entanglement witness for pure entangled states. However, it does not perform reliably for mixed entangled states. This paper constructs a classifier by employing the relationship between coherence and entanglement for supervised machine learning methods. This method encodes multiple Bell-type inequalities for the relative entropy of coherence into an artificial neural network to detect the entangled and separable states in a quantum dataset.
In this work, we investigate the application of Machine Learning (ML) algorithms to the identification and quantitative characterization of quantum entanglement in polarization-entangled photon pairs. The analysis is based on simulated symmetric, informationally complete, positive operator-valued measure (SIC-POVM) measurement data, where each two-qubit state is represented by a 16-dimensional measurement vector corresponding to experimentally accessible coincidence counts. The generated SIC-POVM measurement data include Poissonian shot noise. Several supervised ML algorithms, including Logistic Regression, k-Nearest Neighbors, Decision Trees, Support Vector Machines, and Random Forests, are applied to the classification of separable and entangled states directly from raw measurement data, without explicit density matrix reconstruction or the use of conventional separability criteria. The study additionally explores clustering methods and nonlinear regression techniques for estimating continuous entanglement measures. The obtained results demonstrate that ML methods can achieve very high classification accuracy, even under extremely limited training conditions. These findings indicate that ML may provide an efficient alternative to conventional quantum-state analysis under simulated Poissonian noise conditions.