Entanglement is a central resource in quantum information and quantum technologies, yet its characterization remains challenging due to both theoretical complexity and measurement requirements. Machine learning has emerged as a promising alternative, enabling entanglement characterization from incomplete measurement data, however model interpretability remains a challenge. In this work, we introduce a unified and interpretable framework for SLOCC entanglement classification of two- and three-qubit states, encompassing both pure and mixed states. We train dense and convolutional neural networks on Pauli-measurement outcomes, provide design guidelines for each architecture, and systematically compare their performance across types of states. To interpret the models, we compute Shapley values to quantify the contribution of each measurement, analyze measurement-importance patterns across different systems, and use these insights to guide a measurement-reduction scheme. Accuracy-versus-measurement curves and comparisons with analytical entanglement criteria demonstrate the minimal resources required for reliable classification and highlight both the capabilities and limitations of Shapley-based interpretability when using machine learning models for entanglement detection and classification.
Entanglement is a central resource in quantum information and quantum technologies, yet its characterization remains challenging due to both theoretical complexity and measurement requirements. Machine learning has emerged as a promising alternative, enabling entanglement characterization from incomplete measurement data, however model interpretability remains a challenge. In this work, we introduce a unified and interpretable framework for SLOCC entanglement classification of two- and three-qubit states, encompassing both pure and mixed states. We train dense and convolutional neural networks on Pauli-measurement outcomes, provide design guidelines for each architecture, and systematically compare their performance across types of states. To interpret the models, we compute Shapley values to quantify the contribution of each measurement, analyze measurement-importance patterns across different systems, and use these insights to guide a measurement-reduction scheme. Accuracy-versus-measurement curves and comparisons with analytical entanglement criteria demonstrate the minimal resources required for reliable classification and highlight both the capabilities and limitations of Shapley-based interpretability when using machine learning models for entanglement detection and classification.
Accurate classification of multipartite entanglement in high-dimensional quantum systems is crucial for advancing quantum communication and information processing. However, conventional methods are resource-intensive, and even many machine-learning-based approaches necessitate large training datasets, creating a significant experimental bottleneck for data acquisition. To address this challenge, we propose a hybrid neural network architecture integrating Convolutional and Bidirectional Long Short-Term Memory networks (CNN-BiLSTM). This design leverages CNNs for local feature extraction and BiLSTMs for sequential dependency modeling, enabling robust feature learning from minimal training data. We investigate two fusion paradigms: Architecture 1 (flattening-based) and Architecture 2 (dimensionality-transforming). When trained on only 100 samples, Architecture 2 maintains classification accuracies exceeding 90% for both 3-qubit and 4-qubit systems, demonstrating rapid loss convergence within tens of epochs. Under full-data conditions (400 000 samples), both architectures achieve accuracies above 99.97%. Comparative benchmarks reveal that our CNN-BiLSTM models, especially Architecture 2, consistently outperform standalone CNNs, BiLSTMs, and MLPs in low-data regimes, albeit with increased training time. These results demonstrates that the tailored CNN-BiLSTM fusion significantly alleviates experimental data acquisition burden, offering a practical pathway toward scalable entanglement verification in complex quantum systems.
Abstract We present a systematic comparative analysis of machine learning and traditional approaches for quantum entanglement characterization in bi-partite ququart systems. Quantifying entanglement traditionally requires full quantum state tomography, necessitating Nmub2D2Ncop measurements, where Nmub is the number of mutually unbiased bases, D is the subsystem dimensionality, and Ncop is the number of identical copies. For ququart systems with D=4, this translates to hundreds of distinct measurement settings, each requiring multiple copies (Ncop typically in thousands)—resulting in hundreds of thousands of total measurements in practice. Our research demonstrates that neural networks achieve comparable or superior accuracy with orders of magnitude fewer measurement settings. We evaluate three architectures—Multi-Layer Perceptron (MLP), Convolutional Neural Network (CNN), and Transformer—against Maximum Likelihood Estimation (MLE) and Bayesian methods across measurement counts ranging from 10 to 400. Neural approaches achieve up to 1650× faster computation times compared to traditional methods while maintaining competitive accuracy. At 100 measurements, the Transformer achieves Mean Squared Error (MSE) of 1.49×10−1, while MLE yields 2.04×10−1—over 10× higher error—despite taking 178 times longer. All neural methods in our study show error reduction scaling as approximately 1/N with increased measurements. While this observed scaling might be influenced by our specific architectures, it provides important practical guidance for experimental design. The Transformer architecture demonstrates exceptional sample efficiency, achieving with 100 measurements what traditional methods require 250-400 measurements to accomplish—a significant advantage for resource-constrained quantum experiments. This research provides a viable pathway for real-time entanglement characterization in higher-dimensional quantum systems where traditional methods become computationally prohibitive.
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.
We design and successfully implement artificial neural networks (ANNs) to detect and classify entanglement for three-qubit systems using limited state features. The overall design principle is a feed forward neural network (FFNN), with the output layer consisting of a single neuron for the detection of genuine multipartite entanglement (GME) and six neurons for the classification problem corresponding to six entanglement classes under stochastic local operations and classical communication (SLOCC). The models are trained and validated on a simulated dataset of randomly generated states. We achieve high accuracy, around 98%, for detecting GME as well as for SLOCC classification. Remarkably, we find that feeding only 7 diagonal elements of the density matrix into the ANN results in an accuracy greater than 94% for both the tasks, showcasing the strength of the method in reducing the required input data while maintaining efficient performance. Reducing the feature set makes it easier to apply ANN models for entanglement classification, particularly in resource-constrained environments, without sacrificing accuracy. The performance of the ANN models was further evaluated by introducing white noise into the data set, and the results indicate that the models are robust and are able to well tolerate noise.
Quantum entanglement detection is one of the fundamental tasks in quantum information science. Conventional methods for quantum state tomography exhibit limitations in scalability as the number of qubits increases, leading to exponential growth in the number of unknown parameters and required measurements. Consequently, the accuracy enhancement achieved by these methods is constrained. In response to this challenge, we developed a tailored convolutional neural network (CNN) model capable of effectively detecting entanglement in two-qubit quantum states, achieving an accuracy exceeding 97.5%. Notably, even in the presence of noise, this model retains its robust performance, displaying resilience against a tolerable level of noise contamination. Furthermore, the inherent generalization power of CNNs allows our model, which was initially trained on a specific spectrum of quantum states, to extend its applicability to wider states, positioning it as an outstanding tool for the further application of machine learning in the field of quantum computing, opening up new pathways for solving entanglement detection problems in quantum information.
Quantum entanglement detection and characterization are crucial for various quantum information processes. Most existing methods for entanglement detection rely heavily on a complete description of the quantum state, which requires numerous measurements and complex setups. This makes these theoretically sound approaches costly and impractical, as the system size increases. In this work, we propose a multiview neural-network model to generate representations suitable for entanglement structure detection. The number of required quantum measurements shows a significant reduction compared to conventional quantum state tomography approaches as the qubit number increases. This remarkable reduction in resource costs makes it possible to detect specific entanglement structures in large-scale systems. Numerical simulations show that our method achieves over 95% detection accuracy for up to 19 qubit systems. By enabling a universal, flexible, and resource-efficient analysis of entanglement structures, our approach enhances the capability of utilizing quantum states across a wide range of applications.