Entanglement classification of pure multipartite quantum states is a challenging problem in quantum information theory that can be mathematically stated as orbit classification for some given group action on the ambient Hilbert space. The group action depends on the grained classification one expects, the finer-grained one being the classification up to local unitary transformation (LU). In this article, we show how a variational quantum circuit approach can be used to learn entanglement orbits, and we apply our findings to build a classifier for four-qubit states.
Entanglement classification of pure multipartite quantum states is a challenging problem in quantum information theory that can be mathematically stated as orbit classification for some given group action on the ambient Hilbert space. The group action depends on the grained classification one expects, the finer-grained one being the classification up to local unitary transformation (LU). In this article, we show how a variational quantum circuit approach can be used to learn entanglement orbits, and we apply our findings to build a classifier for four-qubit states.
With the rapid development of quantum technology, understanding the properties of entanglement states has become an urgent task.Various classifications of entanglement states have been proposed to cater to distinct quantum applications, highlighting the significance of entanglement classification. This paper presents a variational quantum classifier for entanglement classification discrimination which can effectively reduce the measurement resources, specifically for four-qubit entanglement equivalence classifications under SLOCC (Stochastic Local Operations and Classical Communication). Through training one-to-one and one-to-many models, our proposed method achieves excellent performance in the entanglement classification. We further investigate the impact of parameterized quantum circuit layers and various measurement settings on the classifier’s performance. Considering the inherent noise present in near-term quantum computers, we also analyze how noise affects the model’s performance. Moreover, we explore the classifier’s capabilities in the context of multi-qubit entanglement systems. Numerical simulations demonstrate that high-precision entanglement classification tasks can be accomplished with shallow circuit depths, and the model exhibits resilience to noise. Additionally, the results reveal the versatility and potential application of our proposed model in larger-scale quantum systems by effectively handling entanglement classification tasks involving an increased number of qubits.
With the advancement of quantum machine learning, it has demonstrated immense potential in addressing traditionally complex problems. However, existing quantum circuit designs still exhibit limitations in expressibility and model performance. To tackle this challenge, inspired by tensor network structures, this paper proposes an Optimized Tree-Structured Entanglement Circuit (OTSEC). OTSEC employs parameterized quantum gates as fundamental circuit units to construct a hierarchical tree-structured framework for local quantum state initialization and entanglement optimization. Additionally, an Entanglement Adjustment Module (EAM) is introduced to regulate entanglement across different groups of qubits, optimizing long-range correlations and global feature fusion, thereby significantly enhancing the circuit’s expressibility.We further design an Optimized Tree-Structured Variational Quantum Classifier (OT-VQC) and apply it to network intrusion detection tasks. Simulation experiments on the KDD-CUP99 and UNSW-NB15 datasets demonstrate that OT-VQC significantly outperforms conventional variational quantum classifiers with standard circuit structures in key metrics such as classification accuracy, precision, and recall.
Quantum entanglement is a crucial resource in quantum information processing, yet its efficient, scalable and robust classification in multipartite systems remains theoretically challenging. Although supervised machinelearning has been applied to this task, most existing methods still suffer from high measurement costs, computational consumption, and weak noise robustness. In this work, by incorporating multipartite uncertainty relations as prior guidance, we propose a neural network approach to classify distinct Stochastic Local Operations and Classical Communication (SLOCC) multipartite entanglement classes based on states sampled from their local unitary (LU) orbits. Compared with traditional techniques, our method reduces experimental measurement-resource requirements and computational overhead, showing high adaptability to large-scale systems. The classification accuracy of our method reaches 99.5% in 20-qubit systems. The numerical validation is performed on states generated by random LU transformations, which preserve the SLOCC class. Within this setting, the proposed method offers strong effectiveness, scalability, and robustness for multipartite entanglement classification.
Abstract A classification of multipartite entanglement is introduced for pure and mixed states. The classification is based on the distribution of entanglement between the qubits of a given system, with a mathematical framework used to characterize fully entangled states. Then we use current machine learning and deep learning techniques to automatically classify a random state of two, three, and four qubits without the need to compute the amount of the different types of entanglement in each run; rather this is done only in the learning process. The technique shows high, near-perfect, accuracy in the case of pure states. As expected, this accuracy drops, more or less, when dealing with mixed states and when increasing the number of parties involved.
A classification of multipartite entanglement in qubit systems is introduced for pure and mixed states. The classification is based on the robustness of the said entanglement against partial trace operation. Then we use current machine learning and deep learning techniques to automatically classify a random state of two, three and four qubits without the need to compute the amount of the different types of entanglement in each run; rather this is done only in the learning process. The technique shows high, near perfect, accuracy in the case of pure states. As expected, this accuracy drops, more or less, when dealing with mixed states and when increasing the number of parties involved.
Matrix Product States have been extensively explored as a powerful tool for simulating quantum states in image classification task. However, most research has focused on classical simulations or computations involving high-dimensional unitaries, and significant challenges still exist in the practical preparation of Matrix Product States on quantum computers. This paper proposes a novel and practically feasible quantum variational algorithm based on Matrix Product States for image classification task. We design a hardware-efficient quantum circuit with several adjustable entangling operators to prepare the local tensors in Matrix Product States and integrate minimal residuals to ensure computational stability. We demonstrate that our algorithm can reduce the parameter complexity from growing exponentially with the system size to a linear scale. To validate the effectiveness of this quantum variational algorithm, we conducted experiments on the MNIST dataset, achieving accuracies of 99.95% and 95.96% for binary and ten-class classification tasks, which outperforms other related quantum algorithms. This work advances the practical application of quantum machine learning in resource-constrained environments of quantum computing.