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Advanced Quantum Technologies

Machine Learning Experimental Multipartite Entanglement Structure

Yu Peng Tian, Liangyu Che, Xinyue Long, Changliang Ren, Dawei Lu

Published Aug 7, 2022• 12 citations
Publisher

Abstract

Abstract With the rapid growth of controllable qubits in recent years, experimental multipartite entangled states can be created with high fidelity in various moderate‐ and large‐scale physical systems. However, the characterization of multipartite entanglement structure remains a formidable challenge, as traditionally it requires exponential number of local measurements to realize the identification. Machine learning is demonstrated to be an efficient tool to detect the underlying entanglement structure for ideal states, but it has non‐negligible underperformance when tackling imperfect experimental data in reality. Here, a modified classifier based on feed‐forward neural network to predict experimental entanglement structure in terms of entanglement intactness and depth is proposed. By preprocessing the input data, the classifier maintains efficiency and reliability against experimental noises, with the accuracy being enhanced from 69.7% to 91.2% for 6‐qubit entangled states in spin systems. This method is anticipated to shed light on future studies of entanglement structure, in particular when the number of controlled qubits reaches explosive growth in practice.

DOI
10.1002/qute.202200025

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Detecting the entanglement structure, such as intactness and depth, of an n-qubit state is important for understanding the imperfectness of the state preparation in experiments. However, identifying such structure usually requires an exponential number of local measurements. In this letter, we propose an efficient machine learning based approach for predicting the entanglement intactness and depth simultaneously. The generalization ability of this classifier has been convincingly proved, as it can precisely distinguish the whole range of pure generalized GHZ states which never exist in the training process. In particular, the learned classifier can discover the entanglement intactness and depth bounds for the noised GHZ state, for which the exact bounds are only partially known.
Abstract Detecting the entanglement structure, such as intactness and depth, of an n -qubit state is important for understanding the imperfectness of the state preparation in experiments. However, identifying such structure usually requires an exponential number of local measurements. In this letter, we propose an efficient machine learning based approach for predicting the entanglement intactness and depth simultaneously. The generalization ability of this classifier has been convincingly proved, as it can precisely distinguish the whole range of pure generalized Greenberger–Horne–Zeilinger (GHZ) states which never exist in the training process. In particular, the learned classifier can discover the entanglement intactness and depth bounds for the noised GHZ state, for which the exact bounds are only partially known.
Abstract The task of classifying the entanglement properties of a multipartite quantum state poses a remarkable challenge due to the exponentially increasing number of ways in which quantum systems can share quantum correlations. Tackling such challenge requires a combination of sophisticated theoretical and computational techniques. In this paper we combine machine-learning tools and the theory of quantum entanglement to perform entanglement classification for multipartite qubit systems in pure states. We use a parameterisation of quantum systems using artificial neural networks in a restricted Boltzmann machine architecture, known as Neural Network Quantum States, whose entanglement properties can be deduced via a constrained, reinforcement learning procedure. In this way, Separable Neural Network States can be used to build entanglement witnesses for any target state.
Neural networks have emerged as a promising paradigm for quantum information processing, yet they confront the challenge of generating training datasets with sufficient size and rich diversity, which is particularly acute when dealing with multipartite quantum systems. For instance, in the task of classifying different structures of multipartite entanglement in continuous-variable systems, it is necessary to simulate a large number of infinite-dimensional state data that can cover as many types of non-Gaussian states as possible. Here we develop a data-augmented neural network to address this task with homodyne measurement data. A quantum data augmentation method based on classical data processing techniques and quantum physical principles is proposed to efficiently enhance network performance. By testing on randomly generated tripartite and quadripartite states, we demonstrate that the network can infer the entanglement structure among the various partitions, and the accuracies are substantially improved with data augmentation. Our approach allows us to further extend the use of data-driven machine learning techniques to more complex tasks of learning quantum systems encoded in a large Hilbert space. Gao et al. introduce a quantum data augmentation method to enable neural networks to classify multipartite entanglement structures in infinite-dimensional systems, substantially improving accuracy and reducing the data acquisition costs that typically limit training.
Quantum entanglement is a powerful resource for quantum-enhanced technologies. However, its reliable quantification remains challenging due to the exponential scaling of the Hilbert space with system size, which renders full state tomography infeasible. Moreover, experimentally estimating entanglement typically requires a large number of measurement samples leading to a significant overhead. In this work, we present two models, a feed-forward neural network and an attention-based model, to accurately predict the bipartite second Renyi from projective measurements of quantum states. We benchmark their performance against standard classical shadow estimators and find that the machine-learning approaches achieve higher accuracy and improved sample efficiency across a range of system sizes. Our results demonstrate the potential of machine learning for scalable and efficient estimation of quantum correlations.
Entanglement plays a pivotal role in numerous quantum applications, and as technology progresses, entanglement systems continue to expand. However, quantifying entanglement is a complex problem, particularly for multipartite quantum states. The currently available entanglement measures suffer from high computational complexity, and for unknown multipartite entangled states, complete information about the quantum state is often necessary, further complicating calculations. In this paper, we train neural networks to quantify unknown multipartite entanglement using input features based on squared entanglement (SE) and outcome statistics data produced by locally measuring target quantum states. By leveraging machine learning techniques to handle non-linear relations between outcome statistics and entanglement measurement SE, we achieve high-precision quantification of unknown multipartite entanglement states with a linear number of measurements, avoiding the need for global measurements and quantum state tomography. The proposed method exhibits robustness against noise and extends its applicability to pure and mixed states, effectively scaling to large-scale multipartite entanglement systems. The results of the experiment show that the predicted entanglement measures are very close to the actual values, which confirms the effectiveness of the proposed method.