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arXiv:2408.12349 · New Journal of Physics

Machine-learning certification of multipartite entanglement for noisy quantum hardware

Andreas J C Fuchs, Eric Brunner, Jiheon Seong, Hyeokjea Kwon, Seungchan Seo, Joonwoo Bae, Andreas Buchleitner, Edoardo G. Carnio

Published May 29, 2025• 3 citations
arXivHTMLPDF

Abstract

Abstract Entanglement is a fundamental aspect of quantum physics, both conceptually and for its many applications. Classifying an arbitrary multipartite state as entangled or separable—a task referred to as the separability problem—poses a significant challenge, since a state can be entangled with respect to many different of its partitions. We develop a certification pipeline that feeds the statistics of random local measurements into a non-linear dimensionality reduction algorithm, to determine with respect to which partitions a given quantum state is entangled. After training a model on randomly generated quantum states, entangled in different partitions and of varying purity, we verify the accuracy of its predictions on simulated test data, and finally apply it to states prepared on IBM quantum computing hardware.

DOI
10.1088/1367-2630/adde80

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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.
Entanglement depth quantifies how many qubits share genuine multipartite entanglement, but certification typically relies on tailored witnesses or full tomography, both of which scale poorly with system size. We recast entanglement-depth and non-kkk-separability certification as likelihood-based model selection among neural quantum states whose architecture enforces a chosen entanglement constraint. A hierarchy of separable neural quantum states is trained on finite-shot local Pauli outcomes and compared against an unconstrained reference model trained on the same data. When all constrained models are statistically disfavored, the data certify entanglement beyond the imposed limit directly from measurement statistics, without reconstructing the density matrix. We validate the method on simulated six- and ten-qubit datasets targeting GHZ, Dicke, and Bell-pair states, and demonstrate robustness for mixed states under local noise. Finally, we discuss lightweight interpretability diagnostics derived from trained parameters that expose coarse entanglement patterns and qubit groupings directly from bitstring statistics.
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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.
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.