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arXiv:1912.13207 · New Journal of Physics

Entanglement classification via neural network quantum states

Cillian Harney, Stefano Pirandola, Alessandro Ferraro, Mauro Paternostro

Published Apr 1, 2020• 61 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1367-2630/ab783d

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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 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.
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.
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