Entanglement classification via neural network quantum states

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 machinelearning 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. OPEN ACCESS RECEIVED

Support Vector Machines with Quantum State Discrimination

“…The general idea of classification algorithms based on discrimination of quantum states is also supported by recent experimental works on quantum state classification based on classical machine learning methods, such as the proposals in [9][10][11][12][13], for instance. In [14], the authors demonstrate a machine learning approach to construct a classifier of quantum states training a neural network.…”

Opportunities in Quantum Reservoir Computing and Extreme Learning Machines

“…As an example, the task of classifying, through a NN, whether a (multipartite) state is entangled or not was addressed in Ref. [83]. There, the classification is limited to pure states and the extension to mixed ones represents a nontrivial issue.…”

Building separable approximations for quantum states via neural networks

“…A similar approach has been taken in Refs. [34,35], where the authors represent the quantum states with "quantum neural network states" [36,37], and their extension to density matrices [38][39][40][41], as opposed to the dense representation we utilise. Their results show a more limited flexibility in the loss function and in the design of types of separable states.…”