Mixed state entanglement classification using artificial neural networks

Abstract

Reliable methods for the classification and quantification of quantum entanglement are fundamental to understanding its exploitation in quantum technologies. One such method, known as separable neural network quantum states (SNNS), employs a neural network inspired parameterization of quantum states whose entanglement properties are explicitly programmable. Combined with generative machine learning methods, this ansatz allows for the study of very specific forms of entanglement which can be used to infer/measure entanglement properties of target quantum states. In this work, we extend the use of SNNS to mixed, multipartite states, providing a versatile and efficient tool for the investigation of intricately entangled quantum systems. We illustrate the effectiveness of our method through a number of examples, such as the computation of novel tripartite entanglement measures, and the approximation of ultimate upper bounds for qudit channel capacities.

Building separable approximations for quantum states via neural networks

“…Using such an ansatz for the separability problem has been examined in Ref. [35]. Such prospects of further developing the algorithms give the promise of exciting novel numerical tools for a broad range of tasks, both for numerical work and gaining analytic insight.…”

“…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.…”

Geometric measure of entanglement from Wehrl Moments using Artificial Neural Networks

“…In the context of entanglement theory, ANNs have been used to quantify the amount of entanglement in multipartite quantum systems [11,12] and to classify the entanglement in pure states [13] and mixed states [14]. In [11], the authors trained complex-valued ANNs to predict the geometric measure of entanglement (GME) of symmetric states.…”

Scalable quantum state tomography with artificial neural networks

“…Some Bayesian methods [2] gain on (i) by giving up (ii). Many entanglement detection schemes [3,4] as well as shadow tomography [5,6] give up on requirement (iii). A multitude of variational approaches have been developed which restrict the state space in which they seek for an optimal solution, therefore giving up on property (iv).…”

“…5, the corresponding sum in Eq. ( 11) is a weighted average of 4 2 = 6 connected correlators of the form σ z i σ z j − σ z i σ z j . After sampling, one may consider each of these connected correlators as a random variable with a variance and a bias.…”