Transforming Bell’s inequalities into state classifiers with machine learning

Abstract

Quantum information science has profoundly changed the ways we understand, store, and process information. A major challenge in this field is to look for an efficient means for classifying quantum state. For instance, one may want to determine if a given quantum state is entangled or not. However, the process of a complete characterization of quantum states, known as quantum state tomography, is a resource-consuming operation in general. An attractive proposal would be the use of Bell's inequalities as an entanglement witness, where only partial information of the quantum state is needed. The problem is that entanglement is necessary but not sufficient for violating Bell's inequalities, making it an unreliable state classifier. Here we aim at solving this problem by the methods of machine learning. More precisely, given a family of quantum states, we randomly picked a subset of it to construct a quantum-state classifier, accepting only partial information of each quantum state. Our results indicated that these transformed Bell-type inequalities can perform significantly better than the original Bell's inequalities in classifying entangled states. We further extended our analysis to three-qubit and four-qubit systems, performing classification of quantum states into multiple species. These results demonstrate how the tools in machine learning can be applied to solving problems in quantum information science.

Building separable approximations for quantum states via neural networks

“…Previous work on using machine learning for the separability problem has been focused either having the machine choose good measurements and then using an existing entanglement criteria [25,26] , or on viewing the task as a classification problem [27][28][29][30][31][32][33]. For classification, typically a training set is constructed where quantum states are labeled as separable or entangled.…”

Quantum Neuromorphic Computing with Reservoir Computing Networks

“…We will then consider different possible applications of quantum reservoir networks. It should be noted that while many important works in the field of quantum machine learning aim to use classical neural networks to optimize quantum setups [ 38–43 ] or process the results of quantum experiments, [ 44–48 ] the entities of quantum reservoir networks are themselves quantum. As quantum systems, quantum reservoir networks can result in performance advantages for classical tasks and have an enhanced memory capacity, as we will discuss in Section 3.…”

Efficient Characterization of Quantum Evolutions via a Recommender System

“…Sirui Lu and co-workers have shown the separability criteria of entangled state using convex hull approximation and supervised learning [18]. Ma and Yung showed that it is possible to classify the separable and entangled states using artificial neural networks [19]. The work has been further extended to experimental data [20] and later has been applied to simultaneous learning of multiple nonclassical correlations as well [21].…”