Entanglement of graph states of spin system with Ising interaction and its quantifying on IBM's quantum computer

TL;DR

This paper investigates the entanglement properties of graph states generated by Ising interactions in spin systems, quantifies them using IBM quantum computers, and finds a relation between entanglement and graph vertex degree.

Contribution

It analytically derives the geometric measure of entanglement for graph states and experimentally verifies it on IBM's quantum hardware, establishing a link with graph topology.

Findings

Quantum calculations agree with theoretical predictions

Entanglement measure correlates with vertex degree

Demonstrates feasibility of entanglement quantification on IBM quantum computers

Abstract

We consider graph states generated by operator of evolution with Ising Hamiltonian. The geometric measure of entanglement of a spin with other spins in the graph state is obtained analytically and quantified on IBM's quantum computer, IBM Q Valencia. The results of quantum calculations are in good agreement with the theoretical ones. We conclude that the geometric measure of entanglement of a spin with other spins in the graph state is related with degree of vertex representing the spin in the corresponding graph.