# Centrality measure based on continuous-time quantum walks and experimental realization

## TL;DR

This paper introduces a novel continuous-time quantum walk algorithm for network vertex centrality, demonstrating its effectiveness on various graphs and providing the first physical implementation using linear optics.

## Contribution

It presents a new quantum walk-based centrality algorithm that generalizes to arbitrary graphs and reports the first experimental realization of such an algorithm.

## Key findings

- Successful physical implementation using linear optics.
- Algorithm effective on scale-free and Erdős-Rényi networks.
- First demonstration of a quantum centrality algorithm.

## Abstract

Network centrality has important implications well beyond its role in physical and information transport analysis; as such, various quantum walk-based algorithms have been proposed for measuring network vertex centrality. In this work, we propose a continuous-time quantum walk algorithm for determining vertex centrality, and show that it generalizes to arbitrary graphs via a statistical analysis of randomly generated scale-free and Erd\H{o}s-R\'enyi networks. As a proof of concept, the algorithm is detailed on a 4-vertex star graph and physically implemented via linear optics, using spatial and polarization degrees of freedoms of single photons. This paper reports the first successful physical demonstration of a quantum centrality algorithm.