Quantum walks on Erdos-Renyi networks

TL;DR

This paper investigates quantum transport on Erdos-Renyi networks, analyzing how network connectivity influences exciton movement and return probabilities, with implications for understanding quantum dynamics on complex networks.

Contribution

It provides a numerical analysis of quantum walk transport on Erdos-Renyi networks, comparing classical and quantum efficiencies, and explores the impact of network connectivity on return probabilities.

Findings

High return probability at initial node for finite networks.

Return probability increases rapidly as network approaches full connectivity.

Transport efficiency varies with network size and connectivity.

Abstract

We study the coherent exciton transport of continuous-time quantum walks (CTQWs) on Erdos-Renyi networks. The Erdos-Renyi network of N nodes is constructed by connecting every pair of nodes with probability $p$. We numerically calculate the ensemble averaged transition probability of quantum transport between two nodes of the networks. For finite networks, we find that the limiting transition probability is reached very quickly. For infinite networks whose spectral density follows the semicircle law, the efficiencies of the classical and quantum-mechanical transport are compared on networks of different average degree. In the long time limiting, we consider the distribution of the ensemble averaged transition probabilities, and show that there is a high probability to find the exciton at the initial node. Such high return probability almost do not alter in a wide range of connection probability p but increases rapidly when the network approaches to be fully connected. For networks whose topology is not extremely connected, the return probability is inversely proportional to the network size N. Furthermore, the transport dynamics are compared with that on a random graph model in which the degree of each node equals to the average degree of the Erdos-Renyi networks.