On the quantum simulation of complex networks

TL;DR

This paper extends quantum simulation techniques to complex networks with hubs, enabling quantum algorithms to analyze more realistic, densely connected nodes in large sparse graphs, potentially advancing network science applications.

Contribution

It introduces methods for simulating quantum walks on graphs with a few dense hubs, broadening the applicability of quantum algorithms to real-world complex networks.

Findings

Extended quantum simulation methods to graphs with hubs.

Demonstrated potential for quantum algorithms in network science.

Enhanced understanding of quantum walk dynamics on complex networks.

Abstract

Quantum walks provide a natural framework to approach graph problems with quantum computers, exhibiting speedups over their classical counterparts for tasks such as the search for marked nodes or the prediction of missing links. Continuous-time quantum walk algorithms assume that we can simulate the dynamics of quantum systems where the Hamiltonian is given by the adjacency matrix of the graph. It is known that such can be simulated efficiently if the underlying graph is row-sparse and efficiently row-computable. While this is sufficient for many applications, it limits the applicability for this class of algorithms to study real world complex networks, which, among other properties, are characterized by the existence of a few densely connected nodes, called hubs. In other words, complex networks are typically not row-sparse, even though the average connectivity over all nodes can be very small. In this work, we extend the state-of-the-art results on quantum simulation to graphs that contain a small number of hubs, but that are otherwise sparse. Hopefully, our results may lead to new applications of quantum computing to network science.