Universality in random quantum networks

TL;DR

This paper develops an iterative method to evaluate strong connectivity in random quantum networks, revealing that large directed graphs are typically strongly connected, which implies universal features in the evolution of complex quantum systems.

Contribution

It introduces an efficient iterative approach to assess strong connectivity in random directed graphs, demonstrating universal topological properties in large quantum networks.

Findings

Random directed graphs with constant edge probability are usually strongly connected.

Universal features of large quantum networks are topology-independent.

Potential applicability to future quantum internet architectures.

Abstract

Networks constitute efficient tools for assessing universal features of complex systems. In physical contexts, classical as well as quantum, networks are used to describe a wide range of phenomena, such as phase transitions, intricate aspects of many-body quantum systems or even characteristic features of a future quantum internet. Random quantum networks and their associated directed graphs are employed for capturing statistically dominant features of complex quantum systems. Here, we develop an efficient iterative method capable of evaluating the probability of a graph being strongly connected. It is proven that random directed graphs with constant edge-establishing probability are typically strongly connected, i.e. any ordered pair of vertices is connected by a directed path. This typical topological property of directed random graphs is exploited to demonstrate universal features of the asymptotic evolution of large random qubit networks. These results are independent of our knowledge of the details of the network topology. These findings suggest that also other highly complex networks, such as a future quantum internet, may exhibit similar universal properties.