Size of quantum networks

TL;DR

This paper investigates the metric structure of bosonic scale-free and fermionic Cayley-tree quantum networks, revealing how their topology and node distances from the origin depend on temperature, with distinct behaviors at T=0 and T=∞.

Contribution

It provides an analytical comparison of bosonic and fermionic quantum networks' metric properties across different temperature regimes.

Findings

At T=∞, both networks' node distances scale logarithmically with network size.

At T=0, bosonic networks remain highly clustered, with constant node distance.

At T=0, fermionic networks' node distance grows as a power-law with network size.

Abstract

The metric structure of bosonic scale-free networks and fermionic Cayley-tree networks is analyzed focousing on the directed distance of nodes from the origin. The topology of the netwoks strongly depends on the dynamical parameter $T$, called temperature. At $T=\infty$ we show analytically that the two networks have a similar behavior: the distance of a generic node from the origin of the network scales as the logarithm of the number of nodes in the network. At T=0 the two networks have an opposite behavior: the bosonic network remains very clusterized (the distance from the origin remains constant as the network increases the number of nodes) while the fermionic network grows following a single branch of the tree and the distance from the origin grows as a power-law of the number of nodes in the network.