Complex Quantum Networks: From Universal Breakdown to Optimal Transport

TL;DR

This paper investigates how the topology of complex quantum networks influences excitation transport efficiency, revealing a transition from universal breakdown to optimal transport driven by loop reduction.

Contribution

It introduces a systematic analysis of transport efficiency in quantum networks with varying topologies, highlighting a transition mechanism controlled by loop reduction.

Findings

Complete-graph-like subgraphs cause transport breakdown.

Ring-like subgraphs enable optimal transport.

Small-world procedures can induce a transition to optimal transport.

Abstract

We study the transport efficiency of excitations on complex quantum networks with loops. For this we consider sequentially growing networks with different topologies of the sequential subgraphs. This can lead either to a universal complete breakdown of transport for complete-graph-like sequential subgraphs or to optimal transport for ring-like sequential subgraphs. The transition to optimal transport can be triggered by systematically reducing the number of loops of complete-graph-like sequential subgraphs in a small-world procedure. These effects are explained on the basis of the spectral properties of the network's Hamiltonian. Our theoretical considerations are supported by numerical Monte-Carlo simulations for complex quantum networks with a scale-free size distribution of sequential subgraphs and a small-world-type transition to optimal transport.