Transport efficiency of continuous-time quantum walks on graphs

TL;DR

This paper analyzes how graph topology influences the transport efficiency of continuous-time quantum walks, providing benchmarks and revealing that connectivity alone does not predict transport performance.

Contribution

It offers an analytical study of transport efficiency across various graph structures, highlighting the limited role of connectivity and establishing benchmarks for quantum transport.

Findings

Transport efficiency varies with graph topology.

Connectivity is generally uncorrelated with efficiency.

Analytical benchmarks for quantum transport are provided.

Abstract

Continuous-time quantum walk describes the propagation of a quantum particle (or an excitation) evolving continuously in time on a graph. As such, it provides a natural framework for modeling transport processes, e.g., in light-harvesting systems. In particular, the transport properties strongly depend on the initial state and on the specific features of the graph under investigation. In this paper, we address the role of graph topology, and investigate the transport properties of graphs with different regularity, symmetry, and connectivity. We neglect disorder and decoherence, and assume a single trap vertex accountable for the loss processes. In particular, for each graph, we analytically determine the subspace of states having maximum transport efficiency. Our results provide a set of benchmarks for environment-assisted quantum transport, and suggest that connectivity is a poor indicator for transport efficiency. Indeed, we observe some specific correlations between transport efficiency and connectivity for certain graphs, but in general they are uncorrelated.