  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.

Quantum Physics