Transport across quantum networks underlies many problems, from state
transfer on a spin network to energy transport in photosynthetic complexes.
However, networks can contain dark subspaces that block the transportation, and
various methods used to enhance transfer on quantum networks can be viewed as
equivalently avoiding, modifying, or destroying the dark subspace. Here, we
exploit graph theoretical tools to identify the dark subspaces and show that
asymptotically almost surely they do not exist for large networks, while for
small ones they can be suppressed by properly perturbing the coupling rates
between the network nodes. More specifically, we apply these results to
describe the recently experimentally observed and robust transport behaviour of
the electronic excitation travelling on a genetically-engineered
light-harvesting cylinder (M13 virus) structure. We believe that these mainly
topological tools may allow us to better infer which network structures and
dynamics are more favourable to enhance transfer of energy and information
towards novel quantum technologies.Comment: 9 pages, 6 figure
