  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.
