  Coherent transport of an excitation through a network corresponds to
continuous-time quantum walk on a graph, and the transport properties of the
system may be radically different depending on the graph and on the initial
state. The transport efficiency, i.e., the integrated probability of trapping
at a certain vertex, is a measure of the success rate of the transfer process.
Purely coherent quantum transport is known to be less efficient than the
observed excitation transport, e.g., in biological systems, and there is
evidence that environmental noise is indeed crucial for excitation transport.
At variance with this picture, we here address purely coherent transport on
highly symmetric graphs, and show analytically that it is possible to enhance
the transport efficiency without environmental noise, i.e., using only a
minimal perturbation of the graph. In particular, we show that adding an extra
weight to one or two edges, depending on whether the initial state is localized
or in a superposition of two vertex states, breaks the inherent symmetries of
the graph and may be sufficient to achieve unit transport efficiency. We also
briefly discuss the conditions to obtain a null transport efficiency, i.e., to
avoid trapping.
