  Coherent transport of excitations along chains of coupled quantum systems
represents an interesting problem with a number of applications ranging from
quantum optics to solar cell technology. A convenient tool for studying such
processes are quantum walks. They allow to determine in a quantitative way all
the process features. We study the survival probability and the transport
efficiency on a simple, highly symmetric graph represented by a ring. The
propagation of excitation is modeled by a discrete-time (coined) quantum walk.
For a two-state quantum walk, where the excitation (walker) has to leave its
actual position to the neighboring sites, the survival probability decays
exponentially and the transport efficiency is unity. The decay rate of the
survival probability can be estimated using the leading eigenvalue of the
evolution operator. However, if the excitation is allowed to stay at its
present position, i.e. the propagation is modeled by a lazy quantum walk, then
part of the wave-packet can be trapped in the vicinity of the origin and never
reaches the sink. In such a case, the survival probability does not vanish and
the excitation transport is not efficient. The dependency of the transport
efficiency on the initial state is determined. Nevertheless, we show that for
some lazy quantum walks dynamical percolations of the ring eliminate the
trapping effect and efficient excitation transport can be achieved.
