  We consider coherent exciton transport modeled by continuous-time quantum
walks (CTQWs) on long-range interacting cycles (LRICs), which are constructed
by connecting all the two nodes of distance $m$ in the cycle graph. LRIC has a
symmetric structure and can be regarded as the extensions of the cycle graph
(nearest-neighboring lattice). For small values of $m$, the classical and
quantum return probabilities show power law behavior $p(t)\sim t^{-0.5}$ and
$\pi(t)\sim t^{-1}$, respectively. However, for large values of $m$, the
classical and quantum efficiency scales as $p(t)\sim t^{-1}$ and $\pi(t)\sim
t^{-2}$. We give a theoretical explanation of this transition using the method
of stationary phase approximation (SPA). In the long time limit, depending on
the network size $N$ and parameter $m$, the limiting probability distributions
of quantum transport show various patterns. When the network size $N$ is an
even number, we find an asymmetric transition probability of quantum transport
between the initial node and its opposite node. This asymmetry depends on the
precise values of $N$ and $m$. Finally, we study the transport processes in the
presence of traps and find that the survival probability decays faster on
networks of large $m$.
