  We study the effect of small decoherence in continuous-time quantum walks on
long-range interacting cycles, which are constructed by connecting all the two
nodes of distance m on the cycle graph. In our investigation, each node is
continuously monitored by an individual point contact, which induces the
decoherence process. We obtain the analytical probability distribution and the
mixing time upper bound. Our results show that, for small rates of decoherence,
themixing time upper bound is independent of distance parameter m and is
proportional to inverse of decoherence rate.
