  We study the time evolution of continuous-time quantum walks on randomly
changing graphs. At certain moments edges of the graph appear or disappear with
a given probability. We focus on the case when the time interval between
subsequent changes of the graph tends to zero. We derive explicit formulae for
the general evolution in this limit. We find that the percolation in this limit
causes an effective time rescaling. Independently of the graph and the initial
state of the walk, the time is rescaled by the probability of keeping and edge.
Both the individual trajectories for a single system and average properties
with a superoperator formalism are discussed. We give an analytical proof for
our theorem and we also present results from numerical simulations of the
phenomena for different graphs.
