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We study the time evolution of continuous-time quantum walks on randomlychanging graphs. At certain moments edges of the graph appear or disappear witha given probability. We focus on the case when the time interval betweensubsequent changes of the graph tends to zero. We derive explicit formulae forthe general evolution in this limit. We find that the percolation in this limitcauses an effective time rescaling. Independently of the graph and the initialstate of the walk, the time is rescaled by the probability of keeping and edge.Both the individual trajectories for a single system and average propertieswith a superoperator formalism are discussed. We give an analytical proof forour theorem and we also present results from numerical simulations of thephenomena for different graphs.

Time evolution of continuous-time quantum walks on dynamical percolation graphs