  We characterize a close connection between the continuous-time quantum-walk
model and a discrete-time quantum-walk version, based on the staggered model
with Hamiltonians in a class of Cayley graphs, which can be considered as a
discretization of continuous-time quantum walks. This connection provides
examples of perfect state transfer and instantaneous uniform mixing in the
staggered model. On the other hand, we provide some more examples of perfect
state transfer and instantaneous uniform mixing in the staggered model that
cannot be reproduced by the continuous-time model.
