  We analyze continuous-time quantum and classical random walk on spidernet
lattices. In the framework of Stieltjes transform, we obtain density of states,
which is an efficiency measure for the performance of classical and quantum
mechanical transport processes on graphs, and calculate the spacetime
transition probabilities between two vertices of the lattice. Then we
analytically show that there are two power law decays $\sim t^{-3}$ and $\sim
t^{-1.5}$ at the beginning of the transport for transition probability in the
continuous-time quantum and classical random walk respectively. This results
illustrate the decay of quantum mechanical transport processes is quicker than
that of the classical one. Due to the result, the characteristic time $t_c$,
which is the time when the first maximum of the probabilities occur on an
infinite graph, for the quantum walk is shorter than that of the classical
walk. Therefore, we can interpret that the quantum transport speed on spidernet
is faster than that of the classical one. In the end, we investigate the
results by numerical analysis for two examples.
