  We study continuous time quantum random walk on a comb with infinite teeth
and show that the return probability to the starting point decays with time $t$
as $t^{-1}$. We analyse the diffusion along the spine and into the teeth and
show that the walk can escape into the teeth with a finite probability and goes
to infinity along the spine with a finite probability. The walk along the spine
and into the teeth behaves qualitatively as a quantum random walk on a line.
This behaviour is quite different from that of classical random walk on the
comb.
