  We consider the discrete time quantum random walks on a Sierpinski gasket. We
study the hitting probability as the level of fractal goes to infinity in terms
of their localization exponents $\beta_w$ , total variation exponents
$\delta_w$ and relative entropy exponents $\eta_w$ . We define and solve the
amplitude Green functions recursively when the level of the fractal graph goes
to infinity. We obtain exact recursive formulas for the amplitude Green
functions, based on which the hitting probabilities and expectation of the
first-passage time are calculated. Using the recursive formula with the aid of
Monte Carlo integration, we evaluate their numerical values. We also show that
when the level of the fractal graph goes to infinity, with probability 1, the
quantum random walks will return to origin, i.e., the quantum walks on
Sierpinski gasket are recurrent.
