  The effect of unitary noise on the discrete one-dimensional quantum walk is
studied using computer simulations. For the noiseless quantum walk, starting at
the origin (n=0) at time t=0, the position distribution Pt(n) at time t is very
different from the Gaussian distribution obtained for the classical random
walk. Furthermore, its standard deviation, sigma(t) scales as sigma(t) ~ t,
unlike the classical random walk for which sigma(t) ~ sqrt{t}. It is shown that
when the quantum walk is exposed to unitary noise, it exhibits a crossover from
quantum behavior for short times to classical-like behavior for long times. The
crossover time is found to be T ~ alpha^(-2) where alpha is the standard
deviation of the noise.
