  Quantum walks are well-known for their ballistic dispersion, traveling
$\Theta(t)$ away in $t$ steps, which is quadratically faster than a classical
random walk's diffusive spreading. In physical implementations of the walk,
however, the particle may need to tunnel through a potential barrier to hop,
and a naive calculation suggests this could eliminate the ballistic transport.
We show by explicit calculation, however, that such a loss does not occur.
Rather, the $\Theta(t)$ dispersion is retained, with only the coefficient
changing, which additionally gives a way to detect and quantify the hopping
errors in experiments.
