  Hitting times for discrete quantum walks on graphs give an average time
before the walk reaches an ending condition. To be analogous to the hitting
time for a classical walk, the quantum hitting time must involve repeated
measurements as well as unitary evolution. We derive an expression for hitting
time using superoperators, and numerically evaluate it for the discrete walk on
the hypercube. The values found are compared to other analogues of hitting time
suggested in earlier work. The dependence of hitting times on the type of
unitary ``coin'' is examined, and we give an example of an initial state and
coin which gives an infinite hitting time for a quantum walk. Such infinite
hitting times require destructive interference, and are not observed
classically. Finally, we look at distortions of the hypercube, and observe that
a loss of symmetry in the hypercube increases the hitting time. Symmetry seems
to play an important role in both dramatic speed-ups and slow-downs of quantum
walks.
