  Recurrence in the classical random walk is well known and described by the
P\'olya number. For quantum walks, recurrence is similarly understood in terms
of the probability of a localized quantum walker to return to its origin. Under
certain circumstances the quantum walker may also return to an arbitrary
initial quantum state in a finite number of steps. Quantum state revivals in
quantum walks on circles using coin operators which are constant in time and
uniform across the path have been described before but only incompletely. In
this paper we find the general conditions for which full-quantum state revival
will occur.
