  We report here on the structure of reversible quantum cellular automata with
the additional restriction that these are also Clifford operations. This means
that tensor products of Weyl operators (projective representation of a finite
abelian symplectic group) are mapped to multiples of tensor products of Weyl
operators. Therefore Clifford quantum cellular automata are induced by
symplectic cellular automata in phase space. We characterize these symplectic
cellular automata and find that all possible local rules must be, up to some
global shift, reflection invariant with respect to the origin. In the one
dimensional case we also find that all 1D Clifford quantum cellular automata
are generated by a few elementary operations.
