  We construct unitary evolution operators on a phase space with power of two
discretization. These operators realize the metaplectic representation of the
modular group SL(2,Z_{2^n}). It acts in a natural way on the coordinates of the
non-commutative 2-torus, T_{2^n}^2$ and thus is relevant for non-commutative
field theories as well as theories of quantum space-time. The class of
operators may also be useful for the efficient realization of new quantum
algorithms.
