  We construct quantum evolution operators on the space of states, that is
represented by the vertices of the n-dimensional unit hypercube. They realize
the metaplectic representation of the modular group SL(2,Z(2^n)). By
construction this representation acts in a natural way on the coordinates of
the non-commutative 2-torus,T^2, and thus is relevant for noncommutative field
theories as well as theories of quantum space-time.
