  We construct quantum evolution operators on the space of states, that realize
the metaplectic representation of the modular group SL(2,Z_2^n). This
representation acts in a natural way on the coordinates of the non-commutative
2-torus and thus is relevant for noncommutative field theories as well as
theories of quantum space-time. The larger class of operators, thus defined,
may be useful for the more efficient realization of new quantum algorithms.
