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.
Categories: hep-lat