  We develop a semiclassical approximation for the dynamics of quantum systems
in finite-dimensional Hilbert spaces whose classical counterparts are defined
on a toroidal phase space. In contrast to previous models of quantum maps, the
time evolution is in continuous time and, hence, is generated by a
Schr\"odinger equation. In the framework of Weyl quantisation, we construct
discrete, semiclassical Fourier integral operators approximating the unitary
time evolution and use these to prove a Gutzwiller trace formula. We briefly
discuss a semiclassical quantisation condition for eigenvalues as well as some
simple examples.
