  We give a path integral formulation of the time evolution of qudits of odd
dimension. This allows us to consider semiclassical evolution of discrete
systems in terms of an expansion of the propagator in powers of $\hbar$. The
largest power of $\hbar$ required to describe the evolution is a traditional
measure of classicality. We show that the action of the Clifford operators on
stabilizer states can be fully described by a single contribution of a path
integral truncated at order $\hbar^0$ and so are "classical," just like
propagation of Gaussians under harmonic Hamiltonians in the continuous case.
Such operations have no dependence on phase or quantum interference.
Conversely, we show that supplementing the Clifford group with gates necessary
for universal quantum computation results in a propagator consisting of a
finite number of semiclassical path integral contributions truncated at order
$\hbar^1$ , a number that nevertheless scales exponentially with the number of
qudits. The same sum in continuous systems has an infinite number of terms at
order $\hbar^1$.
