  We present a study of the digitized Quantum Annealing protocol proposed by R.
Barends et al., Nature 534, 222 (2016). Our analysis, performed on the
benchmark case of a transverse Ising chain problem, shows that the algorithm
has a well defined optimal working point for the annealing time
$\tau^{\mathrm{opt}}_\mathrm{P}$ --- scaling as
$\tau^{\mathrm{opt}}_\mathrm{P}\sim \mathrm{P}$, where $\mathrm{P}$ is the
number of digital Trotter steps --- beyond which, the residual energy error
shoots-up towards the value characteristic of the maximally disordered state.
We present an analytical analysis for the translationally invariant transverse
Ising chain case, but our numerical evidence suggests that this scenario is
more general, surviving, for instance, the presence of disorder.
