  Adiabatic time evolution can be used to prepare a complicated quantum
many-body state from one that is easier to synthesize and Trotterization can be
used to implement such an evolution digitally. The complex interplay between
non-adiabaticity and digitization influences the infidelity of this process. We
prove that the first-order Trotterization of a complete adiabatic evolution has
a cumulative infidelity that scales as $\mathcal O(T^{-2} \delta t^2)$ instead
of $\mathcal O(T^2 \delta t^2)$ expected from general Trotter error bounds,
where $\delta t$ is the time step and $T$ is the total time. This result
suggests a self-healing mechanism and explains why, despite increasing $T$,
infidelities for fixed-$\delta t$ digitized evolutions still decrease for a
wide variety of Hamiltonians. It also establishes a correspondence between the
Quantum Approximate Optimization Algorithm (QAOA) and digitized quantum
annealing.
