  Quantum annealing is a contender to solve combinatorial optimization problems
based on quantum dynamics. While significant efforts have been undertaken to
investigate the quality of the solutions and the required runtimes, much less
attention has been paid to understanding the dynamics of quantum annealing and
the process leading to the solution during the sweep itself. In this
comprehensive study, we investigate various aspects of the quantum annealing
dynamics using different approaches. We perform quantum annealing, simulated
quantum annealing, and classical annealing on several hundred instances of the
Sherrington-Kirkpatrick model with intermediate system sizes up to 22 spins
using numerical simulations. We observe qualitative differences between the
quantum and classical methods, in particular at intermediate times, where a
peak in the fidelity, also known as diabatic bump, appears for hard instances.
Furthermore, we investigate the two-point correlation functions, which feature
differences at intermediate times as well. At short times, however, the methods
are similar again, which can be explained by relating the short-time expansion
of quantum annealing to a high-temperature expansion, thus allowing in
principle to find the classical solution already at short times, albeit at
prohibitive sampling cost.
