  We argue that a quantum annealer at very long annealing times is likely to
experience a quasistatic evolution, returning a final population that is close
to a Boltzmann distribution of the Hamiltonian at a single (freeze-out) point
during the annealing. Such a system is expected to correlate well with a proper
quantum Monte Carlo simulation. It may also correlate with simulated annealing
if at the freeze-out point the quantum energy eigenvalues are close to the
classical ones. These correlations are just signatures of equilibration and do
not mean that the evolution of the quantum annealer is classical or can be
simulated by quantum Monte Carlo. The computation time extracted from such a
distribution reflects the equilibrium behavior and therefore provides no
information about the underlying quantum dynamics. This makes the search for
quantum speedup in suboptimal quantum annealers problematic. We use an open
quantum master equation with realistic parameters to illustrate quasistatic
evolution in a 16 qubit quantum annealer and discuss its implication for
quantum speedup.
