Searching for quantum speedup in quasistatic quantum annealers

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 with classical algorithms that return the same equilibrium distribution. These correlations do not mean that the evolution of the system is classical or can be simulated by these algorithms. The computation time extracted from such a distribution reflects the equilibrium behavior with no information about the underlying quantum dynamics. This makes the search for quantum speedup problematic.