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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 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.