  Quantum annealing has the potential to provide a speedup over classical
algorithms in solving optimization problems. Just as for any other quantum
device, suppressing Hamiltonian control errors will be necessary before quantum
annealers can achieve speedups. Such analog control errors are known to lead to
$J$-chaos, wherein the probability of obtaining the optimal solution, encoded
as the ground state of the intended Hamiltonian, varies widely depending on the
control error. Here, we show that $J$-chaos causes a catastrophic failure of
quantum annealing, in that the scaling of the time-to-solution metric becomes
worse than that of a deterministic (exhaustive) classical solver. We
demonstrate this empirically using random Ising spin glass problems run on the
two latest generations of the D-Wave quantum annealers. We then proceed to show
that this doomsday scenario can be mitigated using a simple error suppression
and correction scheme known as quantum annealing correction (QAC). By using
QAC, the time-to-solution scaling of the same D-Wave devices is improved to
below that of the classical upper bound, thus restoring hope in the speedup
prospects of quantum annealing.
