  Quantum annealing is guaranteed to find the ground state of optimization
problems in the adiabatic limit. Recent work [Phys. Rev. X 6, 031010 (2016)]
has found that for some barrier tunneling problems, quantum annealing can be
run much faster than is adiabatically required. Specifically, an $n$-qubit
optimization problem was presented for which a non-adiabatic, or diabatic,
annealing algorithm requires only constant runtime, while an adiabatic
annealing algorithm requires a runtime polynomial in $n$.
  Here we show that this non-adiabatic speed-up is a direct result of a
specific symmetry in the studied problems. In the more general case, no such
non-adiabatic speed-up occurs. We furthermore show why the special case
achieves this speed-up compared to the general case. We conclude with the
observation that the adiabatic annealing algorithm has a necessary and
sufficient runtime that is quadratically better than the standard quantum
adiabatic condition suggests.
