  We show clear evidence of a quadratic speedup of a quantum annealing (QA)
Schroedinger dynamics over a Glauber master-equation simulated annealing (SA)
for a random Ising model in one dimension, via an equal-footing exact
deterministic dynamics of the Jordan-Wigner fermionized problems. This is
remarkable, in view of the arguments of Katzgraber et al., PRX 4, 021008
(2014), since SA does not encounter any phase transition, while QA does. We
also find a second remarkable result: that a "quantum-inspired" imaginary-time
Schroedinger QA provides a further exponential speedup, i.e., an asymptotic
residual error decreasing as a power-law $\tau^{-\mu}$ of the annealing time
$\tau$.
