  We discuss quantum annealing of the two-dimensional transverse-field Ising
model on a D-Wave device, encoded on $L \times L$ lattices with $L \le 32$.
Analyzing the residual energy and deviation from maximal magnetization in the
final classical state, we find an optimal $L$ dependent annealing rate $v$ for
which the two quantities are minimized. The results are well described by a
phenomenological model with two powers of $v$ and $L$-dependent prefactors to
describe the competing effects of reduced quantum fluctuations (for which we
see evidence of the Kibble-Zurek mechanism) and increasing noise impact when
$v$ is lowered. The same scaling form also describes results of numerical
solutions of a transverse-field Ising model with the spins coupled to noise
sources. We explain why the optimal annealing time is much longer than the
coherence time of the individual qubits.
