  Quantum annealing (QA) refers to an optimization process that uses quantum
fluctuations to find the global minimum of a rugged energy landscape with many
local minima. Conceptually, QA is often framed in the context of the disordered
transverse field Ising model, in which a magnetic field applied perpendicular
to the Ising axis tunes the quantum fluctuations and enables the system to
tunnel through energy barriers, and hence reach the ground state more quickly.
A solid state material closely related to this model,
LiHo$_{0.45}$Y$_{0.55}$F$_4$, was shown to exhibit faster dynamics after a QA
protocol, compared to thermal annealing (TA), but little is known about the
actual process of optimization involved or the nature of the spin correlations
in the state that is reached. Here, we report on the microscopics of QA in this
material using diffuse magnetic neutron scattering. Comparing a QA to a TA
protocol that reach the same end-point, we find very similar final diffuse
scattering which consists of pinch-point scattering, largely consistent with
critical scattering near a phase boundary in the dipolar Ising ferromagnetic
model. However, comparing the time evolution at the end of the protocols, we
find that the spin correlations evolve more significantly after TA, suggesting
that QA produces a state closer to equilibrium. We also observe experimental
evidence that the transverse field produces random fields, which had been
previously predicted for this material and studied in other contexts. Thus,
while the material does exhibit a quantum speedup under quantum annealing
conditions, it is not a simple annealing problem; the energy landscape being
optimized is changing as the optimization proceeds.
