  Quantum annealing in the transverse-field Ising model (TFIM) with open-system
dynamics is known to use thermally-assisted tunneling to drive computation.
However, it is still subject to debate whether quantum systems in the presence
of decoherence are more useful than those using classical dynamics to drive
computation. We contribute to this debate by introducing the perturbed
ferromagnetic chain (PFC), a chain of frustrated sub-systems where the degree
of frustration scales inversely with the perturbation introduced by a tunable
parameter. This gives us an easily embeddable gadget whereby problem hardness
can be tuned for systems of constant size. We outline the properties of the PFC
and compare classical spin-vector Monte Carlo (SVMC) variants with the
adiabatic quantum master equation. We demonstrate that SVMC methods get trapped
in the exponentially large first-excited-state manifold when solving this
frustrated problem, whereas evolution using quantum dynamics remains in the
lowest energy eigenstates. This results in significant differences in ground
state probability when using either classical or quantum annealing dynamics in
the TFIM.
