  For randomly selected couplers and fields, the D-Wave device typically yields
a highly Boltzmann like distribution [ indicating equilibration. These
equilibrated data however do not contain much useful information about the
dynamics which lead to equilibration. To illuminate the dynamics, special
Hamiltonians can be chosen which contain large energy barriers. In this paper
we generalize this approach by considering a class of Hamiltonians which map
clusters of spin-like qubits into 'superspins', thereby creating an energy
landscape where local minima are separated by large energy barriers. These
large energy barriers allow us to observe signatures of the transverse field
frozen. To study these systems, we assume that the these frozen spins are
describes by the Kibble-Zurek mechanism which was originally developed to
describe formation of topological defects in the early universe. It was soon
realized that it also has applications in analogous superconductor systems and
later realized to also be important for the transverse field Ising model . We
demonstrate that these barriers block equilibration and yield a non-trivial
distribution of qubit states in a regime where quantum effects are expected to
be strong, suggesting that these data should contain signatures of whether the
dynamics are fundamentally classical or quantum. We exhaustively study a class
of 3x3 square lattice superspin Hamiltonians and compare the experimental
results with those obtained by exact diagonalisation. We find that the best fit
to the data occurs at finite transverse field. We further demonstrate that
under the right conditions, the superspins can be relaxed to equilibrium,
erasing the signature of the transverse field. These results are interesting
for a number of reasons. They suggest a route to detect signatures of quantum
mechanics on the device on a statistical level.
