  A finite length ferromagnetic chain with opposite spin polarisation imposed
at its two ends is one of the simplest frustrated spin models. In the clean
classical limit the domain wall inserted on account of the boundary conditions
resides with equal probability on any one of the bonds, and the degeneracy is
precisely equal to the number of bonds. If quantum mechanics is introduced via
a transverse field, the domain wall will behave as a particle in a box, and
prefer to be nearer the middle of the chain rather than the ends. A simple
characteristic of a real quantum annealer is therefore which of these limits
obtains in practice. Here we have used the ferromagnetic chain with
antiparallel boundary spins to test a real flux qubit quantum annealer and
discover that contrary to both expectations, the domain walls found are
non-uniformly distributed on account of effective random longitudinal fields
present notwithstanding tuning carried out to zero out such fields when the
couplings between qubits are nominally zero. We present a simple derivation of
the form of the distribution function for the domain walls, and show also how
the effect we have discovered can be used to determine the strength of the
effective random fields (noise) characterising the annealer. The noise measured
in this fashion is smaller than what is seen during the single qubit tuning
process, but nonetheless qualitatively affects the outcome of the simulation
performed by the annealer.
