  We study the performance of the D-Wave 2X quantum annealing machine on
systems with well-controlled ground-state degeneracy. While obtaining the
ground state of a spin-glass benchmark instance represents a difficult task,
the gold standard for any optimization algorithm or machine is to sample all
solutions that minimize the Hamiltonian with more or less equal probability.
Our results show that while naive transverse-field quantum annealing on the
D-Wave 2X device can find the ground-state energy of the problems, it is not
well suited in identifying all degenerate ground-state configurations
associated to a particular instance. Even worse, some states are exponentially
suppressed, in agreement with previous studies on toy model problems [New J.
Phys. 11, 073021 (2009)]. These results suggest that more complex driving
Hamiltonians are needed in future quantum annealing machines to ensure a fair
sampling of the ground-state manifold.
