  Sampling all ground states of a Hamiltonian with equal probability is a
desired feature of a sampling algorithm, but recent studies indicate that
common variants of transverse field quantum annealing sample the ground state
subspace unfairly. In this note, we present perturbation theory arguments
suggesting that this deficiency can be corrected by employing reverse
annealing-inspired paths. We confirm that this conclusion holds in simulations
of previously studied small instances with degeneracy, as well as larger
instances on quantum annealing hardware.
