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Sampling all ground states of a Hamiltonian with equal probability is adesired feature of a sampling algorithm, but recent studies indicate thatcommon variants of transverse field quantum annealing sample the ground statesubspace unfairly. In this note, we present perturbation theory argumentssuggesting that this deficiency can be corrected by employing reverseannealing-inspired paths. We confirm that this conclusion holds in simulationsof previously studied small instances with degeneracy, as well as largerinstances on quantum annealing hardware.

Achieving fair sampling in quantum annealing