Achieving fair sampling in quantum annealing.

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 previously studied models with degeneracy and propose an algorithm that produces the full set of ground states without additional exponential overhead.