Fair Sampling and Entanglement in Transverse-Field Quantum Annealing

While ground states of a classical Ising model spin glass can be found using transverse-field quantum annealing, for instances with ground state degeneracy, quantum annealing is known not to always efficiently sample all ground states. After annealing, in certain instances all ground states are equally sampled (fair sampling); in other instances the probability of measuring some ground states is reduced. In this work we investigate the entanglement structure of ground states in a fully-connected transverse field Ising spin glass. We use numerical diagonalization to quantify the bipartite entanglement via entanglement entropy during the annealing process. Given the absence of locality in the fully-connected spin glass, we investigate the distribution of entanglement entropy over all equal size bipartitions. We identify signatures of the degeneracy, hamming distance between classical ground states, and fair sampling in the entanglement distribution for weak transverse fields.