  We demonstrate experimentally the ability of a quantum annealer to
distinguish between sets of non-isomorphic graphs that share the same classical
Ising spectrum. Utilizing the pause-and-quench features recently introduced
into D-Wave quantum annealing processors, which allow the user to probe the
quantum Hamiltonian realized in the middle of an anneal, we show that obtaining
thermal averages of diagonal observables of classically indistinguishable
non-isomorphic graphs encoded into transverse-field Ising Hamiltonians enable
their discrimination. We discuss the significance of our results in the context
of the graph isomorphism problem.
