  We formulate and analyze a double-slit proposal for quantum annealing, which
involves observing the probability of finding a two-level system (TLS)
undergoing evolution from a transverse to a longitudinal field in the ground
state at the final time $t_f$. We demonstrate that for annealing schedules
involving two consecutive diabatic transitions, an interference effect is
generated akin to a double-slit experiment. The observation of oscillations in
the ground state probability as a function of $t_f$ (before the adiabatic limit
sets in) then constitutes a sensitive test of coherence between energy
eigenstates. This is further illustrated by analyzing the effect of coupling
the TLS to a thermal bath: increasing either the bath temperature or the
coupling strength results in a damping of these oscillations. The theoretical
tools we introduce significantly simplify the analysis of the generalized
Landau-Zener problem. Furthermore, our analysis connects quantum annealing
algorithms exhibiting speedups via the mechanism of coherent diabatic
transitions to near-term experiments with quantum annealing hardware.
