  The correspondence between long-range interacting quantum spin glasses and
combinatorial optimization problems underpins the physical motivation for
adiabatic quantum computing. On one hand, in disordered (quantum) spin systems,
the focus is on exact methods such as the replica trick that allow the
calculation of system quantities in the limit of infinite system and ensemble
size. On the other hand, when solving a given instance of an optimization
problem, disorder-averaged quantities are of no relevance, as one is solely
interested in instance-specific, finite-size properties, in particular the true
solution. Here, we apply the nonequilibrium Green-function formalism to the
spin coherent-state path integral to obtain the statistical fluctuations and
the collective-excitation spectrum along the annealing path. For the example of
the quantum Sherrington-Kirkpatrick spin glass, by comparing to extensive
numerically exact results, we show that this method provides access to the
instance-specific bottlenecks of the annealing protocol.
