  Quantum annealing is a generic solver of classical optimization problems that
makes full use of quantum fluctuations. We consider work statistics given by a
repetition of quantum annealing processes by employing the Jarzynski equality
proposed in nonequilibrium statistical physics. In particular, we analyze the
distribution of the work performed by a transverse field. A special symmetry,
gauge symmetry, leads to a non-trivial relationship between quantum annealing
toward different targets in the theory of spin glasses. We believe that our
results will be a step toward an alternative realization of efficient quantum
computation as well as our better understanding of nonequilibrium behavior of
systems under quantum control.
