  This paper summarizes a quantum algorithm of [R.D. Somma, et.al., Phys. Rev.
Lett. 101, 130504 (2008)] that simulates a classical annealing process for
solving discrete optimization problems. The complexity of the quantum algorithm
scales with the inverse square root of the spectral gap of an associated
stochastic matrix. This represents a quadratic quantum speedup, in terms of the
gap, with respect to classical simulated annealing.
