  We describe a quantum algorithm that solves combinatorial optimization
problems by quantum simulation of a classical simulated annealing process. Our
algorithm exploits quantum walks and the quantum Zeno effect induced by
evolution randomization. It requires order $1/\sqrt{\delta}$ steps to find an
optimal solution with bounded error probability, where $\delta$ is the minimum
spectral gap of the stochastic matrices used in the classical annealing
process. This is a quadratic improvement over the order $1/\delta$ steps
required by the latter.
