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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 square root of 1/d steps to find an optimal solution with bounded error probability, where d is the minimum spectral gap of the stochastic matrices used in the classical annealing process. This is a quadratic improvement over the order 1/d steps required by the latter.