A new unbiased global optimization approach is proposed, based on quantum staging path integral Monte Carlo sampling and local minimization of individual imaginary time slices. This algorithm uses the quantum tunneling effect to speed up the crossing of energy barriers. This method differs in important ways from previous work on quantum annealing and is able to find all the global minima of Lennard-Jones clusters of size up to N=100, except for N=76, 77, and 98. The comparison between this new algorithm and several other classes of algorithms is presented. (C) 2003 American Institute of Physics.