One of the most widely used strategies for global optimization employs the concept of classical simulated annealing. In the last decade an alternative approach has been suggested based on quantum simulated annealing. Here, we apply quantum annealing ideas to finding minimum energy structures of Lennard-Jones clusters. We find that quantum annealing is superior to classical simulated annealing but is affected by ergodicity breaking difficulties similar to classical simulated annealing. This difficulty is particularly serious for larger clusters with multiple funnel potential energy surfaces. (c) 2005 Elsevier B.V. All rights reserved.