Quantum behaved particle swarm optimization (QPSO) is a recently proposed metaheuristic, which describes bird flocking trajectories by a quantum behavior. It uses only one tunable parameter and suggests a new and interesting philosophy for moving in the search space. It has been successfully applied to several problems. In this paper, we investigate the possibility of extending QPSO to handle multiple objectives. More specifically, we address the way global best solutions are recorded within an archive and used to compute the local attractor point of each particle. For this purpose, a two level selection strategy that uses sigma values and crowding distance information has been defined in order to select the suitable guide for each particle. The rational is to help convergence of each particle using sigma values while favoring less crowded regions in the objective space to attain a uniformly spread out Pareto front. The proposed approach has been assessed on test problems for function optimization from convergence and diversity points of view. Very competitive results have been achieved compared to some state of the art algorithms.