This paper provides a new proposal that aims to solve multi-objective optimization problems (MOPs) using quantum evolutionary paradigm. Three main features characterize the proposed framework. In one hand, it exploits the states superposition quantum concept to derive a probabilistic representation encoding the vector of the decision variables for a given MOP. The advantage of this representation is its ability to encode the entire population of potential solutions within a single chromosome instead of considering only a gene pool of individuals as proposed in classical evolutionary algorithms. In the other hand, specific quantum operators are defined in order to reward good solutions while maintaining diversity. Finally, an evolutionary dynamics is applied on these quantum based elements to allow stochastic guided exploration of the search space. Experimental results show not only the viability of the method but also its ability to achieve good approximation of the Pareto Front when applied on the multi-objective knapsack problem.