RNA structural alignment is one of key issues in bioinformatics. It aims to elucidate conserved structural regions among a set of sequences. Finding an accurate conserved structure is still difficult and a time consuming task that involves structural alignment as a prerequisite. In this work, structural alignment is viewed as an optimization process. A quantum based genetic algorithm is proposed to carry out this process. The main features of this algorithm consist in the quantum structure used to represent alignments and the quantum operators defining the overall evolutionary dynamic of the genetic algorithm. The quantum structure relies on the concept of qubit and allows efficient encoding of individuals. Experiments on a wide range of data sets have shown the effectiveness of the proposed framework and its ability to achieve good quality solutions.