In this paper we are presenting an overview of the existing works that have been published in the quantum optimization of type-1, type-2 and type-3 fuzzy systems, considering both theoretical contributions and applications. The analysis was done considering all kinds of publications: journal papers, chapters in books and conference papers. The database was obtained from Scopus system of Elsevier, which contains most of the indexed publications in the world in all areas. It is relevant to consider Quantum Optimization when designing higher types of fuzzy systems as the number of parameter is higher and correspondingly the design complexity is also higher. Based on the obtained data, relevant conclusions were obtained about the development of the quantum optimization of fuzzy systems, as well as future trends.