In recent years, quantum computing has gained immense popularity with the production of real quantum computers. Researchers have developed quantum-inspired evolutionary algorithms (QIEAs) to solve combinatorial optimization problems and have obtained successful results. As a special case of QIEAs, real-coded quantum evolutionary algorithm (RCQEA) is used in the optimization of high-dimensional complex problems. In this study, a novel mechanism of the quantum rotation gate (QRG) that is used to determine the rotation angle of the qubit in the RCQEA is introduced and implemented to accelerate the evolutionary process and increase the possibility of finding the optimal solution. Moreover, the skeleton of RCQEA is modified by using a clonal selection mechanism, and the real-coded quantum clonal selection algorithm (RCQCSA) is developed. Our proposed QRG accelerates the convergence speed of the algorithm. The main purpose of this study is to present a more effective algorithm that inspires quantum computing principles for optimizing the interval type-2 fuzzy logic controller (IT2FLC) membership functions (MFs). In this study, four different comparisons are made with these two different algorithms that have the original version of QRG and our proposed QRG. Optimized IT2FLC provides stabilization of the inverted pendulum system. The results show that the RCQCSA having our proposed QRG outperforms RCQEA in stabilizing the inverted pendulum system by optimizing the IT2FLC parameters.