Image scrambling methods are necessary for original image processes in applications of quantum image processing like quantum image encryption, which increases the strength of the encryption process, and the resulting image is difficult to identify and detect its details. As well as obtain a high entropy value and a histogram with a uniform peak for the encrypted image. Most researches focus on scrambling the position only or the value only; however, the quantum image scrambling researches focused on scrambling both position and value together is few. The idea of the study is developing a genetic algorithm to generate different schemes of scrambling based on the fast and elementary schemes with changing the quantum logical gate (NOT / C-Not) to get the best scheme that meets the requirements such as the cost, the complexity or the type of the image. One of the essential benefits of the proposed work is developing a general framework for the automatic generation of a suitable scrambling scheme based on image type, method, and logical circuit. The tests are simulated using MATLAB. The result confirms that hybrid value/position schemes with a C-Not gate have an entropy value close to 8 and a flat histogram. It is implicated that this framework will benefit many researchers in selecting the most appropriate scrambling method for their works.