To secure the exchange of a facial image, we extract its region of interest to reduce its size by ignoring the unwanted part. Next, we use the GNEQR representation to store it, followed by a sampled quantum encryption circuit using a quantum-gate sequence encoded in the quantum package of the MATHEMATICA platform. Our encryption protocol is based on the perturbation of pixel locations per block in the grayscale image as a proposed scrambling method and not their values using the GNEQR representation thanks to an achieved MATLAB script in the context of quantum image processing. A statistical analysis is carried out to prove the mean robustness of our encryption model compared with a recent work.