The linear cyclic translation and two-point swapping transformations for quantum images

Geometric transformations are fundamental operations in quantum image processing. We present quantum algorithms to realize two geometric transformations (i.e., the linear cyclic translation and two-point swapping transformations) on quantum images with $$2^n$$ pixels. The circuits for two geometric transformations are designed with the complexity O(n). Comparative analysis and simulation results reveal that the proposed cyclic translation and two-point swapping transformations are efficient.