Fast geometric transformations on quantum images

Circuits to achieve geometric transformations including two-point swapping, flip, coordinate swapping, orthogonal rotations and their variants on N-sized quantum images are proposed based on the basic quantum gates; NOT, CNOT and Toffoli gates. The complexity of the circuits is O(log ² N) for two-point swapping and O(logN) for flip, co-ordinate swapping and orthogonal rotations. The results indicate that local operations like two-point swapping are slower than global operations like flip, co-ordinate swapping, and orthogonal rotations in quantum image processing. This is in contrast to performing such operations in classical image processing where the local operations are faster. All the proposed transformations are confirmed by simulation on a classical computer. With their low complexity, these geometric transformations can be used as the major components to build circuits for other applications on quantum images.