Fast Geometric Transformations on Quantum Images

Abstract

Circuits to achieve geometric trans- formations including two-point swapping, flip, co- ordinate 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 process- ing where the local operations are faster. All the proposed transformations are confirmed by simula- tion on a classical computer. With their low com- plexity, these geometric transformations can be used as the major components to build circuits for other applications on quantum images.