Quantum Hilbert Image Scrambling

Abstract

Analogies between quantum image processing (QIP) and classical one indicate that quantum image scrambling (QIS), as important as quantum Fourier transform (QFT), quantum wavelet transform (QWT) and etc., should be proposed to promote QIP. Image scrambling technology is commonly used to transform a meaningful image into a disordered image by permutating the pixels into new positions. Although image scrambling on classical computers has been widely studied, we know much less about QIS. In this paper, the Hilbert image scrambling algorithm, which is commonly used in classical image processing, is carried out in quantum computer by giving the scrambling quantum circuits. First, a modified recursive generation algorithm of Hilbert scanning matrix is given. Then based on the flexible representation of quantum images, the Hilbert scrambling quantum circuits, which are recursive and progressively layered, is proposed. Theoretical analysis indicates that the network complexity scales squarely with the size of the circuit’s input n.