Implementation and Analysis of Quantum Fourier Transform in Image Processing
Ola Al-Ta’ani, Ali Mohammad Alqudah, Manal Al-Bzoor |Pages: 11-26|

Abstract— There is a growing interest in quantum image processing (QImP) that rose from the desire to exploit the properties of quantum computing to improve the performance of classical techniques and their applications. While Fourier transform (FT) is one of the most important algorithms used in signal and image processing, it is also considered a key ingredient in most modern quantum algorithms. A quantum Fourier transform (QFT) differs from the classical (FT) in that it takes a quantum state in which the initial data have been encoded into probability amplitudes. It alters the amplitudes of the corresponding discrete Fourier transform (DFT). The classical algorithms take an entire complex valued vector; and return the entire DFT in the form of another vector of the same length. These computations are proven to be exponentially faster on quantum computers than those of classical computers. In this paper, we demonstrate a framework of QImP where image information including pixel values and their positions are encoded in a pure quantum state. This framework is more efficient in terms of the number of the required qubits. This framework is supported with an experimental demonstration of the quantum image encoding, processing, and decoding along with a detailed comparison with the conventional ones. Quality assessment of the restored images is also provided where different common measures such as Mean-Squared Error (MSE), Peak Signal-to-Noise Ratio (PSNR), and Structural Similarity Index (SSIM) are used. In general, our experimental results, which were conducted on a classical computer, show similarity of quantum image transformation to its classical counterpart.