Quantum Computation-Based Image Representation, Processing Operations and Their Applications

Abstract

A flexible representation of quantum images (FRQI) was proposed to facilitate the extension of classical (non-quantum)-like image processing applications to the quantum computing domain. The representation encodes a quantum image in the form of a normalized state, which captures information about colors and their corresponding positions in the images. Since its conception, a handful of processing transformations have been formulated, among which are the geometric transformations on quantum images (GTQI) and the CTQI that are focused on the color information of the images. In addition, extensions and applications of FRQI representation, such as multi-channel representation for quantum images (MCQI), quantum image data searching, watermarking strategies for quantum images, a framework to produce movies on quantum computers and a blueprint for quantum video encryption and decryption have also been suggested. These proposals extend classical-like image and video processing applications to the quantum computing domain and offer a significant speed-up with low computational resources in comparison to performing the same tasks on traditional computing devices. Each of the algorithms and the mathematical foundations for their execution were simulated using classical computing resources, and their results were analyzed alongside other classical computing equivalents.Entropy 2014, 16 5291The work presented in this review is intended to serve as the epitome of advances made in FRQI quantum image processing over the past five years and to simulate further interest geared towards the realization of some secure and efficient image and video processing applications on quantum computers.

Metric for Estimating Congruity between Quantum Images

“…Inspired by the utility of image search and retrieval on digital computers, the studies in [15,19,23] explored the possibility of undertaking similar tasks on quantum computers.…”

“…The measurements are performed subject to satisfying some predefined conditions [24]. The ADQC [19] is a newer type of MBQC, which was utilised for the movie reader in [9], exploits the properties of single-qubit projective measurements and the entanglement-based interaction between the ancilla qubit and the register qubit (i.e., strip state encoding the 2 m -ending FRQI images). The measurements are performed subject to satisfying some predefined conditions [24].…”

“…Consequently, the geometric (GTQI) and colour (CTQI) transformations and their restricted variants, which are widely used in FRQI quantum image processing (QIP) to manipulate the spatial and chromatic content of images [17,19], are the main resources employed to manipulate our images. …”

“…After it is prepared and initialised, the quantum image can only be manipulated, and recovered using quantum circuit elements and components, such as the basic unitary gates that were highlighted earlier in Section 2. Many copies of the same image are usually prepared and different circuits designed to manipulate and recover them as required for an intended application [14][15][16][17][18][19][20], albeit, as we shall demonstrate later, oftentimes, this is an expensive undertaking.…”

“…Throughout the rest of this paper, we assume that all images (reference and test images) are encoded as FRQI quantum images using procedures that were highlighted earlier in Section 2 and discussed in detail in [11,12,17,19]. Consequently, the geometric (GTQI) and colour (CTQI) transformations and their restricted variants, which are widely used in FRQI quantum image processing (QIP) to manipulate the spatial and chromatic content of images [17,19], are the main resources employed to manipulate our images.…”