Representation and processing of information in quantum computers

Giuliano Benenti, Giulio Casati, G. Strini

Fei Yan, Abdullah M. Iliyasu, Zhengang Jiang

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. The 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.

Giuliano Benenti, Giulio Casati, G. Strini

Ashima Anand, Amit Kumar Singh

The basics of Quantum Information Processing (QIP) is summarized below, in addition to a comprehensive survey of quantum image-based data hiding techniques. QIP is more efficient and provides higher security than classical information processing. A comparative analysis of the Flexible Representation of Quantum Images (FRQI) and Novel Enhanced Quantum Representation (NEQR) model is also presented. QIP is used in various potential applications, hence offering an interesting and demanding area for researchers [1]. Some of the important applications include medicine, military, environmental monitoring, image processing, communications, computations, and cryptography. This article focusses on the processing of information that can be represented using quantum mechanics [2]. Furthermore, coherence, entanglement, and superposition of quantum states makes quantum computing more suitable to its classical counterpart for information storage and processing [1], [3].

Shikhar Uttam

Sara Felloni, Alberto Leporati, G. Strini

We explore the main processes involved in the evolution of general quantum systems by means of Diagrams of States, a novel method to graphically represent and analyze how quantum information is elaborated during computations performed by quantum circuits. We present quantum diagrams of states for representations of quantum states by density matrices, partial trace operations, density matrix purification and time-evolution by Kraus operators. Following these representations, we describe by diagrams of states the most general transformations related to singlequbit decoherence and errors. Diagrams of states prove to be a useful approach to analyze quantum computations, by offering an intuitive graphic representation of the processing of quantum information. They also help in conceiving novel quantum computations, from describing the desired information processing to deriving the final implementation by quantum gate arrays.