Simulation and Investigation of Quantum Search Algorithm System

Jonathan A. Jones, Michele Mosca, Rasmus H. Hansen

Mark W. Coffey

Abstract : This report documents investigations of the connections between scale space and the linear and nonlinear diffusion of images, as well as investigations of concepts of generalized entropy and quantum entropy and their measures. The generalized entropies included in particular Renyi entropy with parameter q. The diffusion studies were performed with a combination of mathematical analysis and simulations. Analysis of quantum and semi-classical entropies of modeled physical systems was also performed. The feasibility of applying forms of generalized quantum search to scheduling and logistics problems was also investigated. As part of this effort, simulations of adaptive quantum search were performed. Furthermore, the capabilities and constraints of quantum lattice gas algorithms (QLGAs) were investigated, and a new QLGA for the telegraph equation with one spatial dimension was formulated, implemented, and simulated.

Pulak Ranjan Giri, V. E. Korepin

Peng Wang, Gang Xin, Wang Sheng Fang

Recent decades, the emergence of numerous novel algorithms makes it a gimmick to propose an intelligent optimization system based on metaphor, and hinders researchers from exploring the essence of search behavior in algorithms. However, it is difficult to directly discuss the search behavior of an intelligent optimization algorithm, since there are so many kinds of intelligent schemes. To address this problem, an intelligent optimization system is regarded as a simulated physical optimization system in this paper. The dynamic search behavior of such a simplified physical optimization system are investigated with quantum theory. To achieve this goal, the Schroedinger equation is employed as the dynamics equation of the optimization algorithm, which is used to describe dynamic search behaviours in the evolution process with quantum theory. Moreover, to explore the basic behaviour of the optimization system, the optimization problem is assumed to be decomposed and approximated. Correspondingly, the basic search behaviour is derived, which constitutes the basic iterative process of a simple optimization system. The basic iterative process is compared with some classical bare-bones schemes to verify the similarity of search behavior under different metaphors. The search strategies of these bare bones algorithms are analyzed through experiments.

Jincheng Zhang

This paper investigates the application of quantum walk-based search algorithms to address the scalability challenges inherent in classical search algorithms when dealing with massive datasets. The core premise is that quantum superposition and interference, inherent properties of quantum systems, offer a potential pathway to significantly enhance the efficiency of search operations. We propose and analyze quantum walk algorithms designed to explore search spaces more effectively than their classical counterparts. The focus is on theoretical development and algorithmic design, without experimental validation. We explore key concepts such as walker position, probability amplitudes, and interference effects within the framework of quantum walks. The algorithms are designed to be adaptable to both quantum hardware and quantum simulators. This work aims to demonstrate the theoretical feasibility and potential advantages of utilizing quantum walk algorithms for large-scale data search, contributing to the growing field of quantum search algorithms.

Weng-Long Chang, Athanasios V. Vasilakos