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Jisuanji gongcheng yu sheji

Quantum algorithm to resolve TSP

YU Xiao-min

Published Jan 1, 2004• 2 citations
OpenAlex

Abstract

A new method is given to resolve TSP by using the features of quantum waves. An introduction of the fundamental principles of quantum algorithms is described together with some relational concepts, followed by an analysis of the features of the quantum algorithm. Finally the prospect of the development of quantum computation is presented.

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A new method is given to resolve TSP by using the features of quantum waves. An introduction of the fundamental principles of quantum algorithms is described together with some relational concepts, followed by an analysis of the features of the quantum algorithm. Finally the prospect of the development of quantum computation is presented.
This chapter explores the rapidly developing field of quantum computing, which essentially devises the power to change science and technology. After an introductory outline, the fundamental ideas of quantum computing are covered, setting it apart from classical computing. The chapter then goes on to describe the features of a quantum computing system, highlighting its unique traits and possible advantages. The reliance on complex numbers and advanced mathematics is a central point of quantum computing [ 1 ]. Fundamental mathematical concepts are important to understand the quantum algorithms, which are explained in more detailed way. In quantum computing, the main idea is that quantum bits can have several states. The quality of quantum processing is extensively explored in this chapter. The chapter also covers a range of quantum computing techniques, highlighting their resourceful methods for tackling problems. Finally, the uses of quantum computing and its influence in many areas, such as optimization, materials research, and cryptography, are described and analyzed. This ample introduction will provide readers with thoughtful principles and the mathematical and practical significance of quantum computing.
With the decreasing development of the classical computation,quantum computation becomes the increasing hot topic recently.In this paper,the fundamental theory of quantum computation is briefly introduced firstly.Then,we give the state of the art of quantum computation and research principles in this field from two different research directions(quantum algorithms and quantum-inspired algorithms).At last,some trends of quantum computation in the future research are given.Through the review and prospect of the whole field,this paper could give a significant guide for the future development of quantum computation.
Quantum algorithms have emerged as powerful computational tools that leverage the principles of quantum mechanics to address complex problems beyond the scope of classical computing. This chapter explores the foundational concepts, classifications, implementation challenges, and future prospects of quantum algorithms. Key breakthroughs such as Grover's and Shor's algorithms are explored alongside recent developments in quantum machine learning and optimization. The chapter also compares quantum and classical algorithmic complexity, highlighting areas of potential speedup. Practical limitations including hardware constraints, error correction, and resource estimation are critically analyzed. Finally, the chapter outlines emerging research directions and ethical considerations essential for responsible quantum computing development.
This paper presents a new algorithm for solving the travelling salesman problem (TSP). The TSP is one of the most known combinatorial optimisation problems. It is about finding the shortest Hamiltonian cycle relating N cities. The algorithm is inspired from both genetic algorithms and quantum computing fields. It extends the standard genetic algorithms by combining them to some concepts and principles provided from quantum computing field such as quantum bit, states superposition and interference. The obtained results from the application of the proposed algorithm on some instances of TSP are significantly better than those provided by standard genetic algorithms.