This essay mainly introduced Shor algorithm,Grover quantum evolution algorithm and the progress of quantum evolution algorithm based on quantum algorithm theory.It expounded the major problems and research prospect which quantum algorithm had to confront.
The quantum meta heuristic algorithm is developed by applying quantum computing to the meta-heuristic algorithm.This kind of algorithm is good at solving combinatorial and numerical optimization problems,and has the characteristics of acce-lerated convergence,enhanced exploration and development capabilities,and can obtain higher performance results than traditional meta-heuristic algorithms.This paper mainly summarizes and reviews the theoretical methods and applications of quantum meta-heuristic algorithms.Firstly,this paper expounds the basic concepts and principles of quantum computing,and analyzes the challenging problems that need to be solved urgently in the field of quantum computing.Then,this paper expounds the basic principles of six classical quantum meta-heuristic algorithms,analyzes the latest research progress,gives their advantages and disadvantages in solving domain-specific problems,and demonstrates the application of quantum meta-heuristic algorithms in different disciplines and engineering scenarios.Finally,this paper analyzes and explores the existing problems in the theories and methods of quantum meta-heuristic algorithms,and summarizes the future development direction of the theory and application of quantum meta-heuristic algorithms.
According to quantum mechanics,quantum state has many advantages of the coherence and entanglement and the inner parallelism of quantum algorithm is totally different from the classical algorithm.Shor's algorithm shows the advantage of quantum algorithm in solving some classical Non-polynomial problems,then Grover's search algorithm further proves this point.And this brought more and more research on quantum algorithm in many countries and they have got great achievements especially on quantum intelligent algorithm.In this paper,the development and fundamental principles of quantum computing are generalized,then three typical quantum algorithms is introduced,and the superiority of quantum computer is explained.Finally,current research of quantum computation are introduced.
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.
Quantum computing is a high-powered computational model that possess the capability to solve problems that are non-detectable by traditional algorithms. These algorithms primarily exploit well-known rules and principles of quantum mechanics i.e., superposition and entanglement to implement and deploy solutions for sophisticated tasks. Its applications have revolutionized various domains like optimization, cryptography, machine learning, and simulation. With the increasing research in this significant computational field, it is becoming more essential to critically assess that how quantum algorithms are being employed in real-world problem-solving contexts. The comprehensive literature review that has been conducted in this study is primarily based upon the critical assessment of four key quantum algorithms, which are 1) Shor's Algorithm, 2) Grover's Algorithm, 3) the Quantum Approximate Optimization Algorithm (QAOA), and the 4) Quantum Fourier Transform (QFT). We have primarily focused upon their uses in secure communication, machine learning, chemistry, cryptography, and optimization. 30 excellent studies published between 2015 and 2024 were found through a systematic search of IEEE Xplore, SpringerLink, ScienceDirect, arXiv, and Google Scholar. Our results identify major patterns in the usage of algorithms like Grover's, Shor's, QAOA, and VQE and elucidate their applications in tackling theoretical and pragmatic problems. Unlike previous reviews that concentrate narrowly on algorithm design or on particular areas, this SLR presents a wide but organized synthesis that highlights problem-driven applications. Moreover, we have also highlighted the primary research gaps in this area and also suggested possible future directions for further investigation. This review provides a basis for researchers who would like to apply quantum algorithms to new or interdisciplinary problems.
In this thesis,several basic conceptions of quantum computation are introduced,such as entanglement,quantum bit.Several kinds of main quantum algorithms are illustrated,such as Shor algorithm-the quantum algorithm for factoring,Grover search-the search for the disordering database,Hogg search-high structurization search.On the basis of knowledge of basic theories of quantum computation computing and quantum algorithm,two kinds of systems which play important role in the experiment of quantum computation was introduced,Nuclear magnetic resonance and cavity atom system.
Quantum computing is an advanced computational paradigm that leverages principles of quantum mechanics, including superposition, entanglement, and interference, to process information more efficiently than classical systems [1][2]. Unlike classical bits, qubits can exist in multiple states simultaneously, enabling exponential computational capabilities for complex problem-solving. Since its theoretical foundations proposed by Richard Feynman and further developed by David Deutsch, quantum computing has progressed into an active research and industrial domain [2][3]. This paper presents an overview of the core concepts of quantum computation, technological evolution, and key algorithms such as Shor’s and Grover’s, which demonstrate significant computational advantages [9][10]. It also explores major application areas including cryptography, healthcare, artificial intelligence, and optimization, while addressing critical challenges such as decoherence, error correction, and scalability [5][6]. The study highlights future prospects, emphasizing the potential of quantum computing to transform scientific and industrial domains [12][15].