Quantum computers are designed to outperform standard computers by running quantum algorithms. Fields in which quantum algorithms can be applied include cryptography, search and optimization, simulation of quantum systems and solving large systems of linear equations. Here we briefly survey some known quantum algorithms, with an emphasis on a broad overview of their applications rather than their technical details. We focus to introduce the development of entire field, and provide a comprehensive and accurate understanding concerning this field, which may be helpful for interested researchers in this area.
Quantum computers are designed to outperform standard computers by running quantum algorithms. Fields in which quantum algorithms can be applied include cryptography, search and optimization, simulation of quantum systems and solving large systems of linear equations. Here we briefly survey some known quantum algorithms, with an emphasis on a broad overview of their applications rather than their technical details. We focus to introduce the development of entire field, and provide a comprehensive and accurate understanding concerning this field, which may be helpful for interested researchers in this area.
Abstract Quantum computers are designed to outperform standard computers by running quantum algorithms. Areas in which quantum algorithms can be applied include cryptography, search and optimisation, simulation of quantum systems and solving large systems of linear equations. Here we briefly survey some known quantum algorithms, with an emphasis on a broad overview of their applications rather than their technical details. We include a discussion of recent developments and near-term applications of quantum algorithms.
The reason of quantum computer systems is to carry out preferred computer systems through jogging the quantum algorithm. Quantum algorithms can be utilized in a ramification of contexts, such as search and optimization, cryptography, the answer of complex linear equations, and simulation of quantum systems. Right here in this look at a quick survey of some familiar quantum algorithms, with the significance of a large assessment of their application instead of their technical details. Also, cover the application of quantum algorithms and a discussion of latest improvement.
On the basis of its unrivalled potential to solve factorization problems and further application in cryptography, quantum computing is considered as one of the most promising computational models for the future. It provides a new angle for thinking of computation and a new approach for attack various computationally difficult problems. In this article, we give a comprehensive survey of developments in the last twenty years on quantum algorithms, quantum complexity, quantum programming theory, quantum circuits, and quantum cryptography that we hope will serve as references for researchers in related fields. We also outline various research directions and open problems in this area, with the hope of prompting further progress or even solutions.
A groundbreaking advancement in computing theory, quantum search algorithms leverage quantum mechanics to outperform their classical counterparts in solving search issues. With a focus on their theoretical underpinnings, practical applications, and performance in a variety of computational contexts, this systematic review carefully investigates the evolution, progress, and current state of quantum search algorithms. We present a thorough analysis of significant algorithms, such as Grover’s search algorithm, together with recent developments in quantum optimization and quantum-enhanced search techniques. We also go over the challenges with quantum error correction, scalability, and hardware constraints that prevent the broad application of quantum search techniques.
Quantum computing leverages quantum mechanical concepts, including superposition, entanglement, and interference, to solve problems that traditional computers cannot handle efficiently. This study presents a comprehensive overview of the field, covering both the theoretical foundations and the latest developments in quantum hardware and algorithms. This study covers fundamental elements, qubits, gates, and circuits while emphasizing quantum parallelism as a distinctive feature. To illustrate efficiency gains, we explore notable algorithms like Shor’s factorization procedure and Grover’s search algorithm. Furthermore, we analyze recent advancements in quantum hardware, focusing on superconducting qubits, trapped ions, and photonic quantum computers, with an emphasis on implementations by IBM, Google, and other industry leaders. The discussion also addresses major challenges such as decoherence, noise, and the need for quantum error correction to achieve fault tolerance. Finally, we explore emerging applications in cryptography, optimization, quantum machine learning, and material simulation, and identify critical open problems that must be addressed to realize scalable, universal quantum computing. Our review underscores the transformative potential of quantum technologies across science and industry.
Solving linear systems of equations plays a fundamental role in numerous computational problems from different fields of science. The widespread use of numerical methods to solve these systems motivates investigating the feasibility of solving linear systems problems using quantum computers. In this work, we provide a survey of the main advances in quantum linear systems algorithms, together with some applications. We summarize and analyze the main ideas behind some of the algorithms for the quantum linear systems problem in the literature. The analysis begins by examining the Harrow-Hassidim-Lloyd (HHL) solver. We note its limitations and reliance on computationally expensive quantum methods, then highlight subsequent research efforts which aimed to address these limitations and optimize runtime efficiency and precision via various paradigms. We focus in particular on the post-HHL enhancements which have paved the way towards optimal lower bounds with respect to error tolerance and condition number. By doing so, we propose a taxonomy that categorizes these studies. Furthermore, by contextualizing these developments within the broader landscape of quantum computing, we explore the foundational work that have inspired and informed their development, as well as subsequent refinements. Finally, we discuss the potential applications of these algorithms in differential equations, quantum machine learning, and many-body physics.