Abstract The article presents a historical overview of the development of the mathematical idea of a quantum computing model - a new computational strategy based on the postulates of quantum mechanics and having advantages over the traditional computational model based on the Turing machine; clarified the features of the operation of multi-qubit quantum systems, which ensure the creation of efficient algorithms; the principles of quantum computing are outlined and a number of efficient quantum algorithms are described that allow solving the problem of exponential growth of the complexity of certain problems.
Abstract The article presents a historical overview of the development of the mathematical idea of a quantum computing model - a new computational strategy based on the postulates of quantum mechanics and having advantages over the traditional computational model based on the Turing machine; clarified the features of the operation of multi-qubit quantum systems, which ensure the creation of efficient algorithms; the principles of quantum computing are outlined and a number of efficient quantum algorithms are described that allow solving the problem of exponential growth of the complexity of certain problems.
Quantum computing, based on the fundamental principles of quantum mechanics, has become a breakthrough that has the potential to revolutionize computing. At the forefront of this quantum revolution are quantum algorithms that use the origin of qubits to solve computational problems much faster than classical algorithms. This article provides a review of quantum algorithms to introduce their principles, examine famous examples such as the Grover and Shor algorithms, and delve into their applications, including quantum machine learning. Exploring the fundamentals of quantum computing begins with an overview that highlights the unique features of quantum computing compared to classical computing. We then examine several different algorithmic paradigms to highlight the unique advantages that quantum parallelism and interference bring to computing. The best knowledge of quantum algorithms focuses on Grover's blind search, Shor's efficient factorization algorithm, and the quantum phase approach for solving quantum chemistry and eigenvalue problems. As well as celebrating the achievements of quantum algorithms, this research also looks at the challenges and limitations that hinder their widespread use. Topics such as decoherence, error correction, and finding errors in quantum computing are discussed in the context of overcoming obstacles to the use of practical quantum algorithms. In addition, the latest developments are clarified by showing the successes of the experiments and their implications for the future. As we stand at the forefront of a new era in computing, this article not only provides a snapshot of the current state of quantum algorithms but also speculates on future directions. The potential applications of quantum algorithms in many fields and the ongoing quest to overcome current limitations offer exciting opportunities for further research. This research aims to contribute to the ongoing debate about quantum algorithms, gaining a deeper understanding of their impact on the future of computing.
Quantum computing is an emerging paradigm that leverages the principles of quantum mechanics to solve computational problems beyond the reach of classical computers. This article provides an overview of the fundamental concepts of qubits, the distinctive features of quantum mechanics such as superposition and entanglement, and the challenges of building scalable, fault-tolerant systems. It surveys key quantum algorithms and their potential applications in fields including cryptography, optimization, finance, chemistry, and machine learning. Additionally, it highlights the importance of verification frameworks for ensuring the reliability of quantum programs. A literature review of significant contributions is presented, drawing insights from recent surveys on quantum algorithms, qubit technologies, and software verification approaches. The article concludes by discussing ongoing challenges, such as error correction overhead, hardware scalability, and verification complexity, and suggests directions for future research.
Computers have become an indiscipline part of our lives nowadays due to their versatile uses. The advent of computers took place due to the need of efficient mathematical computations. Solving complex problems and running complex algorithms requires powerful processors. Even these powerful processors come with a few limitations and fail to solve problems like simulation of atoms and molecules, solve multi-dimensional computational spaces. This aroused the need for even more efficient and powerful computing systems leading to the rise of quantum computers. The quantum computers are based on laws of quantum mechanics which allows them to leverage the benefits of various principles like Superposition, Coherence, Entanglement. The Quantum computers use qubits unlike bits which are used in computers and can explore multiple states parallelly thereby decreasing computation time exponentially. Multiple domains and fields will benefit from the usage of quantum computing like medicine, finance, logistics, artificial intelligence, and weather forecasting, ushering in a new era of scientific discovery and technological advancement. The paper provides insights into the developments of quantum computing, its underlying principle and the potential it holds.
Quantum computing uses quantum-mechanical principles to enable new models of computation bexond the classical paradigm. This article presents an accessible introduction to the mathematical and conceptual foundations of quantum computing, covering qubits, quantum gates, multi-qubit systems, entanglement, and measurement. The gate-based computation model and quantum circuits are introduced, together with key notations such as universality and reversibility. As an illustrative example, the Deutsch-Josza algorithm is discussed to demonstrate how quantum algorithm can be constucted. The article concludes with a brief overview of the current state and challenges of quantum computing.
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].
Abstract The aim of the research is computer simulation of a quantum algorithm to solve the problem of transforming a classical image using quantum computing tools and methods, studying recognition algorithms and creating a recognition model using quantum methods. The method of quantum modeling makes it possible to convert a classical image into a quantum state, select boundaries and convert a grayscale image to a binary one, and shows the possibilities of the quantum information theory in interpreting classical problems. The main results of the article are the developed quantum algorithm that allows recognizing objects, as well as the quantum method aimed at representing/processing a color pixel image. The scientific novelty of the article is expressed in the construction of a quantum system, an exponential increase in the speed of solving computational NP-complete problems, which on classical machines can be solved in unacceptable time. The motivation for writing the work was a high growth interest in quantum computing and the benefits that they guarantee. The development of the theoretical foundations of creating software systems and the design of algorithms for new information technologies and specialized computing systems is a dynamic field, as evidenced by the number of existing works in this direction. The developed algorithms for various problems of complexity classes can give a significant gain in efficiency in comparison with existing classical ones and provide a solution to a number of complex mathematical (including cryptographic) problems.