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.
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.
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.
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.
This is a set of lectures on tensor networks with a strong emphasis on the core algorithms involving Matrix Product States (MPS) and Matrix Product Operators (MPO). Compared to other presentations, particular care has been given to disentangle aspects of tensor networks from the quantum many-body problem: MPO/MPS algorithms are presented as a way to deal with linear algebra on extremely (exponentially) large matrices and vectors, regardless of any particular application. The lectures include well-known algorithms to find eigenvectors of MPOs (the celebrated DMRG), solve linear problems, and recent learning algorithms that allow one to map a known function into an MPS (the Tensor Cross Interpolation, or TCI, algorithm). The lectures end with a discussion of how to represent functions and perform calculus with tensor networks using the "quantics" representation. They include the detailed analytical construction of important MPOs such as those for differentiation, indefinite integration, convolution, and the quantum Fourier transform. Three concrete applications are discussed in detail: the simulation of a quantum computer (either exactly or with compression), the simulation of a quantum annealer, and techniques to solve partial differential equations (e.g. Poisson, diffusion, or Gross-Pitaevskii) within the "quantics" representation. The lectures have been designed to be accessible to a first-year PhD student and include detailed proofs of all statements.
Quantum computing represents a transformative approach to computation leveraging fundamental principles of quantum mechanics such as superposition, entanglement and interference to store and process information in ways that classical computers cannot achieve.This paper attempts to provide a bona fide bibliographic overview of the principles, computational models, hardware technologies, and potential applications of quantum computing.It analyses how quantum algorithms could outperform classical algorithms in cryptographic analysis, optimization, and big data analysis.The survey integrates viewpoints from recent works; it presents system architectures, software development challenges, and quantum-assisted applications in healthcare, artificial intelligence, cybersecurity, and industrial optimization.Meanwhile, it examines hybrid quantum-classical systems that would allow quantum technologies to be deployed in the near term skirted by the limitations currently posed by quantum hardware.Moreover, the paper discusses foremost hurdles in scaling, error-correction, and maintaining coherence.From reviewing the recent developments and whether possible, this present review work informs researchers, engineers, and practitioners alike on the current state, as well as on the long-run viability, of quantum computing.
The anticipated applications of quantum computers span across science and industry, ranging from quantum chemistry and many-body physics to optimization, finance, and machine learning. Proposed quantum solutions in these areas typically combine multiple quantum algorithmic primitives into an overall quantum algorithm, which must then incorporate the methods of quantum error correction and fault tolerance to be implemented correctly on quantum hardware. As such, it can be difficult to assess how much a particular application benefits from quantum computing, as the various approaches are often sensitive to intricate technical details about the underlying primitives and their complexities. Here we present a survey of several potential application areas of quantum algorithms and their underlying algorithmic primitives, carefully considering technical caveats and subtleties. We outline the challenges and opportunities in each area in an "end-to-end" fashion by clearly defining the problem being solved alongside the input-output model, instantiating all "oracles," and spelling out all hidden costs. We also compare quantum solutions against state-of-the-art classical methods and complexity-theoretic limitations to evaluate possible quantum speedups. The survey is written in a modular, wiki-like fashion to facilitate navigation of the content. Each primitive and application area is discussed in a standalone section, with its own bibliography of references and embedded hyperlinks that direct to other relevant sections. This structure mirrors that of complex quantum algorithms that involve several layers of abstraction, and it enables rapid evaluation of how end-to-end complexities are impacted when subroutines are altered.
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.