arXiv:1804.03719 · ACM Transactions on Quantum Computing
Quantum Algorithm Implementations for Beginners
Abhijith Jayakumar, Adetokunbo A. Adedoyin, John J. Ambrosiano, Petr M. Anisimov, William Casper, Gopinath Chennupati, Carleton Coffrin, Hristo N. Djidjev, David Gunter, Satish Karra, Nathan Lemons, Shizeng Lin, Alexander Malyzhenkov, David Mascareñas, Susan M. Mniszewski, Balu T. Nadiga, Daniel O’Malley, Diane Oyen, Scott Pakin, Lakshman Prasad, Randy Roberts, Phillip Romero, Nandakishore Santhi, Nikolai A. Sinitsyn, Pieter J. Swart, James Wendelberger, Boram Yoon, Richard J. Zamora, Weijun Zhu, Stephan Eidenbenz, Andreas Bärtschi, Patrick J. Coles, Marc Vuffray, Andrey Y. Lokhov
As quantum computers become available to the general public, the need has arisen to train a cohort of quantum programmers, many of whom have been developing classical computer programs for most of their careers. While currently available quantum computers have less than 100 qubits, quantum computing hardware is widely expected to grow in terms of qubit count, quality, and connectivity. This review aims at explaining the principles of quantum programming, which are quite different from classical programming, with straightforward algebra that makes understanding of the underlying fascinating quantum mechanical principles optional. We give an introduction to quantum computing algorithms and their implementation on real quantum hardware. We survey 20 different quantum algorithms, attempting to describe each in a succinct and self-contained fashion. We show how these algorithms can be implemented on IBM’s quantum computer, and in each case, we discuss the results of the implementation with respect to differences between the simulator and the actual hardware runs. This article introduces computer scientists, physicists, and engineers to quantum algorithms and provides a blueprint for their implementations.
As quantum computers become available to the general public, the need has arisen to train a cohort of quantum programmers, many of whom have been developing classical computer programs for most of their careers. While currently available quantum computers have less than 100 qubits, quantum computing hardware is widely expected to grow in terms of qubit count, quality, and connectivity. This review aims at explaining the principles of quantum programming, which are quite different from classical programming, with straightforward algebra that makes understanding of the underlying fascinating quantum mechanical principles optional. We give an introduction to quantum computing algorithms and their implementation on real quantum hardware. We survey 20 different quantum algorithms, attempting to describe each in a succinct and self-contained fashion. We show how these algorithms can be implemented on IBM’s quantum computer, and in each case, we discuss the results of the implementation with respect to differences between the simulator and the actual hardware runs. This article introduces computer scientists, physicists, and engineers to quantum algorithms and provides a blueprint for their implementations.
With the increasing accessibility of quantum computers to the wider population, there is a growing demand for the education and training of a group of quantum programmers. This cohort predominantly consists of individuals who have primarily focused on the development of classical computer programs throughout their professional careers. Although existing quantum computers currently possess fewer than 100 qubits, it is widely anticipated that the quantum computing hardware will experience significant advancements in terms of qubit quantity, quality, and connectivity. The objective of this review is to elucidate the fundamental principles of quantum programming, which diverge significantly from classical programming. This will be achieved through the utilization of concise algebraic expressions, allowing for an optional comprehension of the captivating underlying principles of quantum mechanics. This paper provides an overview of quantum computing algorithms and their practical implementation on physical quantum hardware. In this study, we undertake a comprehensive examination of various quantum algorithms, with the objective of providing concise and self-contained descriptions for each. In this study, we demonstrate the practical implementation of the aforementioned algorithms on IBM's quantum computer. For each algorithm, we thoroughly analyze and compare the outcomes obtained from the implementation on the quantum computer with those obtained from the simulator. This analysis focuses on identifying and discussing any disparities that arise between the results obtained from the simulator and the actual hardware runs. This article serves as an introduction to quantum algorithms for computer scientists, physicists, and engineers, offering a comprehensive guide for their practical implementation.
In the last two decades, the interest in quantum computation has increased significantly among research communities. Quantum computing is the field that investigates the computational power and other properties of computers on the basis of the underlying quantum-mechanical principles. The main purpose is to find quantum algorithms that are significantly faster than any existing classical algorithms solving the same problem. While the quantum computers currently freely available to wider public count no more than two dozens of qubits, and most recently developed quantum devices offer some 50-60 qubits, quantum computer hardware is expected to grow in terms of qubit counts, fault tolerance, and resistance to decoherence. The main objective of this chapter is to present an introduction to the core quantum computing algorithms developed thus far for the field of cryptography.
Quantum Computing: Principles, Algorithms, Technologies and Applications provides a comprehensive introduction to the rapidly developing field of quantum computing. The book explains the fundamental principles of quantum information and connects quantum theory with algorithms, hardware, programming, security, and real-world applications. Beginning with the fundamentals of qubits, superposition, measurement, interference, and entanglement, the book gradually introduces the mathematical concepts required to understand quantum computation. It covers quantum gates and circuits, major quantum algorithms such as Grover’s algorithm, Quantum Fourier Transform, Quantum Phase Estimation, and Shor’s algorithm, along with their computational significance. The book also explores modern quantum computing technologies, including superconducting qubits, trapped ions, photonic systems, neutral atoms, semiconductor spin qubits, and quantum annealing. Readers are introduced to quantum programming and software concepts, quantum simulators, circuit compilation, hybrid quantum-classical computing, and practical quantum development workflows. A dedicated discussion of quantum error correction, fault-tolerant computing, quantum cryptography, quantum key distribution, and post-quantum cryptography explains how quantum technologies influence cybersecurity and secure communication. The book further examines applications of quantum computing in optimization, artificial intelligence, chemistry, drug discovery, finance, materials science, and other emerging areas. Designed for students, researchers, educators, engineers, and technology enthusiasts, this book provides a structured foundation for understanding both the theoretical principles and practical technologies of quantum computing. It also discusses current challenges, scalability, quantum advantage, and future directions toward fault-tolerant and large-scale quantum computing.
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.
Quantum computing has emerged as one of the most transformative technological developments of the twenty-first century. By exploiting the fundamental principles of quantum mechanics—namely superposition, entanglement, and measurement—quantum computers offer the potential to address problems that are beyond the practical reach of classical computing systems. As the field advances from theoretical exploration to real-world implementation, the demand for clear, structured, and comprehensive educational resources continues to grow. This book presents a systematic and accessible introduction to quantum computing, beginning with the essential concepts of classical information and computation and progressively advancing toward modern quantum algorithms and communication protocols. The initial chapters establish a strong foundation in classical bits, logic gates, Boolean algebra, reversible logic, and computational complexity, providing the conceptual bridge necessary to understand quantum computation. The discussion then moves to the quantum bit (qubit), examining its behavior through superposition, measurement, Bloch sphere representation, and physical realization. Special emphasis is placed on linear algebra as the mathematical framework underpinning quantum computing. Through this approach, readers are guided to develop an intuitive yet rigorous understanding of quantum states, quantum gates, and circuit-based computation. The text further extends these ideas to multi-qubit systems, quantum entanglement, universal gate sets, and quantum error correction, integrating theoretical principles with practical insights. To support experiential learning, the book incorporates hands-on exposure to leading quantum programming platforms, including IBM Quantum, OpenQASM, and Qiskit. These sections connect theory with practice, enabling readers to design, simulate, and execute quantum circuits on both simulators and real quantum hardware. Subsequent chapters explore key quantum communication protocols such as superdense coding, quantum teleportation, and quantum key distribution, followed by an in-depth treatment of foundational quantum algorithms including Deutsch–Jozsa, Grover’s search, Simon’s algorithm, and Shor’s factoring algorithm. This text is intended for undergraduate and postgraduate students, research scholars, and industry professionals seeking a coherent and structured pathway into quantum computing. No prior knowledge of quantum mechanics is assumed, although familiarity with linear algebra and classical computation will enhance comprehension. Each chapter is carefully organized to promote conceptual clarity, supported by illustrative examples, circuit diagrams, and concise summaries. Beyond explaining the principles and mechanisms of quantum computation, this book aims to inspire readers to engage with the future of the field—whether through academic research, industrial application, or interdisciplinary innovation. As quantum technologies continue to evolve, it is hoped that this text will serve as a dependable guide and a meaningful entry point into the quantum era.
Quantum computing has emerged as one of the most transformative technological developments of the twenty-first century. By exploiting the fundamental principles of quantum mechanics—namely superposition, entanglement, and measurement—quantum computers offer the potential to address problems that are beyond the practical reach of classical computing systems. As the field advances from theoretical exploration to real-world implementation, the demand for clear, structured, and comprehensive educational resources continues to grow. This book presents a systematic and accessible introduction to quantum computing, beginning with the essential concepts of classical information and computation and progressively advancing toward modern quantum algorithms and communication protocols. The initial chapters establish a strong foundation in classical bits, logic gates, Boolean algebra, reversible logic, and computational complexity, providing the conceptual bridge necessary to understand quantum computation. The discussion then moves to the quantum bit (qubit), examining its behavior through superposition, measurement, Bloch sphere representation, and physical realization. Special emphasis is placed on linear algebra as the mathematical framework underpinning quantum computing. Through this approach, readers are guided to develop an intuitive yet rigorous understanding of quantum states, quantum gates, and circuit-based computation. The text further extends these ideas to multi-qubit systems, quantum entanglement, universal gate sets, and quantum error correction, integrating theoretical principles with practical insights. To support experiential learning, the book incorporates hands-on exposure to leading quantum programming platforms, including IBM Quantum, OpenQASM, and Qiskit. These sections connect theory with practice, enabling readers to design, simulate, and execute quantum circuits on both simulators and real quantum hardware. Subsequent chapters explore key quantum communication protocols such as superdense coding, quantum teleportation, and quantum key distribution, followed by an in-depth treatment of foundational quantum algorithms including Deutsch–Jozsa, Grover’s search, Simon’s algorithm, and Shor’s factoring algorithm. This text is intended for undergraduate and postgraduate students, research scholars, and industry professionals seeking a coherent and structured pathway into quantum computing. No prior knowledge of quantum mechanics is assumed, although familiarity with linear algebra and classical computation will enhance comprehension. Each chapter is carefully organized to promote conceptual clarity, supported by illustrative examples, circuit diagrams, and concise summaries. Beyond explaining the principles and mechanisms of quantum computation, this book aims to inspire readers to engage with the future of the field—whether through academic research, industrial application, or interdisciplinary innovation. As quantum technologies continue to evolve, it is hoped that this text will serve as a dependable guide and a meaningful entry point into the quantum era.