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Iniciativa Digital Politècnica. Oficina de Publicacions Acadèmiques Digitals de la UPC eBooks

Quantum computing : problems and exercises

Santiago Torres, P. Bruna, Pietro Massignan

Published Jul 1, 2020• 0 citations
Publisher

Abstract

Quantum technology is one of the most promising and challenging fields in contemporary science. Quantum computing, quantum cryptography, and more generally quantum information technologies claim that they, in the short term, will change our paradigm of classical computing and communications. Concepts such as duality, superposition, entanglement, teleportation and many others seem to be closer to magic or science fiction than to everyday human experience. However, herein lies also the unlimited power of human thought, which mathematics and physics help us to go beyond our immediate experience of the world. This book, oriented toward undergraduate students pursuing Bachelor’s Degrees in Engineering, draws on the experience of the authors during nearly ten years of work in this field. The book consists of a comprehensive list of exercises with increasing degrees of dificulty. Additional material such as solved problems and a basic compilation of theory is also included in each chapter. The list of topics, which include among others, quantum computing, quantum teleportation, superdense coding, quantum processors or quantum communication protocols, intended for opening doors that will motivate students to continue delving into the field of quantum technologies, which has only just begun to be explored.

DOI
10.5821/ebook-9788498808438

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Quantum technology is one of the most promising and challenging fields in contemporary science. Quantum computing, quantum cryptography, and more generally quantum information technologies claim that they, in the short term, will change our paradigm of classical computing and communications. Concepts such as duality, superposition, entanglement, teleportation and many others seem to be closer to magic or science fiction than to everyday human experience. However, herein lies also the unlimited power of human thought, which mathematics and physics help us to go beyond our immediate experience of the world. This book, oriented toward undergraduate students pursuing Bachelor’s Degrees in Engineering, draws on the experience of the authors during nearly ten years of work in this field. The book consists of a comprehensive list of exercises with increasing degrees of dificulty. Additional material such as solved problems and a basic compilation of theory is also included in each chapter. The list of topics, which include among others, quantum computing, quantum teleportation, superdense coding, quantum processors or quantum communication protocols, intended for opening doors that will motivate students to continue delving into the field of quantum technologies, which has only just begun to be explored.
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Quantum Computing The twenty-first century has witnessed remarkable advancements in computing technologies, transforming every aspect of modern society. As conventional computing systems approach their physical and computational limits, the search for new paradigms capable of solving increasingly complex problems has led to the emergence of Quantum Computing. By harnessing the principles of quantum mechanics, quantum computing represents a revolutionary approach that has the potential to redefine computation, communication, and information processing on an unprecedented scale. Quantum Computing is designed to provide readers with a comprehensive understanding of the concepts, principles, technologies, and applications that form the foundation of this rapidly evolving field. This book aims to bridge the gap between theoretical quantum mechanics and practical computational applications, enabling students, researchers, academicians, and professionals to explore the transformative potential of quantum technologies. The chapters in this book cover a broad spectrum of topics, including the fundamentals of quantum mechanics, quantum bits (qubits), quantum gates, superposition, entanglement, quantum circuits, quantum algorithms, quantum cryptography, quantum communication, and quantum error correction. The book also explores the architecture of quantum computers and examines the challenges involved in building scalable and fault-tolerant quantum systems. As industries increasingly seek innovative solutions to complex computational problems, quantum computing is emerging as a promising technology with applications in cryptography, artificial intelligence, machine learning, optimization, financial modeling, healthcare, pharmaceutical research, materials science, logistics, and climate modeling. The ability of quantum computers to process vast amounts of information simultaneously offers opportunities that were previously beyond the reach of classical computing systems. Special attention has been given to contemporary developments in quantum technologies, including quantum supremacy, hybrid quantum-classical computing, cloud-based quantum platforms, and the growing role of quantum computing in scientific discovery and industrial innovation. The book also discusses ethical, security, and societal implications associated with the advancement of quantum technologies. The primary objective of this book is to equip readers with both foundational knowledge and practical insights into the field of quantum computing. Through a balanced presentation of theory, applications, case studies, and emerging research trends, the book seeks to inspire curiosity, innovation, and further exploration in this transformative domain. We extend our sincere gratitude to the authors, reviewers, researchers, academicians, and industry experts whose valuable contributions have enriched the quality and relevance of this publication. Their dedication and expertise have helped create a resource that reflects the latest developments and future possibilities of quantum computing. We hope that Quantum Computing will serve as a valuable guide for students, educators, researchers, and technology professionals seeking to understand the next frontier of computational science. May this book inspire new ideas, foster innovation, and contribute to the advancement of knowledge in one of the most exciting technological revolutions of our time. Mr. M. Rajeshkumar Dr. R. Mariappan Mr. E.Janakiraman,
Important concepts from the diverse fields of physics, mathematics, engineering and computer science coalesce in this foundational text on the cutting-edge field of quantum information. Designed for undergraduate and graduate students with any STEM background, and written by a highly experienced author team, this textbook draws on quantum mechanics, number theory, computer science technologies, and more, to delve deeply into learning about qubits, the building blocks of quantum information, and how they are used in quantum computing and quantum algorithms. The pedagogical structure of the chapters features exercises after each section as well as focus boxes, giving students the benefit of additional background and applications without losing sight of the big picture. Recommended further reading and answers to select exercises further support learning. Written in approachable and conversational prose, this text offers a comprehensive treatment of the exciting field of quantum information while remaining accessible to students and researchers within all STEM disciplines.
Important concepts from the diverse fields of physics, mathematics, engineering and computer science coalesce in this foundational text on the cutting-edge field of quantum information. Designed for undergraduate and graduate students with any STEM background, and written by a highly experienced author team, this textbook draws on quantum mechanics, number theory, computer science technologies, and more, to delve deeply into learning about qubits, the building blocks of quantum information, and how they are used in quantum computing and quantum algorithms. The pedagogical structure of the chapters features exercises after each section as well as focus boxes, giving students the benefit of additional background and applications without losing sight of the big picture. Recommended further reading and answers to select exercises further support learning. Written in approachable and conversational prose, this text offers a comprehensive treatment of the exciting field of quantum information while remaining accessible to students and researchers within all STEM disciplines.
This book introduces quantum computing and quantum communications at the undergraduate level for students in the physical sciences, engineering, and mathematics, assuming no prior knowledge of quantum mechanics. It is a self-contained guide assuming only that the reader is familiar with physics at the college level, calculus (up to and including ordinary differential equations), and some matrix algebra and complex numbers. The book brings the reader up to speed with fundamental concepts in quantum information processing and builds a working knowledge of basic quantum algorithms, quantum error correction, and quantum communication protocols. It covers various models of quantum computation and some of the most common physical realizations of qubits. There is a good number of practice problems and exercises that rely on computer programming with the Qiskit language. The book can be used to prepare students of physics, mathematics, electrical and computer engineering, computer science, optics and photonics, and mathematics for internships and research experiences in quantum information processing, both during and after their undergraduate studies. It also helps those who plan to apply to graduate school and do research in this area. Key Features: Self-contained coverage of quantum computing and quantum communications, from the motivations to the fundamentals and applications, including key concepts and contemporary topics. Contains practice problems and exercises, including some that require programming in Qiskit (the python-based, high-level language for programming quantum computers, adopted by nearly all quantum hardware providers and completely open source). Very light background knowledge assumed, making this book accessible to a variety of majors in the natural sciences, engineering, and mathematics.
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.