This book aims to provide a pedagogical introduction to the subjects of quantum information and quantum computation. Topics include non-locality of quantum mechanics, quantum computation, quantum cryptography, quantum error correction, fault-tolerant quantum computation as well as some experimental aspects of quantum computation and quantum cryptography. Only knowledge of basic quantum mechanics is assumed. Whenever more advanced concepts and techniques are used, they are introduced carefully. This book is meant to be a self-contained overview. While basic concepts are discussed in detail, unnecessary technical details are excluded. It is well-suited for a wide audience ranging from physics graduate students to advanced researchers.This book is based on a lecture series held at Hewlett-Packard Labs, Basic Research Institute in the Mathematical Sciences (BRIMS), Bristol from November 1996 to April 1997, and also includes other contributions.

Unlock the Potential of Quantum Computing This expertly crafted guide demystifies the complexities of quantum computing through a progressive teaching method, making it accessible to students and newcomers alike. Features Explores quantum systems, gates and circuits, entanglement, algorithms, and more. Unique 'scaffolding approach' for easy understanding. Ideal for educators, students, and self-learners. Authors Dr. Peter Y. Lee (Ph.D., Princeton University) – Expert in quantum nanostructures, extensive teaching experience. Dr. Huiwen Ji (Ph.D., Princeton University) – Solid background in quantum chemistry, award-winning researcher. Dr. Ran Cheng (Ph.D., University of Texas at Austin) – Specializes in condensed matter theory, award-winning physicist.

This book presents written versions of the eight lectures given during the AMS Short Course held at the Joint Mathematics Meetings in Washington, D.C. The objective of this course was to share with the scientific community the many exciting mathematical challenges arising from the new field of quantum computation and quantum information science. The course was geared toward demonstrating the great breadth and depth of this mathematically rich research field. Interrelationships withexisting mathematical research areas were emphasized as much as possible. Moreover, the course was designed so that participants with little background in quantum mechanics would, upon completion, be prepared to begin reading the research literature on quantum computation and quantum informationscience. Based on audience feedback and questions, the written versions of the lectures have been greatly expanded, and supplementary material has been added. The book features an overview of relevant parts of quantum mechanics with an introduction to quantum computation, including many potential quantum mechanical computing devices; introduction to quantum algorithms and quantum complexity theory; in-depth discussion on quantum error correcting codes and quantum cryptography; and finally,exploration into diverse connections between quantum computation and various areas of mathematics and physics.

A thorough exposition of quantum computing and the underlying concepts of quantum physics, with explanations of the relevant mathematics and numerous examples. The combination of two of the twentieth century's most influential and revolutionary scientific theories, information theory and quantum mechanics, gave rise to a radically new view of computing and information. Quantum information processing explores the implications of using quantum mechanics instead of classical mechanics to model information and its processing. Quantum computing is not about changing the physical substrate on which computation is done from classical to quantum but about changing the notion of computation itself, at the most basic level. The fundamental unit of computation is no longer the bit but the quantum bit or qubit. This comprehensive introduction to the field offers a thorough exposition of quantum computing and the underlying concepts of quantum physics, explaining all the relevant mathematics and offering numerous examples. With its careful development of concepts and thorough explanations, the book makes quantum computing accessible to students and professionals in mathematics, computer science, and engineering. A reader with no prior knowledge of quantum physics (but with sufficient knowledge of linear algebra) will be able to gain a fluent understanding by working through the book.

A computer is a piece of hardware that aids in the processing of information by carrying out preprogrammed instructions. One definition of an algorithm is "a procedure that is well-defined and has a finite description for realizing an information-processing task." There is always the possibility of converting an information processing job into a physical one. Working with an idealized computer model may be highly beneficial and is often even necessary when developing sophisticated algorithms and protocols for a variety of information processing jobs. Nevertheless, it is essential to keep in mind the connection between computing and physics whenever one is researching the actual constraints imposed by a piece of computer equipment, particularly when doing so for some kind of useful purpose. The idealized computing model fails to account for the fact that actual computing equipment is embedded in a broader and often more complex physical environment than is shown in the model. Quantum information processing refers to the application of what we learn about the physical world from quantum theory to the objective of carrying out activities that were previously regarded to be either impossible or infeasible. This type of processing was thought to be either impossible or infeasible. Because of this, things that were before thought to be impossible or impossible to achieve are now within reach. Quantum computers are defined as any computers that have the capability of processing quantum information. In this book, we investigate how quantum computers can be used to execute specific tasks more quickly than conventional computers can, as well as how they may be used safely even when errors are likely in the work they are performing. In addition, we analyze the benefits that quantum computers have over conventional computers in terms of the ability to resolve certain categories of problems. The next chapters will expand upon the basis provided in this first chapter by presenting more complex subjects in computation theory and quantum physics. This will be done by building upon the foundation laid in this chapter.

Since the 1980s research on quantum computation has dramatically changed the theoretical perspectives of computer science. Quantum computers could enable unprecedented computational power and revolutionize our cryptographic systems, even our entire electronic communication. This textbook gives an introduction to the theory of quantum computation. The author has chosen an elementary and lean theoretical approach, presupposing mathematical and physical knowledge which is standard in undergraduate courses of scientific or engineering studies, in essence linear algebra and complex numbers. The necessary mathematical notions are given in the appendix. Contents - Strange quantum world, qubits und quantum gates - Quantum Fourier transformation and QFT algorithms - Quantum search, quantum communication, error correcting quantum codes - How to build and simulate a quantum computer - Density operators and measurements - Complexity theory and quantum logic Who should read this book? - Students of engineering, especially electronic engineering - Students of computer science, physics, or mathematics - Practitioners in business and economy who want to understand, apply, or evaluate this new technology

We introduce refined concepts for neutrosophic quantum computing such as neutrosophic quantum states and transformation gates, neutrosophic Hadamard matrix, coherent and decoherent superposition states, entanglement and measurement notions based on neutrosophic quantum states. We also give some observations using these principles. We present a number of quantum computational matrix transformations based on neutrosophic logic and clarify quantum mechanical notions relying on neutrosophic states. The paper is intended to extend the work of Smarandache by introducing a mathematical framework for neutrosophic quantum computing and presenting some results.

This book provides a general survey of the main concepts, questions and results that have been developed in the recent interactions between quantum information, quantum computation and logic. Divided into 10 chapters, the books starts with an introduction of the main concepts of the quantum-theoretic formalism used in quantum information. It then gives a synthetic presentation of the main “mathematical characters” of the quantum computational game: qubits, quregisters, mixtures of quregisters, quantum logical gates. Next, the book investigates the puzzling entanglement-phenomena and logically analyses the Einstein–Podolsky–Rosen paradox and introduces the reader to quantum computational logics, and new forms of quantum logic. The middle chapters investigate the possibility of a quantum computational semantics for a language that can express sentences like “Alice knows that everybody knows that she is pretty”, explore the mathematical concept of quantum Turing machine, and illustrate some characteristic examples that arise in the framework of musical languages. The book concludes with an analysis of recent discussions, and contains a Mathematical Appendix which is a survey of the definitions of all main mathematical concepts used in the book.

ONE-VOLUME INTRODUCTION TO QUANTUM COMPUTING Clearly explains core concepts, terminology, and techniques Covers the foundational physics, math, and information theory you need Provides hands-on practice with quantum programming The perfect beginner's guide for anyone interested in a quantum computing career Dr. Chuck Easttom brings together complete coverage of basic quantum computing concepts, terminology, and issues, along with key skills to get you started. Drawing on 30+ years as a computer science instructor, consultant, and researcher, Easttom demystifies the field's underlying technical concepts and math, shows how quantum computing systems are designed and built, explains their implications for cyber security, and previews advances in quantum-resistant cryptography. Writing clearly and simply, he introduces two of today's leading quantum programming languages, Microsoft Q# and QASM, and guides you through sample projects. Throughout, tests, projects, and review questions help you deepen and apply your knowledge. Whether you're a student, professional, or manager, this guide will prepare you for the quantum computing revolution--and expand your career options, too. Master the linear algebra and other mathematical skills you'll need Explore key physics ideas such as quantum states and uncertainty Review data structures, algorithms, and computing complexity Work with probability and set theory in quantum computing Familiarize yourself with basic quantum theory and formulae Understand quantum entanglement and quantum key distribution Discover how quantum computers are architected and built Explore several leading quantum algorithms Compare quantum and conventional asymmetric algorithms See how quantum computing might break traditional cryptography Discover several approaches to quantum-resistant cryptography Start coding with Q#, Microsoft's quantum programming language Simulate quantum gates and algorithms with QASM

Quantum computers are machines that use the properties of quantum physics to store data and perform computations. This can be extremely advantageous for certain tasks where they could vastly outperform even our best supercomputers. Classical computers, which include smartphones and laptops, encode information in binary “bits” that can either be 0s or 1s. In a quantum computer, the basic unit of memory is a quantum bit or qubit. Qubits are made using physical systems, such as the spin of an electron or the orientation of a photon. These systems can be in many different arrangements all at once, a property known as quantum superposition. Qubits can also be inextricably linked together using a phenomenon called quantum entanglement. The result is that a series of qubits can represent different things simultaneously. For instance, eight bits is enough for a classical computer to represent any number between 0 and 255. But eight qubits is enough for a quantum computer to represent every number between 0 and 255 at the same time. A few hundred entangled qubits would be enough to represent more numbers than there are atoms in the universe. This is where quantum computers get their edge over classical ones. In situations where there are a large number of possible combinations, quantum computers can consider them simultaneously. Examples include trying to find the prime factors of a very large number or the best route between two places. However, there may also be plenty of situations where classical computers will still outperform quantum ones. So the computers of the future may be a combination of both these types. For now, quantum computers are highly sensitive: heat, electromagnetic fields and collisions with air molecules can cause a qubit to lose its quantum properties. This process, known as quantum decoherence, causes the system to crash, and it happens more quickly the more particles that are involved. Quantum computers need to protect qubits from external interference, either by physically isolating them, keeping them cool or zapping them with carefully controlled pulses of energy. Additional qubits are needed to correct for errors that creep into the system.