Explorations in Quantum Computing

Description

By the year 2020, the basic memory components of a computer will be the size of individual atoms. At such scales, the current theory of computation will become invalid. “Quantum computing” is reinventing the foundations of computer science and information theory in a way that is consistent with quantum physics – the most accurate model of reality currently known. Remarkably, this theory predicts that quantum computers can perform certain tasks exponentially faster than classical computers and, better yet, can accomplish “impossible” feats such as teleporting information, breaking supposedly “unbreakable” codes, generating true random numbers, and communicating with messages that betray the presence of eavesdropping. This widely anticipated second edition of Explorations in Quantum Computing explains the field from a fresh perspective, emphasizing lesser known quantum transforms, and practical applications of quantum algorithms and quantum information theory. The required mathematical machinery is developed systematically, and the students’ knowledge tested through several end-of-chapter exercises. This easy-to-read, time-tested, and comprehensive textbook provides a unique perspective on the capabilities of quantum computers, and supplies readers with the tools necessary to make their own foray into this exciting field. Topics and features: Concludes each chapter with exercises and a summary of the material coveredProvides an introduction to the mathematical formalism of quantum computing, and the quantum effects that can be harnessed to achieve unparalleled new capabilitiesDiscusses the concepts of quantum gates, entangling power, quantum circuits, quantum Fourier, wavelet, and cosine transforms, quantum universality, quantum computability, and quantum complexityExamines the potential applications of quantum computers in areas such as search, code-breaking, solving NP-Complete problems, quantum simulation, quantum chemistry, and mathematicsDescribes uses of quantum information, including quantum teleportation, superdense coding, quantum data compression, quantum cloning, quantum negation, and quantum cryptographyReviews the advancements made towards practical quantum computers covering developments in quantum error correction, quantum error avoidance, and alternative models of quantum computation This text/reference is ideal for anyone wishing to learn more about this incredible, perhaps “ultimate,” computer revolution. Dr. Colin P. Williams is Program Manager for Advanced Computing Paradigms at the NASA Jet Propulsion Laboratory, California Institute of Technology, and formerly acting Associate Professor of Computer Science at Stanford University where he taught courses on quantum computing and quantum information theory, and computer-algebra systems. He has spent over a decade working in quantum computing, and inspiring and leading high technology teams. Today his interests include quantum computing, artificial intelligence, cognitive computing, evolutionary computing, computational material design, computer visualization, and computationally-enabled remote olfaction. He was formerly a Research Scientist at Xerox PARC and a Research Assistant to Prof. Stephen W. Hawking at Cambridge University. Front Matter....Pages I-XXII Front Matter....Pages 1-1 Introduction....Pages 3-49 Quantum Gates....Pages 51-122 Quantum Circuits....Pages 123-199 Quantum Universality, Computability, & Complexity....Pages 201-237 Front Matter....Pages 239-239 Performing Search with a Quantum Computer....Pages 241-262 Code Breaking with a Quantum Computer....Pages 263-292 Solving NP-Complete Problems with a Quantum Computer....Pages 293-318 Quantum Simulation with a Quantum Computer....Pages 319-348 Quantum Chemistry with a Quantum Computer....Pages 349-367 Mathematics on a Quantum Computer....Pages 369-399 Front Matter....Pages 401-401 Quantum Information....Pages 403-482 Quantum Teleportation....Pages 483-505 Quantum Cryptography....Pages 507-563 Front Matter....Pages 565-565 Quantum Error Correction....Pages 567-625 Alternative Models of Quantum Computation....Pages 627-662 Back Matter....Pages 663-717