Explorations in Quantum Computing

1. Front Matter

   Pages I-XXII

   PDF

2. What is Quantum Computing?

   1. Front Matter

      Pages 1-1

      PDF

   2. Introduction

      • Colin P. Williams

      Pages 3-49

   3. Quantum Gates

      • Colin P. Williams

      Pages 51-122

   4. Quantum Circuits

      • Colin P. Williams

      Pages 123-199

   5. Quantum Universality, Computability, & Complexity

      • Colin P. Williams

      Pages 201-237

3. What Can You Do with a Quantum Computer?

   1. Front Matter

      Pages 239-239

      PDF

   2. Performing Search with a Quantum Computer

      • Colin P. Williams

      Pages 241-262

   3. Code Breaking with a Quantum Computer

      • Colin P. Williams

      Pages 263-292

   4. Solving NP-Complete Problems with a Quantum Computer

      • Colin P. Williams

      Pages 293-318

   5. Quantum Simulation with a Quantum Computer

      • Colin P. Williams

      Pages 319-348

   6. Quantum Chemistry with a Quantum Computer

      • Colin P. Williams

      Pages 349-367

   7. Mathematics on a Quantum Computer

      • Colin P. Williams

      Pages 369-399

4. What Can You Do with Quantum Information?

   1. Front Matter

      Pages 401-401

      PDF

   2. Quantum Information

      • Colin P. Williams

      Pages 403-482

   3. Quantum Teleportation

      • Colin P. Williams

      Pages 483-505

   4. Quantum Cryptography

      • Colin P. Williams

      Pages 507-563

5. Towards Practical Quantum Computers

   1. Front Matter

      Pages 565-565

      PDF

   2. Quantum Error Correction

      • Colin P. Williams

      Pages 567-625

   3. Alternative Models of Quantum Computation

      • Colin P. Williams

      Pages 627-662

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 breathtakingly faster than classical computers – and, better yet, can accomplish mind-boggling 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 these burgeoning developments in simple terms, and describes the key technological hurdles that must be overcome to make quantum computers a reality. This easy-to-read, time-tested, and comprehensive textbook provides a fresh 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 covered; provides an introduction to the basic mathematical formalism of quantum computing, and the quantum effects that can be harnessed for non-classical computation; discusses the concepts of quantum gates, entangling power, quantum circuits, quantum Fourier, wavelet, and cosine transforms, and quantum universality, computability, and complexity; examines the potential applications of quantum computers in areas such as search, code-breaking, solving NP-Complete problems, quantum simulation, quantum chemistry, and mathematics; investigates the uses of quantum information, including quantum teleportation, superdense coding, quantum data compression, quantum cloning, quantum negation, and quantum cryptography; reviews the advancements made towards practical quantum computers, covering developments in quantum error correction and 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 CEO of Xtreme Energetics, Inc. an advanced solar energy company. Dr. Williams has taught quantum computing and quantum information theory as an acting Associate Professor of Computer Science at Stanford University. He has spent over a decade inspiring and leading high technology teams and building business relationships with and Silicon Valley companies. Today his interests include terrestrial and Space-based power generation, quantum computing, cognitive computing, computational material design, visualization, artificial intelligence, evolutionary computing, and remote olfaction. He was formerly a Research Scientist at Xerox PARC and a Research Assistant to Prof. Stephen W. Hawking, Cambridge University.

From the reviews of the second edition:

“This book suggests that as computers decrease in scale, we should take a closer look at the relationship between the physical world in which computers live, and the theoretical aspects of what and how they compute. … This book is intended for graduate-level computer science students. … The book includes exercises at the end of each chapter. … The bibliography is extensive, demonstrating that the field has matured somewhat over time.” (William Fahle, ACM Computing Reviews, August, 2011)

“It is a truly impressive object, clearly a labor of love, and I learned a great deal in reading it. … I enjoyed reading this book. … Explorations in quantum computing is a good and useful entry in the growing pedagogical literature on quantum information. It is not the most tightly focused book, but it is full-to-bursting with interesting facts and discussions. The book is well written and interesting, and experts as well as newcomers to the field will enjoy dipping into it.” (Todd A. Brun, Mathematical Reviews, February, 2013)

• NASA Jet Propulsion Lab., California Institute of Technology, Pasadena, USA

  Colin P. Williams