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### Summary

### Summary

As miniaturisation deepens, and nanotechnology and its machines become more prevalent in the real world, the need to consider using quantum mechanical concepts to perform various tasks in computation increases. Such tasks include: the teleporting of information, breaking heretofore "unbreakable" codes, communicating with messages that betray eavesdropping, and the generation of random numbers. This is the first book to apply quantum physics to the basic operations of a computer, representing the ideal vehicle for explaining the complexities of quantum mechanics to students, researchers and computer engineers, alike, as they prepare to design and create the computing and information delivery systems for the future. Both authors have solid backgrounds in the subject matter at the theoretical and more practical level. While serving as a text for senior/grad level students in computer science/physics/engineering, this book has its primary use as an up-to-date reference work in the emerging interdisciplinary field of quantum computing - the only prerequisite being knowledge of calculus and familiarity with the concept of the Turing machine.

### Author Notes

Colin P. Williams is a Principal Scientist and Manager of the Quantum Algorithms and Technologies Group at the Jet Propulsion Laboratory, California Institute of Technology.

### Reviews 1

### Choice Review

Einstein did not believe it, Feynman said no one understands it, but by wide consensus quantum mechanics now ranks as the most successful and precise physical theory in history. For nearly a century, quantum mechanics has suffered a split personality as the Dr. Jekyll of epoch-making applications (like semiconductors and lasers) and the Mr. Hyde of pathological paradoxes (like Schr"odinger's Cat and EPR). Suddenly, the brink of a new century brings the prospect of a radical merger of these two personalities; the twisted logic of the supposed paradoxes has reinvented itself as the very foundation and essence of spectacular emerging technologies. P. Shor's stunning (as yet unimplemented) quantum computer algorithm for factoring large composite integers represents the paradigmatic theoretical result and the 1998 Chuang-Gershenfeld-Kubinec NMR quantum computer the first actual working prototype. The first of its type, this book by Williams (computer science, Stanford Univ.) and consultant Clearwater explains all the breaking news for nonspecialists but includes enough fine detail to gratify more knowledgeable readers as well. Highly recommended for all libraries. Upper-division undergraduates and up. D. V. Feldman; University of New Hampshire

### Table of Contents

Preface | p. xi |

Chapter 1 Computing at the Edge of Nature | p. 1 |

Rethinking Computers | |

Shrinking Technology | |

A Peek Into Quantumland | |

The Qubit: Ultimate Zero and One | |

Are Bits Driving Us Bankrupt? | |

An Overview of This Book | |

Chapter 2 Quantum Computing | p. 23 |

Tricks of the Trade | |

Quantum Memory Registers | |

The prepare--evolve--measure Cycle | |

Quantum Gates and Quantum Circuits | |

Example of a Quantum Computation | |

Summary | |

Chapter 3 What Can Computers Do? | p. 45 |

The Turing Machine | |

Quantum Turing Machines | |

Universality | |

Computability | |

Proving versus Providing Proof | |

Complexity | |

Searching a Quantum Phone Book | |

Chapter 4 Breaking "Unbreakable" Codes | p. 89 |

The Art of Concealment | |

Encryption Schemes | |

Public Key Cryptography | |

Code Breaking on a Classical Computer | |

Code Breaking on a Quantum Computer | |

Example Trace of Shor's Algorithm | |

Summary | |

Chapter 5 The Crapshoot Universe | p. 117 |

The Concept of Randomness | |

Uses of Random Numbers | |

Does Randomness Exist in Nature? | |

Pseudorandomness: The Art of Faking It | |

The Plague of Correlations | |

Randomness and Quantum Computers | |

Chapter 6 The Keys to Quantum Secrets | p. 143 |

Some Underlying Concepts | |

Polarization | |

Quantum Cryptography with Polarized Photons | |

Working Prototypes | |

Other Approaches to Quantum Cryptography | |

Chapter 7 Teleportation: The Ultimate Ticket to Ride | p. 157 |

Factorizable Quantum States | |

Entanglement: Non-factorizable States | |

Spooky Action at a Distance | |

Bell's Inequality | |

Locality: For Whom the Bell Tolls | |

Quantum Teleportation | |

Working Prototypes | |

Chapter 8 Swatting Quantum Bugs | p. 173 |

Laissez-Faire | |

Error Correction | |

Fault-Tolerant Computing | |

Topological Quantum Computing | |

Chapter 9 Generation-Q Computing: Where Do You Want to Go Tomorrow? | p. 191 |

Quantum Conditional Logic | |

Ion Traps | |

"Flying Qubit"--Based Quantum Computers | |

NMR | |

The Kane Mutiny | |

Summary | |

Chapter 10 It Is Now Safe to Turn Off Your Quantum Computer | p. 217 |

Quantum Interferometry: It's All Done with Mirrors! | |

Quantum Bomb-Testing | |

Counterfactual Computing: Computing Without Computing | |

Epilogue: Quantum Technologies in the Twenty-First Century | p. 233 |

References | p. 237 |

Index | p. 247 |