Fundamentals of Quantum Information
by Sagawa, Hiroyuki; Yoshida, nobuakiFormat: Hardcover
Pub. Date: 2010-07-12
Publisher(s): Textstream
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Summary
This book provides an introduction to the basic ideas and concepts of quantum computation and information for both undergraduate and graduate students. The book starts with the quantum bits and the entangled states which turn out to bring revolutionary ideas in information theory. This book is self-contained and unified in its description of the cross-disciplinary nature of this field. The book aims to provide intuitive and transparent ideas of the subjects, and is not strictly mathematical. Quantum mechanics and mathematical tools (especially, number theory) are explained with many examples and illustrations. The students can obtain practical problem-solving ability by solving the exercises at the end of each chapter. Detailed solutions to all problems are provided at the end of the book.
Table of Contents
| Preface | p. v |
| Introduction | p. 1 |
| Mathematical Realization of Quantum Mechanics | p. 7 |
| State vector | p. 7 |
| Operator | p. 11 |
| Time evolution of wave function | p. 13 |
| Eigenvalue and eigenstate of Hamiltonian | p. 14 |
| Problems | p. 17 |
| Basic Concepts of Quantum Mechanics | p. 19 |
| Wave function and probability interpretation | p. 19 |
| Commutation relation and uncertainty relation | p. 20 |
| Quantum states of spin ½ particles | p. 23 |
| Quantum bit | p. 28 |
| Angular momentum, spin and rotation | p. 29 |
| Problems | p. 35 |
| EPR Pair and Measurement | p. 37 |
| EPR pair | p. 37 |
| Transmission of quantum states | p. 39 |
| Einstein's locality principle in quantum mechanics | p. 41 |
| Measurement of two correlated particles and hidden variable theorem | p. 46 |
| CHSH inequality | p. 46 |
| Classical correlation vs. quantal correlation: a case of nuclear fission | p. 51 |
| EPR experiment by photon pairs | p. 54 |
| Four-photon GHZ states | p. 59 |
| Problems | p. 63 |
| Classical Computers | p. 65 |
| Turing machine | p. 65 |
| von Neumann computer | p. 70 |
| Possibility and complexity of computation | p. 71 |
| Arithmetic operations | p. 72 |
| Factorization and decision of prime numbers | p. 73 |
| Combination problem | p. 74 |
| Computational complexity and amount of computation | p. 78 |
| Logic gates | p. 78 |
| Logic circuits | p. 80 |
| Sequential circuit and memory | p. 83 |
| Problem | p. 88 |
| Quantum Gates | p. 89 |
| Quantum gates | p. 90 |
| Controlled-operation gates | p. 95 |
| Quantum Turing machine | p. 101 |
| Quantum Fourier transformation (3 bit case) | p. 102 |
| Problems | p. 105 |
| Theory of Information and Communication | p. 107 |
| Shannon entropy | p. 107 |
| Amount of information | p. 107 |
| Entropy | p. 108 |
| Coding information | p. 110 |
| Von Neumann entropy | p. 113 |
| Transmission error in communication | p. 113 |
| Errors and channel capacity | p. 113 |
| Shannon's theorem | p. 116 |
| Problem | p. 119 |
| Quantum Computation | p. 121 |
| Quantum bit and quantum register | p. 122 |
| Deutsch-Jozsa algorithm | p. 125 |
| Shor's factorization algorithm | p. 127 |
| Quantum Fourier transformation with n bits | p. 130 |
| Quantum phase estimation and order finding algorithm | p. 133 |
| Calculation of modular exponentials | p. 141 |
| Problems | p. 143 |
| Quantum Cryptography | p. 145 |
| Secret key cryptography | p. 145 |
| "One-time pad" cryptography | p. 147 |
| Public key cryptography | p. 148 |
| Quantum key distribution | p. 153 |
| Non-cloning theorem | p. 154 |
| BB84 protocol | p. 155 |
| B92 protocol | p. 161 |
| E91 protocol | p. 162 |
| Problems | p. 167 |
| Quantum Search Algorithm | p. 169 |
| Oracle function | p. 170 |
| Quantum oracle | p. 170 |
| Problem | p. 180 |
| Physical Devices of Quantum Computers | p. 181 |
| Nuclear magnetic resonance (NMR) computers | p. 182 |
| Principles of NMR computers | p. 182 |
| NMR and spin rotations | p. 184 |
| Statistical treatment | p. 188 |
| Experiment of quantum factorization | p. 191 |
| Ion trap computers | p. 196 |
| Basic principles | p. 196 |
| Ion trap | p. 196 |
| Computation | p. 203 |
| Preparation of the initial states | p. 204 |
| Reading results | p. 205 |
| Example of quantum gate | p. 206 |
| Quantum dot computer | p. 208 |
| Principle | p. 208 |
| Problem | p. 215 |
| Basic Theory of Numbers | p. 217 |
| Congruence | p. 217 |
| Euler's theorem (Fermat's little theorem) | p. 221 |
| Euclid's algorithm | p. 224 |
| Diophantus equation (Indeterminate equation) | p. 225 |
| Chinese remainder theorem | p. 227 |
| Continued fractions | p. 230 |
| Solutions of Problems | p. 235 |
| Bibliography | p. 249 |
| Index | p. 251 |
| Table of Contents provided by Ingram. All Rights Reserved. |
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