Quantum Approach to Informatics

1. Auflage 2005
ISBN: 978-0-471-73610-3
Verlag: Wiley

Buch, Englisch, 256 Seiten, Format (B × H): 162 mm x 243 mm, Gewicht: 470 g

An essential overview of quantum information

Information, whether inscribed as a mark on a stone tablet or encoded as a magnetic domain on a hard drive, must be stored in a physical object and thus made subject to the laws of physics. Traditionally, information processing such as computation occurred in a framework governed by laws of classical physics. However, information can also be stored and processed using the states of matter described by non-classical quantum theory. Understanding this quantum information, a fundamentally different type of information, has been a major project of physicists and information theorists in recent years, and recent experimental research has started to yield promising results.

Quantum Approach to Informatics fills the need for a concise introduction to this burgeoning new field, offering an intuitive approach for readers in both the physics and information science communities, as well as in related fields. Only a basic background in quantum theory is required, and the text keeps the focus on bringing this theory to bear on contemporary informatics. Instead of proofs and other highly formal structures, detailed examples present the material, making this a uniquely accessible introduction to quantum informatics.

Topics covered include:

- An introduction to quantum information and the qubit
- Concepts and methods of quantum theory important for informatics
- The application of information concepts to quantum physics
- Quantum information processing and computing
- Quantum gates
- Error correction using quantum-based methods/li>
- Physical realizations of quantum computing circuits

A helpful and economical resource for understanding this exciting new application of quantum theory to informatics, Quantum Approach to Informatics provides students and researchers in physics and information science, as well as other interested readers with some scientific background, with an essential overview of the field.

Autoren/Hrsg.

Stenholm, Stig

Suominen, Kalle-Antti

Fachgebiete

• Mathematik | Informatik EDV | Informatik Technische Informatik Quantencomputer, DNA-Computing
• Naturwissenschaften Physik Quantenphysik

Inhaltsverzeichnis

PREFACE ix

1 INTRODUCTION 1
1.1 Background 1
1.2 Quantum Information Unit 3
1.3 Representation of the Qubit 9
1.3.1 Bloch Sphere 9
1.3.2 Poincare Sphere 11
1.4 The Appetizer: Secure Communication 16
1.5 References 18

2 QUANTUM THEORY 20
2.1 Quantum Mechanics 20
2.1.1 Structure of Quantum Theory 20
2.1.2 Quantum Ensembles 29
2.2 Nonlocality of Quantum Mechanics 38
2.2.1 Nonsignaling by Quantum Observations 38
2.2.2 No Cloning of Quantum States 39
2.2.3 Teleportation 42
2.2.4 Bell Inequalities 46
2.2.5 GHZ States and Reality 49
2.3 The Process of Measurement 54
2.3.1 Introducing the Meter 54
2.3.2 Measurement Transformation 56
2.3.3 Observation on Nonorthogonal States 56
2.3.4 Special Cases 59
2.4 Introduction of Irreversibility 61
2.4.1 Master Equation 61
2.4.2 Unraveling the Master Equation 66
2.4.3 Continuous Measurements 68
2.4.4 Completely Positive Maps 69
2.5 References 74

3 QUANTUM COMMUNICATION AND INFORMATION 76
3.1 Classical Communication 76
3.1.1 Information Theory 76
3.1.2 Coding Theory 86
3.2 Quantum Communication 98
3.2.1 Quantum Information 98
3.2.2 Quantum Channel 103
3.2.3 Use of Generalized Measurements 108
3.2.4 Neumark Extension 119
3.3 Distance Between States 121
3.3.1 Trace Distance 121
3.3.2 Fidelity 124
3.3.3 Relative Entropy 126
3.4 References 129

4 QUANTUM COMPUTING 130
4.1 Logic Operations 130
4.1.1 Classical Logic Operations 130
4.1.2 Quantum Logic Functions 133
4.1.3 Simple Quantum Operations 136
4.1.4 The Deutsch Problem 139
4.2 The Computer 141
4.2.1 Classical Universal Computer 141
4.2.2 Computational Complexity 144
4.2.3 Quantum Computer 145
4.2.4 Quantum Computing Circuits 146
4.2.5 Universal Quantum Gates 154
4.2.6 Quantum Measurement Circuit 154
4.2.7 Quantum Fourier Transform 157
4.3 Quantum Algorithms 160
4.3.1 Public Key Code 161
4.3.2 Quantum Factoring Algorithm 163
4.3.3 Quantum Algorithms 167
4.4 Errors in Quantum Computing 175
4.4.1 Types of Errors in Quantum States 175
4.4.2 Quantum Error Correction 180
4.5 Energetics of Quantum Computations 183
4.5.1 Energy Used by a Classical Computer 183
4.5.2 Resetting Energy 186
4.6 References 190

5 PHYSICAL REALIZATION OF QUANTUM INFORMATION PROCESSING 192
5.1 General Considerations 192
5.2 Requirements for Quantum Computers 194
5.3 Logic in Electromagnetic Cavities 197
5.3.1 Cavity Quantum Electrodynamics 197
5.3.2 Conditional Logic 203
5.3.3 Dissipative Processes in Cavity QED 206
5.4 Logic with Ions in Traps 208
5.4.1 Trapping Cool Ions 208
5.4.2 Quantum Logic in an Ion Trap 212
5.4.3 Computing with Hot Ions 216
5.5 Solid-State Systems 217
5.5.1 General Considerations 217
5.5.2 Special Examples 218
5.6 Macromolecules and Optical Lattices 222
5.6.1 Nuclear Spin in Molecules 222
5.6.2 Optical Lattices 226
5.7 Conclusions 226
5.8 References 227

REFERENCES 229
INDEX 235

Über Autor(innen)

STIG STENHOLM, PhD, was Professor of Laser Physics and Quantum Optics at the Royal Institute of Technology, Stockholm, up until his retirement in 2004. He previously held positions at the University of Helsinki and the Academy of Finland. His research interests include laser physics and spectroscopy, quantum optics, laser-induced atomic and molecular processes, quantum information, and quantum dynamics.

KALLE-ANTTI SUOMINEN, PhD, is Professor of Physics at the University of Turku in Finland. He previously worked at the Helsinki Institute of Physics and the University of Oxford. His current research concentrates on field-induced quantum dynamics in atomic and molecular systems, cold atomic collisions, and Bose-Einstein condensates of atoms and molecules.