Quantum Computation and Quantum Communication: (eBook)

Theory and Experiments

Mladen Pavicic (Autor)

eBook Download: PDF

2007 | 2006
XVI, 223 Seiten
Springer US (Verlag)
978-0-387-28900-7 (ISBN)

Infos

The field of quantum computing has experienced rapid development and many different experimental and theoretical groups have emerged worldwide.This book presents the key elements of quantum computation and communication theories and their implementation in an easy-to-read manner for readers coming from physics, mathematics and computer science backgrounds. Integrating both theoretical aspects and experimental verifications of developing quantum computers, the author explains why particular mathematical methods, physical models and realistic implementations might provide critical steps towards achieving the final goal - constructing quantum computers and quantum networks. The book serves as an excellent introduction for new researchers and also provides a useful review for specialists in the field

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The attraction of quantum computation and quantum communica- tion theory and experiments hes in the fact that we engineer both them themselves and the quantum systems they treat. This approach has turned out to be very resiUent. Driven by the final goal of calculating exponentially faster and communicating infinitely more securely than we do today, as soon as we encounter a limitation in either a theory or experiment, a new idea around the no-go emerges. As soon as the decoherence "e;demon"e; threatened the first computation models, quan- tum error correction theory was formulated and applied not only to computation theory but also to communication theory to make it un- conditionally secure. As soon as liquid-state nuclear magnetic resonance experiments started to approach their limits, solid-based nuclear spin experiments-the Kane computer-came in. As soon as it was proved that it is theoretically impossible to completely distinguish photon Bell states, three new approaches appeared: hyperentanglement, the use of continuous variables, and the Knill-Laflamme-Milburn proposal. There are many more such examples. What facilitated all these breakthroughs is the fact that at the present stage of development of quantum computation and communication, we deal with elementary quantum systems consisting of several two-level systems. The complexity of handling and controlHng such simple sys- tems in a laboratory has turned out to be tremendous, but the basic physical models we follow and calculate for the systems themselves are not equally intricate.

Inhalt

Contents 6
Preface 8
Acknowledgments 10
Chapter 1 BITS AND QUBITS: THEORY AND ITS IMPLEMENTATION 15
1.1 The Turing Machine vs. a Computing Machine 15
1.2 Definition of a Turing Machine 16
1.3 Turing Computability 18
1.4 Bit Computability: Boolean Algebra 21
1.5 Bit Implementation: Transistors and Their Limits 23
1.6 Irreversible Bits: Logic Gates 26
1.7 Reversible Gates 28
1.8 Quantum Bits: Qubits 31
1.9 Flying Qubits and Circular Polarization 34
1.10 Superposition of Qubits 36
1.11 Bra—Ket Qubit Formalism 38
1.13 Detecting Qubits 41
1.14 Quantum Gates and Circuits 43
1.15 Qubit Computation and E- Business 45
1.16 Numbers and Bits 50
1.17 Entangled Qubits 53
1.18 General Single Qubit Formalism 59
1.19 Other Qubits and Universal Gates 65
1.20 Teleportation of Copies and the No- Cloning Theorem 70
1.21 Quantum Cryptography 78
1.22 Quantum Error Correction 86
1.23 Unconditional Security of Quantum Cryptography 95
Chapter 2 EXPERIMENTS 100
2.1 Technological Candidates for Quantum Computers 100
2.2 Zeeman Effects 101
2.3 Liquid- State Nuclear Magnetic Resonance 107
2.4 Silicon- Based Nuclear Spins 112
2.5 Ion Traps 122
2.6 Future Experiments 136
2.7 Quantum Communication Implementation 138
Chapter 3 PERSPECTIVES 147
3.1 Quantum Network 149
3.2 Quantum- Classical Coupling 171
3.3 Quantum Algorithms 185
3.4 Quantum Turing Machines vs. Quantum Algebra 202
References 210
Index 222

Produkt-Details

• Erscheint lt. Verlag: 15.1.2007
• Zusatzinfo: XVI, 223 p.
• Verlagsort: New York
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik ► Theorie / Studium
• Themenwelt: Mathematik / Informatik ► Mathematik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
• Themenwelt: Technik ► Maschinenbau
• Themenwelt: Technik ► Nachrichtentechnik
• Schlagworte: Communication • Quantum Communication • quantum computer • Quantum Computing • quantum network • Qubit
• ISBN-10: 0-387-28900-3 / 0387289003
• ISBN-13: 978-0-387-28900-7 / 9780387289007