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E-grāmata: Fundamentals Of Quantum Information

(Kansai Univ, Japan), (Univ Of Aizu, Japan)
  • Formāts: 268 pages
  • Izdošanas datums: 04-Nov-2010
  • Izdevniecība: World Scientific Publishing Co Pte Ltd
  • Valoda: eng
  • ISBN-13: 9789813107984
  • Formāts - PDF+DRM
  • Cena: 21,41 €*
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  • Formāts: 268 pages
  • Izdošanas datums: 04-Nov-2010
  • Izdevniecība: World Scientific Publishing Co Pte Ltd
  • Valoda: eng
  • ISBN-13: 9789813107984

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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.
Preface v
1 Introduction
1(6)
2 Mathematical Realization of Quantum Mechanics
7(12)
2.1 State vector
7(4)
2.2 Operator
11(2)
2.3 Time evolution of wave function
13(1)
2.4 Eigenvalue and eigenstate of Hamiltonian
14(3)
2.5 Problems
17(2)
3 Basic Concepts of Quantum Mechanics
19(18)
3.1 Wave function and probability interpretation
19(1)
3.2 Commutation relation and uncertainty relation
20(3)
3.3 Quantum states of spin 1/2 particles
23(5)
3.4 Quantum bit
28(1)
3.5 Angular momentum, spin and rotation
29(6)
3.6 Problems
35(2)
4 EPR Pair and Measurement
37(28)
4.1 EPR pair
37(2)
4.2 Transmission of quantum states
39(2)
4.3 Einstein's locality principle in quantum mechanics
41(5)
4.4 Measurement of two correlated particles and hidden variable theorem
46(8)
4.4.1 CHSH inequality
46(5)
4.4.2 Classical correlation vs. quantal correlation: a case of nuclear fission
51(3)
4.5 EPR experiment by photon pairs
54(5)
4.6 Four-photon GHZ states
59(4)
4.7 Problems
63(2)
5 Classical Computers
65(24)
5.1 Turing machine
65(5)
5.2 von Neumann computer
70(1)
5.3 Possibility and complexity of computation
71(7)
5.3.1 Arithmetic operations
72(1)
5.3.2 Factorization and decision of prime numbers
73(1)
5.3.3 Combination problem
74(4)
5.3.4 Computational complexity and amount of computation
78(1)
5.4 Logic gates
78(2)
5.5 Logic circuits
80(3)
5.6 Sequential circuit, and memory
83(5)
5.7 Problem
88(1)
6 Quantum Gates
89(18)
6.1 Quantum gates
90(5)
6.2 Controlled-operation gates
95(6)
6.3 Quantum Turing machine
101(1)
6.4 Quantum Fourier transformation (3 bit case)
102(3)
6.5 Problems
105(2)
7 Theory of Information and Communication
107(14)
7.1 Shannon entropy
107(6)
7.1.1 Amount of information
107(1)
7.1.2 Entropy
108(2)
7.1.3 Coding information
110(3)
7.1.4 Von Neumann entropy
113(1)
7.2 Transmission error in communication
113(6)
7.2.1 Errors and channel capacity
113(3)
7.2.2 Shannon's theorem
116(3)
7.3 Problem
119(2)
8 Quantum Computation
121(24)
8.1 Quantum bit and quantum register
122(3)
8.2 Deutsch-Jozsa algorithm
125(2)
8.3 Shor's factorization algorithm
127(3)
8.4 Quantum Fourier transformation with n bits
130(3)
8.5 Quantum phase estimation and order finding algorithm
133(8)
8.6 Calculation of modular exponentials
141(2)
8.7 Problems
143(2)
9 Quantum Cryptography
145(24)
9.1 Secret key cryptography
145(2)
9.2 "One-time pad" cryptography
147(1)
9.3 Public key cryptography
148(5)
9.4 Quantum key distribution
153(14)
9.4.1 Non-cloning theorem
154(1)
9.4.2 BB84 protocol
155(6)
9.4.3 B92 protocol
161(1)
9.4.4 E91 protocol
162(5)
9.5 Problems
167(2)
10 Quantum Search Algorithm
169(12)
10.1 Oracle function
170(1)
10.2 Quantum oracle
170(10)
10.3 Problem
180(1)
11 Physical Devices of Quantum Computers
181(36)
11.1 Nuclear magnetic resonance (NMR) computers
182(14)
11.1.1 Principles of NMR computers
182(2)
11.1.2 NMR and spin rotations
184(4)
11.1.3 Statistical treatment
188(3)
11.1.4 Experiment of quantum factorization
191(5)
11.2 Ion trap computers
196(12)
11.2.1 Basic principles
196(1)
11.2.2 Ion trap
196(7)
11.2.3 Computation
203(1)
11.2.4 Preparation of the initial states
204(1)
11.2.5 Reading results
205(1)
11.2.6 Example of quantum gate
206(2)
11.3 Quantum dot computer
208(7)
11.3.1 Principle
208(7)
11.4 Problem
215(2)
Appendix A Basic Theory of Numbers
217(18)
A.1 Congruence
217(4)
A.2 Euler's theorem (Fermat's little theorem)
221(3)
A.3 Euclid's algorithm
224(1)
A.4 Diophantus equation (Indeterminate equation)
225(2)
A.5 Chinese remainder theorem
227(3)
A.6 Continued fractions
230(5)
Appendix B Solutions of Problems
235(14)
Bibliography 249(2)
Index 251