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Fundamentals Of Quantum Information (Extended Edition) Extended ed. [Hardback]

(Univ Of Aizu, Japan), (Kansai Univ, Japan)
  • Formāts: Hardback, 312 pages
  • Izdošanas datums: 05-Oct-2020
  • Izdevniecība: World Scientific Publishing Co Pte Ltd
  • ISBN-10: 9811227217
  • ISBN-13: 9789811227219
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  • Cena: 93,73 €
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  • Formāts: Hardback, 312 pages
  • Izdošanas datums: 05-Oct-2020
  • Izdevniecība: World Scientific Publishing Co Pte Ltd
  • ISBN-10: 9811227217
  • ISBN-13: 9789811227219
Citas grāmatas par šo tēmu:
Sagawa and Yoshida update their textbook to account for the significant changes in quantum information during the previous decade, including quantum computers based on a different concept, new algorithms, and a growth in the scale of computing power that has had qualitative as well as quantitative implications. Their topics include the mathematical realization of quantum mechanics, basic concepts of quantum mechanics, quantum gates, theory of information and communication, quantum cryptography, physical devices of quantum computers, and quantum annealing. Annotation ©2020 Ringgold, Inc., Portland, OR (protoview.com)

This expanded version to the 2010 edition features quantum annealing algorithm and its application for optimization problems. Recent progress on quantum computing, especially, advanced topics such as Shor's algorithm, quantum search, quantum cryptography and architecture of quantum bit are also included.Book is self-contained and unified in its description of the cross-disciplinary nature of this field. It is not strictly mathematical, but aims to provide intuitive and transparent ideas of the subjects. The book starts from basic quantum mechanics and EPR pair and its measurements. Fundamental concepts of classical computer are given in order to extend it to quantum computer. Classical information theory is also explained in detail such as Shannon and Von Neumann entropy. Then quantum algorithm is introduced starting from Dutch-Josza and ending up with Shor's factorization algorithms. Quantum cryptography is also introduced such as BB84 Protocol, B92 protocol and E91 protocol. Eventually quantum search algorithm is explained.In summary, the book starts from basic quantum mechanics and eventually comes up to state-of-the art quantum algorithm of quantum computations and computers. Students can obtain practical problem-solving ability by attempting the exercises at the end of each chapter. Detailed solutions to all problems are provided.
Preface v
Preface vii
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(2)
9.4.4 E91 protocol
163(4)
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 Problems
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(11)
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(1)
11.3 Quantum dot computer
207(8)
11.3.1 Principle
208(7)
11.4 Problems
215(2)
12 Quantum Annealing
217(32)
12.1 What is the quantum annealing?
217(5)
12.2 Formulation of quantum annealing
222(8)
12.2.1 A case in which the Hamiltonians H0 and H1 do not depend on the time
222(3)
12.2.2 The wave function of the time-dependent Hamiltonian
225(2)
12.2.3 Adiabatic approximation
227(3)
12.3 Quantum search problems
230(2)
12.4 The Ising model
232(10)
12.4.1 What is the Ising model?
232(2)
12.4.2 Application to quantum computers
234(1)
12.4.3 Optimization by the quantum annealing
235(1)
12.4.4 Application to the traveling salesman problem (TSP)
236(6)
12.5 Construction of the quantum annealing computer
242(5)
12.5.1 Parameter control in the quantum annealing
243(1)
12.5.2 Hardware structure
244(3)
12.6 Problems
247(2)
Appendix A Basic Theory of Numbers
249(18)
A.1 Congruence
249(4)
A.2 Euler's theorem (Fermat's little theorem)
253(3)
A.3 Euclid's algorithm
256(1)
A.4 Diophantus equation (Indeterminate equation)
257(2)
A.5 Chinese remainder theorem
259(3)
A.6 Continued fractions
262(5)
Appendix B Solutions of Problems
267(24)
Bibliography 291(2)
Index 293