Principles of Quantum Computation and Information, Volume 1

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World Scientific, 2004 - Mathematics - 256 pages
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Quantum computation and information is a new, rapidly developing interdisciplinary field. Therefore, it is not easy to understand its fundamental concepts and central results without facing numerous technical details. This book provides the reader a useful and not-too-heavy guide. It offers a simple and self-contained introduction; no previous knowledge of quantum mechanics or classical computation is required.Volume I may be used as a textbook for a one-semester introductory course in quantum information and computation, both for upper-level undergraduate students and for graduate students. It contains a large number of solved exercises, which are an essential complement to the text, as they will help the student to become familiar with the subject. The book may also be useful as general education for readers who want to know the fundamental principles of quantum information and computation and who have the basic background acquired from their undergraduate course in physics, mathematics, or computer science.
 

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Contents

Introduction
1
Introduction to Classical Computation
9
111 Addition on a Turing machine
12
112 The ChurchTuring thesis
13
113 The universal Turing machine
14
115 The halting problem
15
121 Binary arithmetics
17
123 Universal classical computation
22
37 Function evaluation
132
38 The quantum adder
137
39 Deutschs algorithm
140
391 The DeutschJozsa problem
141
392 An extension of Deutschs algorithm
143
310 Quantum search
144
3101 Searching one item out of four
145
3102 Searching one item out of N
148

13 Computational complexity
24
131 Complexity classes
27
132 The Chernoff bound
30
141 Deterministic chaos
31
142 Algorithmic complexity
33
15 Energy and information
35
152 Londoners principle
37
153 Extracting work from information
40
16 Reversible computation
41
161 Toffoli and Fredkin gates
43
162 The billiardball computer
45
17 A guide to the bibliography
47
Introduction to Quantum Mechanics
49
21 The SternGerlach experiment
50
22 Youngs doubleslit experiment
53
23 Linear vector spaces
57
24 The postulates of quantum mechanics
76
25 The EPR paradox and Bells inequalities
88
26 A guide to the bibliography
97
Quantum Computation
99
31 The qubit
100
311 The Bloch sphere
102
312 Measuring the state of a qubit
103
32 The circuit model of quantum computation
105
33 Singlequbit gates
108
331 Rotations of the Bloch sphere
110
34 Controlled gates and entanglement generation
112
341 The Bell basis
118
351 Preparation of the initial state
127
36 Unitary errors
130
3103 Geometric visualization
149
311 The quantum Fourier transform
152
312 Quantum phase estimation
155
313 Finding eigenvalues and eigenvectors
158
314 Period finding and Shors algorithm
161
315 Quantum computation of dynamical systems
164
3152 The quantum bakers map
168
3153 The quantum sawtooth map
170
3154 Quantum computation of dynamical localization
174
316 First experimental implementations
178
3161 Elementary gates with spin qubits
179
3162 Overview of the first implementations
181
317 A guide to the bibliography
185
Quantum Communication
189
411 The Vernam cypher
190
412 The publickey crypto system
191
413 The RSA protocol
192
42 The nocloning theorem
194
421 Fasterthanlight transmission of information?
197
43 Quantum cryptography
198
431 The BB84 protocol
199
432 The E91 protocol
202
44 Dense coding
205
45 Quantum teleportation
208
46 An overview of the experimental implementations
213
47 A guide to the bibliography
214
Solutions to the exercises
215
Bibliography
241
Index
253
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