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More About This Textbook
Overview
Building on the basic concepts introduced in Vol I, this second volume deals with various important aspects, both theoretical and experimental, of quantum computation and information in depth. The areas include quantum data compression, accessible information, entanglement concentration, limits to quantum computation due to decoherence, quantum error-correction, and the first experimental implementations of quantum information protocols. This volume also includes a selection of special topics: chaos and quantum to classical transition, quantum trajectories, quantum computation and quantum chaos, and the Zeno effect.
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Table of Contents
Preface ix
Introduction 1
Introduction to Classical Computation 9
The Turing machine 9
Addition on a Turing machine 12
The Church-Turing thesis 13
The universal Turing machine 14
The probabilistic Turing machine 14
The halting problem 15
The circuit model of computation 15
Binary arithmetics 17
Elementary logic gates 17
Universal classical computation 22
Computational complexity 24
Complexity classes 27
The Chernoff bound 30
Computing dynamical systems 30
Deterministic chaos 31
Algorithmic complexity 33
Energy and information 35
Maxwell's demon 35
Landauer's principle 37
Extracting work from information 40
Reversible computation 41
Toffoli and Fredkin gates 43
The billiard-ball computer 45
A guide to the bibliography 47
Introduction to Quantum Mechanics 49
The Stern-Gerlach experiment 50
Young's double-slit experiment 53
Linear vector spaces 57
The postulates of quantum mechanics 76
The EPR paradox and Bell's inequalities 88
A guide to the bibliography 97
Quantum Computation 99
The qubit 100
The Bloch sphere 102
Measuring the state of a qubit 103
The circuit model of quantum computation 105
Single-qubit gates 108
Rotations of the Bloch sphere 110
Controlled gates and entanglement generation 112
The Bell basis 118
Universal quantum gates 118
Preparation of the initial state 127
Unitary errors 130
Function evaluation 132
The quantum adder 137
Deutsch's algorithm 140
The Deutsch-Jozsa problem 141
An extension of Deutsch's algorithm 143
Quantum search 144
Searching one item out of four 145
Searching one item out of N 147
Geometric visualization 149
The quantum Fourier transform 152
Quantum phase estimation 155
Finding eigenvalues and eigenvectors 158
Period finding and Shor's algorithm 161
Quantum computation of dynamical systems 164
Quantum simulation of the Schrodinger equation 164
The quantum baker's map 168
The quantum sawtooth map 170
Quantum computation of dynamical localization 174
First experimental implementations 178
Elementary gates with spin qubits 179
Overview of the first implementations 181
A guide to the bibliography 185
Quantum Communication 189
Classical cryptography 189
The Vernam cypher 190
The public-key cryptosystem 191
The RSA protocol 192
The no-cloning theorem 194
Faster-than-light transmission of information? 197
Quantum cryptography 198
The BB84 protocol 199
The E91 protocol 202
Dense coding 204
Quantum teleportation 208
An overview of the experimental implementations 213
A guide to the bibliography 214
Solutions to the exercises 215
Bibliography 241
Index 253