Principles Of Quantum Computation And Information - Volume I

Basic Concepts

By: Giuliano Benenti, Giulio Casati, Giuliano Strini

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Paperback | 19 April 2004

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272 Pages

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15.6 x 22.6 x 1.6

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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 1 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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.,." provides a unique perspective on the blending and cross-fertilization between the methods of quantum information and quantum chaos ..."

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Non-Fiction Reference, Information & Interdisciplinary Subjects Research & Information Information theory Science Physics Quantum Physics & Quantum Mechanics & Quantum Field Theory Computing & I.T.Computer Science Mathematics Booktopia Publisher Services World Scientific Publishing

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Preface	p. vii
Introduction	p. 1
Introduction to Classical Computation	p. 9
The Turing machine	p. 9
Addition on a Turing machine	p. 12
The Church-Turing thesis	p. 13
The universal Turing machine	p. 14
The probabilistic Turing machine	p. 14
The halting problem	p. 15
The circuit model of computation	p. 15
Binary arithmetics	p. 17
Elementary logic gates	p. 17
Universal classical computation	p. 22
Computational complexity	p. 24
Complexity classes	p. 27
The Chernoff bound	p. 30
Computing dynamical systems	p. 30
Deterministic chaos	p. 31
Algorithmic complexity	p. 33
Energy and information	p. 35
Maxwell's demon	p. 35
Landauer's principle	p. 37
Extracting work from information	p. 40
Reversible computation	p. 41
Toffoli and Fredkin gates	p. 43
The billiard-ball computer	p. 45
A guide to the bibliography	p. 47
Introduction to Quantum Mechanics	p. 49
The Stern-Gerlach experiment	p. 50
Young's double-slit experiment	p. 53
Linear vector spaces	p. 57
The postulates of quantum mechanics	p. 76
The EPR paradox and Bell's inequalities	p. 88
A guide to the bibliography	p. 97
Quantum Computation	p. 99
The qubit	p. 100
The Bloch sphere	p. 102
Measuring the state of a qubit	p. 103
The circuit model of quantum computation	p. 105
Single-qubit gates	p. 108
Rotations of the Bloch sphere	p. 110
Controlled gates and entanglement generation	p. 112
The Bell basis	p. 118
Universal quantum gates	p. 118
Preparation of the initial state	p. 127
Unitary errors	p. 130
Function evaluation	p. 132
The quantum adder	p. 137
Deutsch's algorithm	p. 140
The Deutsch-Jozsa problem	p. 141
An extension of Deutsch's algorithm	p. 143
Quantum search	p. 144
Searching one item out of four	p. 145
Searching one item out of N	p. 148
Geometric visualization	p. 149
The quantum Fourier transform	p. 152
Quantum phase estimation	p. 155
Finding eigenvalues and eigenvectors	p. 158
Period finding and Shor's algorithm	p. 161
Quantum computation of dynamical systems	p. 164
Quantum simulation of the Schrodinger equation	p. 164
The quantum baker's map	p. 168
The quantum sawtooth map	p. 170
Quantum computation of dynamical localization	p. 174
First experimental implementations	p. 178
Elementary gates with spin qubits	p. 179
Overview of the first implementations	p. 181
A guide to the bibliography	p. 185
Quantum Communication	p. 189
Classical cryptography	p. 189
The Vernam cypher	p. 190
The public-key cryptosystem	p. 191
The RSA protocol	p. 192
The no-cloning theorem	p. 194
Faster-than-light transmission of information?	p. 197
Quantum cryptography	p. 198
The BB84 protocol	p. 199
The E91 protocol	p. 202
Dense coding	p. 205
Quantum teleportation	p. 208
An overview of the experimental implementations	p. 213
A guide to the bibliography	p. 214
Solutions to the exercises	p. 215
Bibliography	p. 241
Index	p. 253
Table of Contents provided by Rittenhouse. All Rights Reserved.

Principles Of Quantum Computation And Information - Volume I

Basic Concepts

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

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Physics for Beginners

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