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Principles Of Quantum Computation And Information - Volume I : Basic Concepts - Giuliano Benenti

Principles Of Quantum Computation And Information - Volume I

Basic Concepts

Paperback Published: 30th April 2004
ISBN: 9789812388582
Number Of Pages: 272

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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.

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

Prefacep. vii
Introductionp. 1
Introduction to Classical Computationp. 9
The Turing machinep. 9
Addition on a Turing machinep. 12
The Church-Turing thesisp. 13
The universal Turing machinep. 14
The probabilistic Turing machinep. 14
The halting problemp. 15
The circuit model of computationp. 15
Binary arithmeticsp. 17
Elementary logic gatesp. 17
Universal classical computationp. 22
Computational complexityp. 24
Complexity classesp. 27
The Chernoff boundp. 30
Computing dynamical systemsp. 30
Deterministic chaosp. 31
Algorithmic complexityp. 33
Energy and informationp. 35
Maxwell's demonp. 35
Landauer's principlep. 37
Extracting work from informationp. 40
Reversible computationp. 41
Toffoli and Fredkin gatesp. 43
The billiard-ball computerp. 45
A guide to the bibliographyp. 47
Introduction to Quantum Mechanicsp. 49
The Stern-Gerlach experimentp. 50
Young's double-slit experimentp. 53
Linear vector spacesp. 57
The postulates of quantum mechanicsp. 76
The EPR paradox and Bell's inequalitiesp. 88
A guide to the bibliographyp. 97
Quantum Computationp. 99
The qubitp. 100
The Bloch spherep. 102
Measuring the state of a qubitp. 103
The circuit model of quantum computationp. 105
Single-qubit gatesp. 108
Rotations of the Bloch spherep. 110
Controlled gates and entanglement generationp. 112
The Bell basisp. 118
Universal quantum gatesp. 118
Preparation of the initial statep. 127
Unitary errorsp. 130
Function evaluationp. 132
The quantum adderp. 137
Deutsch's algorithmp. 140
The Deutsch-Jozsa problemp. 141
An extension of Deutsch's algorithmp. 143
Quantum searchp. 144
Searching one item out of fourp. 145
Searching one item out of Np. 148
Geometric visualizationp. 149
The quantum Fourier transformp. 152
Quantum phase estimationp. 155
Finding eigenvalues and eigenvectorsp. 158
Period finding and Shor's algorithmp. 161
Quantum computation of dynamical systemsp. 164
Quantum simulation of the Schrodinger equationp. 164
The quantum baker's mapp. 168
The quantum sawtooth mapp. 170
Quantum computation of dynamical localizationp. 174
First experimental implementationsp. 178
Elementary gates with spin qubitsp. 179
Overview of the first implementationsp. 181
A guide to the bibliographyp. 185
Quantum Communicationp. 189
Classical cryptographyp. 189
The Vernam cypherp. 190
The public-key cryptosystemp. 191
The RSA protocolp. 192
The no-cloning theoremp. 194
Faster-than-light transmission of information?p. 197
Quantum cryptographyp. 198
The BB84 protocolp. 199
The E91 protocolp. 202
Dense codingp. 205
Quantum teleportationp. 208
An overview of the experimental implementationsp. 213
A guide to the bibliographyp. 214
Solutions to the exercisesp. 215
Bibliographyp. 241
Indexp. 253
Table of Contents provided by Rittenhouse. All Rights Reserved.

ISBN: 9789812388582
ISBN-10: 9812388583
Audience: Tertiary; University or College
Format: Paperback
Language: English
Number Of Pages: 272
Published: 30th April 2004
Publisher: World Scientific Publishing Co Pte Ltd
Country of Publication: SG
Dimensions (cm): 22.23 x 15.24  x 1.91
Weight (kg): 0.4
Edition Type: New edition