Quantum Computing for Computer Scientists

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  • Edition: 1st
  • Format: Hardcover
  • Copyright: 2008-08-11
  • Publisher: Cambridge University Press
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The multidisciplinary field of quantum computing strives to exploit some of the uncanny aspects of quantum mechanics to expand our computational horizons. Quantum Computing for Computer Scientists takes readers on a tour of this fascinating area of cutting-edge research. Written in an accessible yet rigorous fashion, this book employs ideas and techniques familiar to every student of computer science. The reader is not expected to have any advanced mathematics or physics background. After presenting the necessary prerequisites, the material is organized to look at different aspects of quantum computing from the specific standpoint of computer science. There are chapters on computer architecture, algorithms, programming languages, theoretical computer science, cryptography, information theory, and hardware. The text has step-by-step examples, more than two hundred exercises with solutions, and programming drills that bring the ideas of quantum computing alive for today's computer science students and researchers.

Table of Contents

Prefacep. xi
Complex Numbersp. 7
Basic Definitionsp. 8
The Algebra of Complex Numbersp. 10
The Geometry of Complex Numbersp. 15
Complex Vector Spacesp. 29
C[superscript n] as the Primary Examplep. 30
Definitions, Properties, and Examplesp. 34
Basis and Dimensionp. 45
Inner Products and Hilbert Spacesp. 53
Eigenvalues and Eigenvectorsp. 60
Hermitian and Unitary Matricesp. 62
Tensor Product of Vector Spacesp. 66
The Leap from Classical to Quantump. 74
Classical Deterministic Systemsp. 74
Probabilistic Systemsp. 79
Quantum Systemsp. 88
Assembling Systemsp. 97
Basic Quantum Theoryp. 103
Quantum Statesp. 103
Observablesp. 115
Measuringp. 126
Dynamicsp. 129
Assembling Quantum Systemsp. 132
Architecturep. 138
Bits and Qubitsp. 138
Classical Gatesp. 144
Reversible Gatesp. 151
Quantum Gatesp. 158
Algorithmsp. 170
Deutsch's Algorithmp. 171
The Deutsch-Jozsa Algorithmp. 179
Simon's Periodicity Algorithmp. 187
Grover's Search Algorithmp. 195
Shor's Factoring Algorithmp. 204
Programming Languagesp. 220
Programming in a Quantum Worldp. 220
Quantum Assembly Programmingp. 221
Toward Higher-Level Quantum Programmingp. 230
Quantum Computation Before Quantum Computersp. 237
Theoretical Computer Sciencep. 239
Deterministic and Nondeterministic Computationsp. 239
Probabilistic Computationsp. 246
Quantum Computationsp. 251
Cryptographyp. 262
Classical Cryptographyp. 262
Quantum Key Exchange I: The BB84 Protocolp. 268
Quantum Key Exchange II: The B92 Protocolp. 273
Quantum Key Exchange III: The EPR Protocolp. 275
Quantum Teleportationp. 277
Information Theoryp. 284
Classical Information and Shannon Entropyp. 284
Quantum Information and von Neumann Entropyp. 288
Classical and Quantum Data Compressionp. 295
Error-Correcting Codesp. 302
Hardwarep. 305
Quantum Hardware: Goals and Challengesp. 306
Implementing a Quantum Computer I: Ion Trapsp. 311
Implementing a Quantum Computer II: Linear Opticsp. 313
Implementing a Quantum Computer III: NMR and Superconductorsp. 315
Future of Quantum Warep. 316
Historical Bibliography of Quantum Computingp. 319
Reading Scientific Articlesp. 319
Models of Computationp. 320
Quantum Gatesp. 321
Quantum Algorithms and Implementationsp. 321
Quantum Cryptographyp. 323
Quantum Informationp. 323
More Milestones?p. 324
Answers to Selected Exercisesp. 325
Quantum Computing Experiments with MATLABp. 351
Playing with Matlabp. 351
Complex Numbers and Matricesp. 351
Quantum Computationsp. 354
Keeping Abreast of Quantum News: Quantum Computing on the Web and in the Literaturep. 357
Keeping Abreast of Popular Newsp. 357
Keeping Abreast of Scientific Literaturep. 358
The Best Way to Stay Abreast?p. 359
Selected Topics for Student Presentationsp. 360
Complex Numbersp. 361
Complex Vector Spacesp. 362
The Leap from Classical to Quantump. 363
Basic Quantum Theoryp. 364
Architecturep. 365
Algorithmsp. 366
Programming Languagesp. 368
Theoretical Computer Sciencep. 369
Cryptographyp. 370
Information Theoryp. 370
Hardwarep. 371
Bibliographyp. 373
Indexp. 381
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