Quantum Computing for Computer Scientists

by Noson S. Yanofsky , Mirco A. Mannucci

• ISBN13: 9780521879965
• ISBN10: 0521879965
• Edition: 1st
• Format: Hardcover
• Copyright: 2008-08-11
• Publisher: Cambridge University Press

Summary

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

Preface	p. xi
Complex Numbers	p. 7
Basic Definitions	p. 8
The Algebra of Complex Numbers	p. 10
The Geometry of Complex Numbers	p. 15
Complex Vector Spaces	p. 29
C[superscript n] as the Primary Example	p. 30
Definitions, Properties, and Examples	p. 34
Basis and Dimension	p. 45
Inner Products and Hilbert Spaces	p. 53
Eigenvalues and Eigenvectors	p. 60
Hermitian and Unitary Matrices	p. 62
Tensor Product of Vector Spaces	p. 66
The Leap from Classical to Quantum	p. 74
Classical Deterministic Systems	p. 74
Probabilistic Systems	p. 79
Quantum Systems	p. 88
Assembling Systems	p. 97
Basic Quantum Theory	p. 103
Quantum States	p. 103
Observables	p. 115
Measuring	p. 126
Dynamics	p. 129
Assembling Quantum Systems	p. 132
Architecture	p. 138
Bits and Qubits	p. 138
Classical Gates	p. 144
Reversible Gates	p. 151
Quantum Gates	p. 158
Algorithms	p. 170
Deutsch's Algorithm	p. 171
The Deutsch-Jozsa Algorithm	p. 179
Simon's Periodicity Algorithm	p. 187
Grover's Search Algorithm	p. 195
Shor's Factoring Algorithm	p. 204
Programming Languages	p. 220
Programming in a Quantum World	p. 220
Quantum Assembly Programming	p. 221
Toward Higher-Level Quantum Programming	p. 230
Quantum Computation Before Quantum Computers	p. 237
Theoretical Computer Science	p. 239
Deterministic and Nondeterministic Computations	p. 239
Probabilistic Computations	p. 246
Quantum Computations	p. 251
Cryptography	p. 262
Classical Cryptography	p. 262
Quantum Key Exchange I: The BB84 Protocol	p. 268
Quantum Key Exchange II: The B92 Protocol	p. 273
Quantum Key Exchange III: The EPR Protocol	p. 275
Quantum Teleportation	p. 277
Information Theory	p. 284
Classical Information and Shannon Entropy	p. 284
Quantum Information and von Neumann Entropy	p. 288
Classical and Quantum Data Compression	p. 295
Error-Correcting Codes	p. 302
Hardware	p. 305
Quantum Hardware: Goals and Challenges	p. 306
Implementing a Quantum Computer I: Ion Traps	p. 311
Implementing a Quantum Computer II: Linear Optics	p. 313
Implementing a Quantum Computer III: NMR and Superconductors	p. 315
Future of Quantum Ware	p. 316
Historical Bibliography of Quantum Computing	p. 319
Reading Scientific Articles	p. 319
Models of Computation	p. 320
Quantum Gates	p. 321
Quantum Algorithms and Implementations	p. 321
Quantum Cryptography	p. 323
Quantum Information	p. 323
More Milestones?	p. 324
Answers to Selected Exercises	p. 325
Quantum Computing Experiments with MATLAB	p. 351
Playing with Matlab	p. 351
Complex Numbers and Matrices	p. 351
Quantum Computations	p. 354
Keeping Abreast of Quantum News: Quantum Computing on the Web and in the Literature	p. 357
Keeping Abreast of Popular News	p. 357
Keeping Abreast of Scientific Literature	p. 358
The Best Way to Stay Abreast?	p. 359
Selected Topics for Student Presentations	p. 360
Complex Numbers	p. 361
Complex Vector Spaces	p. 362
The Leap from Classical to Quantum	p. 363
Basic Quantum Theory	p. 364
Architecture	p. 365
Algorithms	p. 366
Programming Languages	p. 368
Theoretical Computer Science	p. 369
Cryptography	p. 370
Information Theory	p. 370
Hardware	p. 371
Bibliography	p. 373
Index	p. 381
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