| 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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