| |
| |
| Preface | |
| |
| |
| |
| Complex Numbers | |
| |
| |
| |
| Basic Definitions | |
| |
| |
| |
| The Algebra of Complex Numbers | |
| |
| |
| |
| The Geometry of Complex Numbers | |
| |
| |
| |
| Complex Vector Spaces | |
| |
| |
| |
| C[superscript n] as the Primary Example | |
| |
| |
| |
| Definitions, Properties, and Examples | |
| |
| |
| |
| Basis and Dimension | |
| |
| |
| |
| Inner Products and Hilbert Spaces | |
| |
| |
| |
| Eigenvalues and Eigenvectors | |
| |
| |
| |
| Hermitian and Unitary Matrices | |
| |
| |
| |
| Tensor Product of Vector Spaces | |
| |
| |
| |
| The Leap from Classical to Quantum | |
| |
| |
| |
| Classical Deterministic Systems | |
| |
| |
| |
| Probabilistic Systems | |
| |
| |
| |
| Quantum Systems | |
| |
| |
| |
| Assembling Systems | |
| |
| |
| |
| Basic Quantum Theory | |
| |
| |
| |
| Quantum States | |
| |
| |
| |
| Observables | |
| |
| |
| |
| Measuring | |
| |
| |
| |
| Dynamics | |
| |
| |
| |
| Assembling Quantum Systems | |
| |
| |
| |
| Architecture | |
| |
| |
| |
| Bits and Qubits | |
| |
| |
| |
| Classical Gates | |
| |
| |
| |
| Reversible Gates | |
| |
| |
| |
| Quantum Gates | |
| |
| |
| |
| Algorithms | |
| |
| |
| |
| Deutsch's Algorithm | |
| |
| |
| |
| The Deutsch-Jozsa Algorithm | |
| |
| |
| |
| Simon's Periodicity Algorithm | |
| |
| |
| |
| Grover's Search Algorithm | |
| |
| |
| |
| Shor's Factoring Algorithm | |
| |
| |
| |
| Programming Languages | |
| |
| |
| |
| Programming in a Quantum World | |
| |
| |
| |
| Quantum Assembly Programming | |
| |
| |
| |
| Toward Higher-Level Quantum Programming | |
| |
| |
| |
| Quantum Computation Before Quantum Computers | |
| |
| |
| |
| Theoretical Computer Science | |
| |
| |
| |
| Deterministic and Nondeterministic Computations | |
| |
| |
| |
| Probabilistic Computations | |
| |
| |
| |
| Quantum Computations | |
| |
| |
| |
| Cryptography | |
| |
| |
| |
| Classical Cryptography | |
| |
| |
| |
| Quantum Key Exchange I: The BB84 Protocol | |
| |
| |
| |
| Quantum Key Exchange II: The B92 Protocol | |
| |
| |
| |
| Quantum Key Exchange III: The EPR Protocol | |
| |
| |
| |
| Quantum Teleportation | |
| |
| |
| |
| Information Theory | |
| |
| |
| |
| Classical Information and Shannon Entropy | |
| |
| |
| |
| Quantum Information and von Neumann Entropy | |
| |
| |
| |
| Classical and Quantum Data Compression | |
| |
| |
| |
| Error-Correcting Codes | |
| |
| |
| |
| Hardware | |
| |
| |
| |
| Quantum Hardware: Goals and Challenges | |
| |
| |
| |
| Implementing a Quantum Computer I: Ion Traps | |
| |
| |
| |
| Implementing a Quantum Computer II: Linear Optics | |
| |
| |
| |
| Implementing a Quantum Computer III: NMR and Superconductors | |
| |
| |
| |
| Future of Quantum Ware | |
| |
| |
| |
| Historical Bibliography of Quantum Computing | |
| |
| |
| |
| |
| Reading Scientific Articles | |
| |
| |
| |
| Models of Computation | |
| |
| |
| |
| Quantum Gates | |
| |
| |
| |
| Quantum Algorithms and Implementations | |
| |
| |
| |
| Quantum Cryptography | |
| |
| |
| |
| Quantum Information | |
| |
| |
| |
| More Milestones? | |
| |
| |
| |
| Answers to Selected Exercises | |
| |
| |
| |
| Quantum Computing Experiments with MATLAB | |
| |
| |
| |
| Playing with Matlab | |
| |
| |
| |
| Complex Numbers and Matrices | |
| |
| |
| |
| Quantum Computations | |
| |
| |
| |
| Keeping Abreast of Quantum News: Quantum Computing on the Web and in the Literature | |
| |
| |
| |
| |
| Keeping Abreast of Popular News | |
| |
| |
| |
| Keeping Abreast of Scientific Literature | |
| |
| |
| |
| The Best Way to Stay Abreast? | |
| |
| |
| |
| Selected Topics for Student Presentations | |
| |
| |
| |
| Complex Numbers | |
| |
| |
| |
| Complex Vector Spaces | |
| |
| |
| |
| The Leap from Classical to Quantum | |
| |
| |
| |
| Basic Quantum Theory | |
| |
| |
| |
| Architecture | |
| |
| |
| |
| Algorithms | |
| |
| |
| |
| Programming Languages | |
| |
| |
| |
| Theoretical Computer Science | |
| |
| |
| |
| Cryptography | |
| |
| |
| |
| Information Theory | |
| |
| |
| |
| Hardware | |
| |
| |
| Bibliography | |
| |
| |
| Index | |