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Index
Cover
Title
Copyright
Contents
Preface
Introduction
1 Complex Numbers
1.1 Basic Definitions
1.2 The Algebra of Complex Numbers
1.3 The Geometry of Complex Numbers
2 Complex Vector Spaces
2.1 Cn As the Primary Example
2.2 Definitions, Properties, and Examples
2.3 Basis and Dimension
2.4 Inner Products and Hilbert Spaces
2.5 Eigenvalues and Eigenvectors
2.6 Hermitian and Unitary Matrices
2.7 Tensor Product of Vector Spaces
3 The Leap from Classical to Quantum
3.1 Classical Deterministic Systems
3.2 Probabilistic Systems
3.3 Quantum Systems
3.4 Assembling Systems
4 Basic Quantum Theory
4.1 Quantum States
4.2 Observables
4.3 Measuring
4.4 Dynamics
4.5 Assembling Quantum Systems
5 Architecture
5.1 Bits and Qubits
5.2 Classical Gates
5.3 Reversible Gates
5.4 Quantum Gates
6 Algorithms
6.1 Deutsch’s Algorithm
6.2 The Deutsch–Jozsa Algorithm
6.3 Simon’s Periodicity Algorithm
6.4 Grover’s Search Algorithm
6.5 Shor’s Factoring Algorithm
7 Programming Languages
7.1 Programming in a Quantum World
7.2 Quantum Assembly Programming
7.3 Toward Higher-Level Quantum ProgramminG
7.4 Quantum Computation Before Quantum Computers
8 Theoretical Computer Science
8.1 Deterministic and Nondeterministic Computations
8.2 Probabilistic Computations
8.3 Quantum Computations
9 Cryptography
9.1 Classical Cryptography
9.2 Quantum Key Exchange I: The BB84 Protocol
9.3 Quantum Key Exchange II: The B92 Protocol
9.4 Quantum Key Exchange III: The EPR Protocol
9.5 Quantum Teleportation
10 Information Theory
10.1 Classical Information and Shannon Entropy
10.2 Quantum Information and von Neumann Entropy
10.3 Classical and Quantum Data Compression
10.4 Error-Correcting Codes
11 Hardware
11.1 Quantum Hardware: Goals and Challenges
11.2 Implementing a Quantum Computer I: Ion Traps
11.3 Implementing a Quantum Computer II: Linear Optics
11.4 Implementing a Quantum Computer III: NMR and Superconductors
11.5 Future of Quantum Ware
Appendix A Historical Bibliography of Quantum Computing
A.1 Reading Scientific Articles
A.2 Models of Computation
A.3 Quantum Gates
A.4 Quantum Algorithms and Implementations
A.5 Quantum Cryptography
A.6 Quantum Information
A.7 More Milestones?
Appendix B Answers to Selected Exercises
Appendix C Quantum Computing Experiments with MATLAB
C.1 Playing with Matlab
C.2 Complex Numbers and Matrices
C.3 Quantum Computations
Appendix D Keeping Abreast of Quantum News: Quantum Computing on the Web and in the Literature
D.1 Keeping Abreast of Popular News
D.2 Keeping Abreast of Scientific Literature
D.3 The Best Way to Stay Abreast?
Appendix E Selected Topics for Student Presentations
E.1 Complex Numbers
E.2 Complex Vector Spaces
E.3 The Leap from Classical to Quantum
E.4 Basic Quantum Theory
E.5 Architecture
E.6 Algorithms
E.7 Programming Languages
E.8 Theoretical Computer Science
E.9 Cryptography
E.10 Information Theory
E.11 Hardware
Bibliography
Index
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