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Preface 1 Complex Numbers, Vector Space, and Dirac Notation
1.1 Complex Numbers
1.2 Complex Conjugation
1.3 Vector Space
1.4 Basis Set
1.5 Dirac Notation
1.5.1 Ket
1.5.2 Bra
1.6 Inner Product
1.7 Linearly Dependent and Independent Vectors
1.8 Dual Vector Space
1.9 Computational Basis
1.10 Outer Product References 2 Basics of Quantum Mechanics
2.1 Limitations of Classical Physics
2.1.1 Blackbody Radiation
2.1.2 Planck''s Constant
2.2 Photoelectric Effect
2.3 Classical Electromagnetic Theory
2.4 Rutherford''s Model of the Atom
2.5 Bohr''s Model of Atoms
2.6 Particle and Wave Nature of Light
2.7 Wave Function
2.8 Postulates of Quantum Mechanics References 3 Matrices and Operators
3.1 Matrices
3.2 Square Matrices
3.3 Diagonal (or Triangular) Matrix
3.4 Operators
3.4.1 Rules for Operators
3.5 Linear Operator
3.6 Commutator
3.7 Matrix Representation of a Linear Operator
3.8 Symmetric Matrix
3.9 Transpose Operation
3.10 Orthogonal Matrices
3.11 Identity Operator
3.12 Adjoint Operator
3.13 Hermitian Operator
3.14 Unitary Operators
3.14.1 Properties of Unitary Operators
3.15 Projection Operator References 4 Boolean Algebra, Logic Gates, and Quantum Information Processing
4.1 Boolean Algebra
4.2 Classical Circuit Computation Model
4.3 Universal Logic Gates
4.4 Quantum Computation
4.5 The Quantum Bit and Its Representations
4.6 Superposition in Quantum Systems
4.7 Quantum Register References 5 Quantum Gates and Circuits
5.1 X Gate
5.2 Y Gate
5.3 Z Gate
5.4 (Square Root of NOT) Gate
5.5 Hadamard Gate
5.6 Phase Gate
5.7 T Gate
5.8 Reversible Logic
5.9 CNOT Gate
5.10 Controlled-U Gate
5.11 Reversible Gates
5.11.1 Fredkin Gate (Controlled Swap Gate)
5.11.2 Toffoli Gate (Controlled-Controlled-NOT)
5.11.3 Peres Gate References 6 Tensor Products, Superposition, and Quantum Entanglement
6.1 Tensor Products
6.2 Multi-Qubit Systems
6.3 Superposition
6.4 Entanglement
6.5 Decoherence References 7 Teleportation and Superdense Coding
7.1 Quantum Teleportation
7.2 No-Cloning Theorem
7.3 Superdense Coding References 8 Quantum Error Correction
8.1 Classical Error-Correcting Codes
8.2 Quantum Error-Correcting Codes
8.3 Shor''s 3-Qubit Bit-Flop Code
8.4 Error Correction
8.4.1 Bit-Flip Error Correction
8.4.2 Phase Error Correction
8.5 Shor''s 9 Qubit Code References 9 Quantum Algorithms
9.1 Deutsch''s Algorithm
9.2 Deutsch-Jozsa Algorithm
9.3 Grover''s Search Algorithm
9.3.1 Details of Grover''s Algorithm
9.4 Shor''s Factoring Algorithm References 10 Quantum Cryptography
10.1 Principles of Information Security
10.2 One-Time Pad
10.3 Public Key Cryptography
10.4 RSA Coding Scheme
10.5 Quantum Cryptography
10.6 Quantum Key Distribution
10.7 BB84
10.8 Ekart 91 References Index