Intro
Preface
References
Acknowledgments
Contents
About the Authors
1 Introduction
1.1 Interview on Quantum Computers
References
Part I Fundamentals
2 Binary Numbers, Vectors, Matrices and Tensor Products
2.1 Binary Representation
2.2 Linear Vector Space
2.3 N-Dimensional Complex Linear Vector Space
2.4 Matrices
2.5 Properties of N timesN Matrices
2.5.1 Hermitian Conjugation
2.6 Tensor (Outer) Product
2.7 Square Matrices
2.8 Dirac Bracket: Vector Notation
2.9 Tensor and Outer Product: Strings and Gates
2.9.1 3-Bits String

4.2.2 Discrete Degrees of Freedom: Qubits
4.3 Hermitian and Unitary Operators
4.4 The Schrödinger Equation
4.4.1 Key Features of the Schrödinger Equation
4.5 Quantum Measurement: Born Rule
4.6 Quantum Measurements and Degrees of Freedom
4.7 No-Cloning Theorem
4.8 Copenhagen Interpretation: Open Questions
4.9 Summary of Quantum Mechanics
4.10 Generalized Born Rule
4.10.1 Example
4.11 Consistency of Generalized Born Rule
4.12 Quantum Mechanics and Quantum Computers
References
5 Quantum Superposition and Entanglement
5.1 Quantum Superposition

5.11 Maximally Entangled States
5.11.1 An Entangled State of Two Binary Degrees of Freedom
5.12 Pure and Mixed Density Matrix
References
6 Binary Degrees of Freedom and Qubits
6.1 Introduction
6.2 Degrees of Freedom and Qubits
6.3 Single Qubit
6.3.1 Density Matrix
6.4 Bell Entangled Qubits
6.5 Bell States: Maximally Entangled
7 Quantum Gates and Circuits
7.1 Quantum Gates
7.2 Superposed and Entangled Qubits
7.3 Two- and Three-Qubit Quantum Gates
7.4 Arithmetic Addition of Binary Qubits
7.5 Quantum Measurements of Qubits
7.5.1 Partial Measurement