Foreword
Preface
1 Introduction
2 What is a qubit?
2.1 The polarization of light
2.2 Photon polarization
2.3 Mathematical formulation: the qubit
2.4 Principles of quantum mechanics
2.5 Quantum cryptography
2.6 Exercises
2.7 Further reading
3 Manipulating qubits
3.1 The Bloch sphere, spin 1/2
3.2 Dynamical evolution
3.3 Manipulating qubits: Rabi oscillations
3.4 Principles of NMR and MRI
3.5 Exercises
3.6 Further reading
4 Quantum correlations
4.1 Two-qubit states
4.2 The state operator (or density operator)
4.3 The quantum no-cloning theorem
4.4 Decoherence
4.5 The Bell inequalities
4.6 Exercises
4.7 Further reading
5 Introduction to quantum computing
5.1 General remarks
5.2 Reversible calculation
5.3 Quantum logic gates
5.4 The Deutsch algorithm
5.5 Generalization to n ~ m qubits
5.6 The Grover search algorithm
5.7 The quantum Fourier transform
5.8 The period of a function
5.9 Classical algorithms and quantum algorithms
5.10 Exercises
5.11 Further reading
6 Physical realizations
6.1 NMR as a quantum computer
6.2 Trapped ions
6.3 Superconducting qubits
6.4 Quantum dots
6.5 Exercises
6.6 Further reading
7 Quantum information
7.1 Teleportation
7.2 Shannon entropy
7.3 yon Neumann entropy
7.4 Quantum error correction
7.5 Exercises
7.6 Further reading
References
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