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Introduction to the Tenth Anniversary Edition

Afterword to the Tenth Anniversary Edition

Preface

Acknowledgements

Nomenclature and notation

Part I Fundamental concepts

1 Introduction and overview

1.1 Global perspectives

1.1.1 History of quantum computation and quantum information

1.1.2 Future directions

1.2 Quantum bits

1.2.1 Multiple qubits

1.3 Quantum computation

1.3.1 Single qubit gates

1.3.2 Multiple qubit gates

1.3.3 Measurements in bases other than the computational basis

1.3.4 Quantum circuits

1.3.5 Qubit copying circuit?

1.3.6 Example: Bell states

1.3.7 Example: quantum teleportation

1.4 Quantum algorithms

1.4.1 Classical computations on a quantum computer

1.4.2 Quantum parallelism

1.4.3 Deutsch`s algorithm

1.4.4 The Deutsch–Jozsa algorithm

1.4.5 Quantum algorithms summarized

1.5 Experimental quantum information processing

1.5.1 The Stern–Gerlach experiment

1.5.2 Prospects for practical quantum information processing

1.6 Quantum information

1.6.1 Quantum information theory: example problems

1.6.2 Quantum information in a wider context

2 Introduction to quantum mechanics

2.1 Linear algebra

2.1.1 Bases and linear independence

2.1.2 Linear operators and matrices

2.1.3 The Pauli matrices

2.1.4 Inner products

2.1.5 Eigenvectors and eigenvalues

2.1.6 Adjoints and Hermitian operators

2.1.7 Tensor products

2.1.8 Operator functions

2.1.9 The commutator and anti-commutator

2.1.10 The polar and singular value decompositions

2.2 The postulates of quantum mechanics

2.2.1 State space

2.2.2 Evolution

2.2.3 Quantum measurement

2.2.4 Distinguishing quantum states

2.2.5 Projective measurements

2.2.6 POVM measurements

2.2.7 Phase

2.2.8 Composite systems

2.2.9 Quantum mechanics: a global view

2.3 Application: superdense coding

2.4 The density operator

2.4.1 Ensembles of quantum states

2.4.2 General properties of the density operator

2.4.3 The reduced density operator

2.5 The Schmidt decomposition and purifications

2.6 EPR and the Bell inequality

3 Introduction to computer science

3.1 Models for computation

3.1.1 Turing machines

3.1.2 Circuits

3.2 The analysis of computational problems

3.2.1 How to quantify computational resources

3.2.2 Computational complexity

3.2.3 Decision problems and the complexity classes P and NP

3.2.4 A plethora of complexity classes

3.2.5 Energy and computation

3.3 Perspectives on computer science

Part II Quantum computation

4 Quantum circuits

4.1 Quantum algorithms

4.2 Single qubit operations

……

5 The quantum Fourier transform and its applications

6 Quantum search algorithms

7 Quantum computers: physical realization

Part III Quantum information

8 Quantum noise and quantum operations

9 Distance measures for quantum information

10 Quantum error-correction

11 Entropy and information

12 Quantum information theory

Appendices

Bibliography

Index