Cambridge Series on Information and the Natural Sciences. 10th Anniversary edition
Cambridge University Press
Dec. 2010
ISBN: 1107002176 9781107002173
710 pages
PDF
This comprehensive textbook describes such remarkable effects as fast quantum algorithms, quantum teleportation, quantum cryptography and quantum error-correction. Quantum mechanics and computer science are introduced before moving on to describe what a quantum computer is, how it can be used to solve problems faster than 'classical' computers and its real-world implementation. It concludes with an in-depth treatment of quantum information. Containing a wealth of figures and exercises, this well-known textbook is ideal for courses on the subject, and will interest beginning graduate students and researchers in physics, computer science, mathematics, and electrical engineering.
One of the the best textbook in quantum science. This 10th anniversary edition includes an introduction from the authors setting the work in context.
- The best introduction to quantum computing and quantum information, written by experts on the subject
- Gives a comprehensive introduction to the main ideas and techniques, with hundreds of exercises and figures
- Contains extensive background material so it can be understood without prior knowledge of quantum mechanics or quantum science
Contents
Introduction to the Tenth Anniversary Edition
Afterword to the Tenth Anniversary Edition
Preface
Structure of the book
How to use this book
Acknowledgements
Nomenclature and notation
Linear algebra and quantum mechanics
Information theory and probability
Miscellanea
Frequently used quantum gates and circuit symbols
I Fundamental concepts
1 Introduction and overview
1.1 Global perspectives
1.2 Quantum bits
1.2.1 Multiple qubits
1.3 Quantum computation
1.4 Quantum algorithms
1.5 Experimental quantum information processing
1.6 Quantum information
2 Introduction to quantum mechanics
2.1 Linear algebra
2.2 The postulates of quantum mechanics
2.3 Application: superdense coding
2.4 The 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
3.2 The analysis of computational problems
3.3 Perspectives on computer science
History and further reading
II Quantum computation
4 Quantum circuits
4.1 Quantum algorithms
4.2 Single qubit operations
4.3 Controlled operations
4.4 Measurement
4.5 Universal quantum gates
4.5.4 Approximating arbitrary unitary gates is generically hard
4.5.5 Quantum computational complexity
4.6 Summary of the quantum circuit model of computation
4.7 Simulation of quantum systems
5 The quantum Fourier transform and its applications
5.1 The quantum Fourier transform
5.2 Phase estimation
5.3 Applications: order-finding and factoring
5.4 General applications of the quantum Fourier transform
6 Quantum search algorithms
6.1 The quantum search algorithm
6.2 Quantum search as a quantum simulation
6.3 Quantum counting
6.4 Speeding up the solution of NP-complete problems
6.5 Quantum search of an unstructured database
6.6 Optimality of the search algorithm
6.7 Black box algorithm limits
7 Quantum computers: physical realization
7.1 Guiding principles
7.2 Conditions for quantum computation
7.3 Harmonic oscillator quantum computer
7.4 Optical photon quantum computer
7.5 Optical cavity quantum electrodynamics
7.6 Ion traps
7.7 Nuclear magnetic resonance
7.8 Other implementation schemes
III Quantum information
8 Quantum noise and quantum operations
8.1 Classical noise and Markov processes
8.2 Quantum operations
8.3 Examples of quantum noise and quantum operations
8.4 Applications of quantum operations
8.5 Limitations of the quantum operations formalism
9 Distance measures for quantum information
9.1 Distance measures for classical information
9.2 How close are two quantum states?
9.3 How well does a quantum channel preserve information?
10 Quantum error-correction
10.1 Introduction
10.1.2 Three qubit phase flip code
10.2 The Shor code
10.3 Theory of quantum error-correction
10.4 Constructing quantum codes
10.5 Stabilizer codes
10.6 Fault-tolerant quantum computation
11 Entropy and information
11.1 Shannon entropy
11.2 Basic properties of entropy
11.3 Von Neumann entropy
11.4 Strong subadditivity
12 Quantum information theory
12.2 Data compression
12.2.1 Shannon’s noiseless channel coding theorem
12.2.2 Schumacher’s quantum noiseless channel coding theorem
12.3 Classical information over noisy quantum channels
12.4 Quantum information over noisy quantum channels
12.5 Entanglement as a physical resource
12.6 Quantum cryptography
Appendix 1: Notes on basic probability theory History and further reading
Appendix 2: Group theory
A2.1 Basic definitions
A2.1.1 Generators
A2.1.2 Cyclic groups
A2.1.3 Cosets
A2.2 Representations
A2.2.1 Equivalence and reducibility
A2.2.2 Orthogonality
A2.2.3 The regular representation
A2.3 Fourier transforms
Appendix 3: The Solovay–Kitaev theorem
Appendix 4: Number theory
A4.1 Fundamentals
A4.2 Modular arithmetic and Euclid’s algorithm
A4.3 Reduction of factoring to order-finding
A4.4 Continued fractions
Appendix 5: Public key cryptography and the RSA cryptosystem
Appendix 6: Proof of Lieb’s theorem
Bibliography
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