Introduction to quantum computation and quantum information

✍ Scribed by Adriano Barenco (editor), Andrew M Steane (editor), Timothy P Spiller (editor), Daniel Rohrlich (editor), John Preskill (editor), Sandu Popescu (editor), Hoi-Kwong Lo (editor), Richard Jozsa (editor), Isaac L Chuang (editor), Charles H Bennett (editor), Hugo Zbinden (editor)

• Publisher: World Scientific Publishing Company
• Year: 1998
• Tongue: English
• Leaves: 364
• Category: Library

✦ Synopsis

This book aims to provide a pedagogical introduction to the subjects of quantum information and quantum computation. Topics include non-locality of quantum mechanics, quantum computation, quantum cryptography, quantum error correction, fault-tolerant quantum computation as well as some experimental aspects of quantum computation and quantum cryptography. Only knowledge of basic quantum mechanics is assumed. Whenever more advanced concepts and techniques are used, they are introduced carefully. This book is meant to be a self-contained overview. While basic concepts are discussed in detail, unnecessary technical details are excluded. It is well-suited for a wide audience ranging from physics graduate students to advanced researchers.This book is based on a lecture series held at Hewlett-Packard Labs, Basic Research Institute in the Mathematical Sciences (BRIMS), Bristol from November 1996 to April 1997, and also includes other contributions.

✦ Table of Contents

CONTENTS
FOREWORD
PREFACE
BASIC ELEMENTS OF QUANTUM INFORMATION TECHNOLOGY
1 Introduction
2 Quantum mechanics
3 Quantum cryptography
4 Quantum computing
THE JOY OF ENTANGLEMENT
1 What is entanglement?
2 Hidden variables?
3 A thought experiment
4 Nonlocality
5 Manipulating entanglement
6 Thermodynamics and entanglement
7 Entangled density matrices
QUANTUM INFORMATION AND ITS PROPERTIES
1 Quantum Information - What is it?
2 Quantum Dense Coding
3 Quantum Teleportation
4 Density Matrices
5 Compression of Information
6 Von Neumann Entropy
7 Schumacher Compression of Quantum Information
8 Conclusions
QUANTUM CRYPTOLOGY a
1 Introduction
2 Novel Properties of Quantum Information
3 An Illustrative Example: Quantum Money h
4 Cryptography
5 Quantum Key Distribution (QKD)
6 Is Quantum Key Distribution Really Secure?
7 Practical Considerations
8 Beyond Quantum Key Distribution?
9 Quantum Cryptanalysis
10 Thoughts For The Future
11 What Quantum Cryptography Is Telling Us About Quantum Mechanics?
EXPERIMENTAL QUANTUM CRYPTOGRAPHY
1 Introduction
2 Standard polarization coding set-up
3 Standard phase coding set-up
4 QC using Faraday mirrors
5 The performance of a QC-setup: transmission length, data rate and quantum bit error rate
6 QC with single photon sources
7 Practical eavesdropping
8 Open air QC
QUANTUM COMPUTATION: AN INTRODUCTION
1 Computation and Physics
2 Complexity theory
3 Fundamental definitions
4 Simple algorithm: Deutsch’s problem
5 Simon’s problem
6 Shor's factorisation algorithm
7 Grover’s searching algorithm
8 Towards Quantum Networks
9 Coupling with the environment: the decoherence problem
QUANTUM ERROR CORRECTION
1 Introduction
2 Three bit code
3 Binary fields and discrete vector spaces
4 Classical error correction
5 Basic principles of quantum error correction
6 Code construction and syndrome extraction
7 Further development
FAULT-TOLERANT QUANTUM COMPUTATION
1 The need for fault tolerance
2 Quantum error correction: the 7-qubit code
3 Fault-tolerant recovery
4 Fault-tolerant quantum gates
5 The accuracy threshold for quantum computation
6 Error models
7 Topological Quantum Computation
QUANTUM COMPUTERS, ERROR-CORRECTION AND NETWORKING: QUANTUM OPTICAL APPROACHES
1 Introduction
2 The ion-trap quantum computer
3 The cavity quantum electrodynamics quantum computer
4 Experimentally feasible quantum error-correction
5 Quantum networking
6 Conclusions
QUANTUM COMPUTATION WITH NUCLEAR MAGNETIC RESONANCE
1 Introduction
2 Physics of Nuclear Magnetic Resonance
3 Computation with NMR
4 Theory of Bulk Quantum Computation
5 Experimental Results
FUTURE DIRECTIONS FOR QUANTUM INFORMATION THEORY
1 Introduction
2 Comparison of Classical and Quantum Information Processing
3 Open Problems