Problems and Solutions in Quantum Computing and Quantum Information

by Steeb, Willi-Hans; Hardy, Yorick

• ISBN13: 9789812387899
• ISBN10: 9812387897
• Format: Hardcover
• Copyright: 2004-07-12
• Publisher: World Scientific Pub Co Inc

Summary

Quantum computing and quantum information are two of the fastest-growing and most exciting research areas in physics. The possibilities of using non-local behaviour of quantum mechanics to factorize integers in random polynomial time have added to this new interest. This invaluable book provides a collection of problems in quantum computing and quantum information together with detailed solutions. It consists of two parts: in the first part finite-dimensional systems are considered, while the second part deals with finite-dimensional systems. All the important concepts and topics are included, such as quantum gates and quantum circuits, entanglement, teleportation, Bell states, Bell inequality, Schmidt decomposition, quantum Fourier transform, magic gates, von Neumann entropy quantum cryptography, quantum error correction, coherent states, squeezed states, POVM measurement, beam splitter and Kerr-Hamilton operator. The topics range in difficulty from elementary o advanced. Almost all of the problems are solved in detail and most of them are self-contained. All relevant definitions are given. Students can learn from this book important principles and strategies required for problem solving. Teachers will find it useful as a supplement, since important concepts and techniques are developed through the problems. It can also be used as a text or a supplement for linear and multilinear algebra or matrix theory.

Table of Contents

Finite-dimensional Hilbert spaces
Qubits	p. 3
Kronecker product and tensor product	p. 14
Matrix properties	p. 24
Density operators	p. 49
Partial trace	p. 58
Unitary transforms and quantum gates	p. 66
Measurement	p. 88
Entanglement	p. 98
Teleportation	p. 132
Cloning	p. 141
Quantum algorithms	p. 143
Quantum error correction	p. 158
Quantum cryptography	p. 162
Infinite-dimensional Hilbert spaces
Harmonic oscillator and Bose operators	p. 169
Coherent states	p. 193
Squeezed states	p. 205
Entanglement	p. 212
Teleportation	p. 225
Swapping and cloning	p. 227
Hamilton operators	p. 232
Table of Contents provided by Blackwell. All Rights Reserved.