Quantum computation and quantum information: | Guide books

Quantum computation and quantum informationAugust 2000

Publisher:

Cambridge University Press
40 W. 20 St. New York, NY
United States

ISBN:978-0-521-63503-5

Published:01 August 2000

Pages:

676

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Reviewer: H. H. H. Homeier

Nielsen and Chuang provide a thorough and readable introduction to the main ideas and techniques in the field of quantum computation and quantum information. This is an important new field of computing, crossing the disciplines of computer science, mathematics, and physics. The basic idea of quantum computing is to use quantum bits and their unitary transformations, governed by the laws of quantum mechanics, to perform computations. This allows access, to a certain extent, to all the possible results of a computation simultaneously, and thus offers the opportunity to find quantum algorithms that outperform classical algorithms. The main drawback of the method is that up until now, the number of qbits was strongly limited, since no large-scale quantum computers have been built. In the first part of the book, the reader is given an overview of the field, and briefly introduced to the main ideas of quantum mechanics and computer science. The second part of the book addresses quantum computation by first discussing the basic model of quantum circuits that allows simulation of quantum systems. This is followed by detailed descriptions of some quantum algorithms. Here, the quantum Fourier transform is discussed, along with important applications like the crypto-relevant factoring of large integers, and computation of discrete logarithms. Quantum search algorithms are also discussed; these offer the opportunity to speed up the solution of NP-complete problems, in comparison to classical algorithms. The last chapter of the second part discusses the physical systems that could be used to build quantum computers, like ion traps, nuclear magnetic spin systems, or photons. The third part of the book focuses on quantum information, and discusses the role of noise in quantum computers, as well as quantum error-correction possibilities. This part also addresses fundamental information theory concepts, for example entropy in quantum systems, accessing the information of quantum states, coding theorems for noiseless channels, and information transfer over noisy classical and quantum channels. Quantum cryptography-based topics like quantum key distribution are also discussed. The book’s presentation is clear. Usually, key ideas are presented in basic examples before more general discussions are presented: the approach found in good physics textbooks. The book should be accessible to graduate students with a good knowledge of mathematics. There are also a large number of exercises, ranging from basic to research problems. Here, the book could be improved by adding worked-out solutions for at least some of the exercises. In summary, the book offers a good introduction to the rapidly developing field of quantum mechanical computing methodologies. Online Computing Reviews Service

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Integrable quantum computation

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Integrable quantum computation

Quantum correlation swapping

Quantum Fisher information, quantum entanglement and correlation close to quantum critical phenomena