Quantum Computing: A Gentle Introduction

May 24, 2012

Authors: Eleanor Rieffel and Wolfgang Polak

Edition: First

Publisher: MIT Press

Pages: 392

Price: £31.95

ISBN: 9780262015066

Quantum computing is a rapidly evolving research discipline combining quantum physics, computer science and information theory. It offers tantalising possibilities for new forms of computation while highlighting some strange intellectual concepts that are not yet fully understood.

Eleanor Rieffel and Wolfgang Polak's book explores these issues and provides us with a rich tapestry containing many threads of thought. Their decision to not discuss physical realisations of quantum computing elements in detail is correct, as this area is just too young. Nevertheless, this theoretically focused text rises sublimely to its challenge, namely to make quantum computing accessible to a wide audience.

The theory is mathematical, and the authors have devoted much thought to how to develop this in a progressive way. References to supporting texts are abundant, and the reader is often invited to reflect and to complete some wonderful exercises. Rieffel and Polak have produced a pedagogical triumph. While reviewing this book, I designed and delivered a first-year undergraduate computing lecture and workshop drawing on its content, with excellent impact.

One of the threads woven through the chapters is the discussion of entanglement. At first it seems to be an oddity, but then clear practical applications are discussed, and finally we are invited to reflect on the folk wisdom that entanglement explains quantum computing speed-up. The simplistic nature of this argument is revealed, and the point is made that many efficient quantum algorithms do not use entangled states.

Another thread is that of application. Rieffel and Polak effectively focus on quantum communication throughout the book (including dense coding and teleportation) to ground the theory. The concept of notation forms another thread, and here the standard discussion of quantum circuits is present, but this is challenged. I found useful the authors' invention of a novel pseudo-code notation, presented in such a way as to be more concise and potentially expressive.

However, the most fundamental thread is the request that we should be critical of the standard wisdom. In chapter 5, we are given three cautions: first, to appreciate the difference between the quantum state space and the associated vector space; second, to reflect on the notion of control and target bits in n-qubit gates that could be misinterpreted and restricting; and third, to be cautious in reading quantum circuit diagrams that may not fully communicate the circuit's behaviour.

In chapter 9.6 we are offered some cautionary insights about possible misunderstandings of the implications of Grover's algorithm, which may turn out to have limited application. Similar nuggets are found in chapter 7.6, where the idea that quantum superposition generates quantum parallelism is challenged, and in chapter 13.7 the wisdom concerning the need for entanglement is challenged.

Overall, Rieffel and Polak's careful interweaving of threads is a masterpiece. Perhaps it is no accident that the front cover depicts a tapestry.

Who is it for? Undergraduates will enjoy this book, providing they are willing to work hard. The potential readership includes students of the sciences (including computing), engineers and mathematicians, and it will also be useful to postgraduates.

Presentation: Well thought out and easy to pick up to continue reading.

Would you recommend it? A masterpiece that should be read by all who are interested in quantum computing.

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