An Introduction to Quantum Computing , Phillip Kaye , Raymond Laflamme , and Michele Mosca , Oxford U. Press, New York, 2007. $150.00 (274 pp.). ISBN 978-0-19-857000-4, ISBN 978-0-19-857049-3 paper
Introduction to Quantum Information Science , Vlatko Vedral , Oxford U. Press, New York, 2006. $70.00 (183 pp.). ISBN 978-0-19-9215706
There was a time when computer and information science appeared to be a discipline of pure logical reasoning, divorced from physics. Questions of what a computer could do and what resources would be needed to do it seemed to be largely independent of its physical construction. The connection between information and physics, thermodynamics in particular, has been developed during the past 50 years or so. A famous example of that relation was discovered by Rolf Landauer, who in 1961 showed that erasing, or otherwise irreversibly losing, a bit of information in a computer must dissipate at least kT ln2 of energy.
That idea, now called Landauer’s principle, was succinctly summarized in his declaration that “information is physical,” which has become a mantra in the fields of quantum information science and quantum computing. (See Landauer’s article in Physics Today, Physics Today 0031-9228 44 5 1991 23 https://doi.org/10.1063/1.881299 May 1991, page 23 .) We now know that a computer that exploits the unique features of quantum mechanics can solve some problems more efficiently than any classical computer, a result that firmly links computer and information science to physics. Quantum information science, broadly defined, has expanded enormously over the past two decades, and numerous books on the subject at all levels have appeared, including Phillip Kaye, Raymond Laflamme, and Michele Mosca’s An Introduction to Quantum Computing and Vlatko Vedral’s Introduction to Quantum Information Science.
An Introduction to Quantum Computing covers a small subset of the topics in Michael Nielsen and Isaac Chuang’s Quantum Computation and Quantum Information (Cambridge U. Press, 2000), which has become a standard text in the field. That tome, still relevant eight years after its publication, is probably too unwieldy for most undergraduates looking for an introduction to the field. In contrast, Kaye, Laflamme, and Mosca’s book is very accessible. LaFlamme and Mosca are on the faculty of the Institute for Quantum Computing at the University of Waterloo in Canada and are well-known researchers in quantum information science; Kaye is a doctoral student at the university. Based on a course taught by the authors, the text is tightly focused on quantum computing and carefully leads the reader through Deutsch’s, Shor’s, and Grover’s algorithms, among others. Coupled with the authors’ careful exposition is a cadre of exercises, integrated into the text, that forms an important pedagogical aid. A series of exercises presented early in the book, for example, guide the reader to the existence of a universal set of quantum gates. For better or worse, in some places important results are simply declared as theorems without proof.
The authors do an excellent job breaking up Shor’s factoring algorithm into pieces that students can easily digest. They take the approach—not original, but deftly presented—of reducing the order-finding problem at the heart of factoring to the problem of finding the eigenvalues of a unitary operator, delegating much of the work to the reader through exercises. The book contains a chapter on quantum complexity that is more formal than the rest of the text and may not appeal to some readers. However, readers who skip or skim that chapter will have little trouble digesting the remainder of the text.
Vedral’s Introduction to Quantum Information Science is billed as a graduate text but is not really—it contains no exercises. Distilled from a series of lectures by Vedral, a professor of quantum information science at the University of Leeds in the UK, it is a bit uneven, both in the selection of topics and style of presentation. Sometimes more space is given to the algebra of a simple example than to a fairly abstract proof.
Most of the book focuses on quantifying quantum entanglement, the author’s primary current research field, and quantum information by using entropic measures. That approach pervades his treatment of quantum computing, measurement, and error correction. Formal results are sometimes followed by clear discussions of analogies to thermodynamics. Error correction, for example, is cast in terms of swapping quantum states and entropy into environmental degrees of freedom. The book is a good, technical read, with many pithy or whimsical footnotes sprinkled throughout. Unfortunately, Vedral’s text contains numerous typographical errors and notational ambiguities. Most are merely distracting, but some may lead to real confusion. In contrast, the few errors I found in Kaye, Laflamme, and Mosca’s text are almost entirely inconsequential.
Both An Introduction to Quantum Computing and Introduction to Quantum Information Science would benefit from a stronger adherence to Landauer’s dictum. If information is physical, discussions of quantum information need to be coupled with concrete examples of physical implementations. Although the fundamental results of quantum information science depend on the logical structure of quantum mechanics—unitary evolution in Hilbert space and, perhaps, the projection postulate—and not on any specific qubit implementation, neglecting experimental realizations is unwise. A novice reading Kaye, Laflamme, and Mosca’s book, for example, might reasonably reach the conclusion that if there is a universal set of gates, clearly delineated quantum algorithms, and error-correcting codes on paper, then a large-scale quantum computer should be just around the corner. The reader should at least be given a glimpse of the challenges involved in making a robust controlled-NOT gate or performing a complete Bell-state measurement; both are primitives on the quantum information theorist’s palette but are challenging to perform in the lab. The closest these books come to discussing experiments are brief mentions of idealized Mach–Zehnder interferometers. Remarkably, because of an algebra mistake, Vedral gets that example wrong—the photon exits the wrong way from the symmetric interferometer.
There is another, deeper reason experiments in this field deserve more attention. If researchers fail to construct a large-scale quantum computer, it may be because of some practical limitation, or it may be the sign of something more interesting. A spectacular, albeit speculative, possibility is that we find quantum mechanics breaks down, and there emerge some fundamentally new laws of physics and, by extension, of information.