Quantum Computation and Quantum Information

Michael Nielsen and Isaac L. "Ike" Chuang have produced a highly readable, thorough, and timely survey of the field of theoretical quantum information science. Their Quantum Computation and Quantum Information is probably destined to become a standard text for researchers in this still emerging, rapidly developing field. Quantum information science is the application of the fundamental quantum physics phenomena to the storage, communication, and processing of information; it represents a complete paradigm shift for information processing technology. Phenomena such as superposition and entanglement, in theory, allow the solution of important mathematical problems thought to be intractable with standard electronic computers.

Research in quantum information science, which has seen remarkable growth in the last five years or so, is highly interdisciplinary, encompassing mathematics, computer science, physics, electrical engineering, materials science, and physical chemistry. Nielsen, an associate professor at the University of Queensland node of the Australian Special Research Center for Quantum Computing Technology, in Sydney, Australia, and Chuang, an associate professor at the MIT Media Laboratory, are two of the brightest young scientists in a field replete with bright young scientists. They have made numerous important theoretical and experimental contributions to this field, most notably the first experimental implementation of a quantum algorithm, by Chuang and coworkers, in 1997.

The book is divided into three sections, dealing respectively with fundamental concepts, quantum computation, and quantum information. The authors rightly choose to examine key issues in depth rather than attempt a mile-wide, inch-deep, catholic approach. They concentrate on the development of an understanding of quantum information theory, of what a quantum computer can do and why it will be powerful, rather than on how such a device can be constructed. Descriptions of experiments are confined to a single chapter that serves to whet the appetite and direct the reader to other sources.

While all of the topics covered in the book are of considerable importance and interest, others of possibly equal or greater import--such as decoherence-free subspaces, continuous variable quantum information processing, or the characterization of quantum state entanglement--are covered only in passing or not at all. When describing an emerging field such as this, it is difficult to know what will be the most popular topic a few months hence, let alone judge which are of lasting importance to the field as a whole. Thus, I cannot really level criticism at the authors for such omissions; indeed, the background material needed to assimilate such new developments is all very well covered.

In a work of this size, minor errors are inevitable. The authors are maintaining a web site with errata at http://www.squint.org/qci.

There are quite a few books published on quantum information science, none with either the scope or depth of the Nielsen-Chuang work, but which nevertheless might serve as suitable complements to it. The compendium works The Physics of Quantum Information, edited by Dirk Bouwmeester, Artur Ekert, and Anton Zeilinger (Springer, 2000), and Scalable Quantum Computers: Paving the Way to Realization, edited by Sam Braunstein and Hoi-Kwong Lo (Wiley, 2001), offer much more information on experiments and technology development. Other books on this field, aimed at working physicists (as opposed to the plethora of semipopular works), are: Explorations in Quantum Computing by Colin Williams and Scott Clearwater (Telos, 1998, with a new edition to appear), Introduction to Quantum Computers by Gennady Berman, Gary Doolen, Ronnie Mainieri, and Vladimir Tsifrinovitch (World Scientific, 1998), and Introduction to Quantum Computation and Information, edited by Hoi-Kwong Lo, Sandu Popescu, and Tim Spiller (World Scientific, 1998), all of which are shorter, more introductory works.

The book is very well written and a pleasure to read. The authors assume initially only minimal knowledge of quantum theory and/or computer science, and bring the reader up to the current state of the art as it pertains to this field. Problem sets to aid the student and instructor are included. The text is enlivened with occasional insertions of wit and apt quotations. In this spirit, I will conclude with a quotation from Niccolò Machiavelli's The Prince: "There is nothing more difficult to take in hand, more perilous to conduct, or more uncertain in its success, than to take the lead in the introduction of a new order of things.