This book is designed to be a textbook for a one-semester course in quantum computing and quantum information theory. Recommended prerequisites includes basic undergraduate finite probability theory, linear algebra, and some abstract algebra up through group theory. Some parts of the book are more challenging – particularly the later ones - and probably a better fit for graduate students. Even some of the early chapters would challenge typical undergraduates.

Unlike similar texts this one puts a good deal more emphasis on information theory. The author treats quantum information theory as a straightforward adaptation of Shannon’s original information theory. Another unusual aspect of the book is its exploration of the connections between quantum information theory and representation theory. The book does indeed provide a mathematical perspective that comparable textbooks do not.

The author begins with classical and probabilistic computation, partly a review and partly a treatment based on linear algebra designed to lead the way to quantum computation. With this, the reader is reminded of the context in which quantum computation developed. Following this is a very good description of the quantum mechanics behind quantum computation. It is the best I have seen among the several comparable texts, and it gives a good sense of the concepts of quantum entangling, super-intense coding via qubits, quantum teleportation and the quantum weirdness implied by John Bell’s work.

Treatment of the basics of quantum computing follows. It includes the algorithms of Grover for searching, of Shor for factoring, and several others. The discussion here is more rigorous, proofs are presented, and the necessary elementary number theory background is also provided.

The remainder of the book treats aspects of information theory beginning with Shannon’s classical information theory. The author then devotes a whole chapter to develop the language and background for quantum information theory. This includes a reformulation of the postulates of quantum mechanics presented earlier in the book. Following this reformulation and a discussion of its consequences, the author presents quantum information theory as a straightforward adaptation of Shannon’s theory to the quantum setting, one that is capable of handling quantum entanglement and its consequences.

The last chapter describes the role representation theory can play in quantum information theory. It includes a very condensed treatment of the basics of representation theory.

Exercises are provided throughout, and an appendix includes some hints and some solutions. Two other appendices offer basic background in algebra/linear algebra and probability. There is also an extensive bibliography.

Bill Satzer (bsatzer@gmail.com), now retired from 3M Company, spent most of his career as a mathematician working in industry on a variety of applications. He did his PhD work in dynamical systems and celestial mechanics.