Quantum information theory and quantum computation are two recent and quite active research fields that, by building upon the fascinating and puzzling world of quantum mechanics, offer ways of managing information and performing computations that go beyond what our everyday “classical” computers can ever hope to achieve. Many books are devoted to these fields (one sometimes hears that there are unfortunately more of them than existing quantum algorithms). In this short monograph, the author offers to view them, somewhat unusually, through the eyes of a theoretical physics research scientist.
After a short introduction, ten chapters provide a fast-paced presentation of the field of quantum information theory and computation. The first three chapters build the foundations of classical, semiclassical, and quantum physics, using a single framework that underlines the key commonalities and differences between these theories. Chapters 5 and 6 study the most basic quantum system, the qubit, and its manipulations. Some of the most counterintuitive features of quantum physics, such as entanglement and nonlocal actions, show up when one looks at composite systems, the focus of chapter 7; quantum operations on such systems, for example, teleportation, are then addressed. In eight short pages, chapter 8 surveys quantum gates, Grover’s search algorithm, and the quantum Fourier transform. Chapters 9 and 10 deal with information theory, using the classical approach (Shannon entropy and coding) and the quantum approach (Von Neumann entropy). At the end of each chapter, exercises, with corrections, provide worthwhile additional material.
As this brief outline shows, the author puts more emphasis on the presentation of principles and foundations (a lot of them, indeed) than on the detailed explanations of quantum algorithms. In fact, the description of the latter ones is rather informal compared to the abstract descriptions and presentations of quantum mechanical concepts. I would thus advise the reader to carefully look at each word of the book title and what it implies before deciding whether this book is of interest. Although book titles can be somewhat vague or misleading, this is definitely not the case here: the document is very short for the material covered, and thus rather dense. One must understand that theoretical physicists are familiar with such abstract notions as phase spaces, density matrices, and Bloch spheres. The advertised emphasis is more on information theory than on computation; for instance, adiabatic quantum computing and Shor’s number factorization algorithm are not introduced. Of course, and again as implied by the title, implementation issues and technological barriers to the deployment of quantum computing systems such as decorrelation and error-correcting codes are not addressed.
Thus, as a whole, I would not recommend this book to computer scientists who want to get a quick grasp of this field. To mathematically inclined researchers well aware of quantum computation, however, it offers a concise tour of the formal foundations of their domain. Finally, this book, coming out of lectures on the subject given to physics students at Eötvös University, suffers from some minor editing defects: a couple of references are made to material covered in later chapters, some of the English is approximate, and there are some typographical errors.
