Customer Reviews

Approaching Quantum Computing

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There are a number of good books about quantum computing around. Unfortunately, because it has a number of errors, and because the explanations are not always clear, this is not one of them. I know somebody who, after reading this book's section on superdense coding and teleportation, ended up more confused than he started out. This is because not only is teleportation presented using a forest of bewildering 8x8 matrices (correct, but only useful if this is explained well), but the words accompanying these matrices are actually wrong. For example in superdense coding Alice is said to send Bob a quantum bit in a state described by a 4-dimensional vector. This vector actually describes the joint state of Alice and Bob's quantum bits, and there is no way to describe Alice's quantum bit alone. This is a very important distinction to make if you want to comprehend the material, and this book does not make it here. We also learn that in teleportation, "The transfer of quantum information appears to happen instantly, though Bob needs to first receive classical information regarding the result of Alice's measurement before validating his own result." I'm not even sure what this sentence is trying to say. What does validating mean in this context?

The definition of uniformity is wrong. The authors do not appear to understand the concepts behind this definition, or if they do, they are incapable of communicating these concepts to the reader.

In the factoring algorithm, the second condition in the definition of order of r modulo N is incorrect. First it has a 1 in the right-hand-side, and the authors meant to put a 0 there. Second, this condition does not belong in the correct mathematical definition of order. And finally, they don't need this condition since they don't seem to use it anywhere. To make matters worse, Figure 5.10, which illustrates the factorization process for 21, shows 1 times 11 being equal to 16.

To be fair to the authors, these errors have now been corrected in the errata, and I haven't looked at earlier chapters of the book, which may be better than the chapters I did look at.

In planning a course on quantum computing, an instructor would want to cover the significant highpoints in the subject: Shor's factoring algorithm, Grover's search algorithm, Deutsch's problem, the hidden subgroup problem. I for one found that this book does precisely that. Students will want an accessible and attractive presentation. This book is beautifully presented, nicely organized, and pedagogically presented with motivation, clear explanations, and well chosen exercises.

While the subject has a variety of facets, physics, math, computer science, this book emphasizes the last two. In a highly interdisciplinary subject, each author (or team of authors) must make selections. In selecting what to cover, the authors had the classroom and students in mind.

More precisely the subject here is presented in the form of quantum gates, channels, and circuits. Yet, quantum physics and the foundations are not neglected.

The graphic presentation (figures and diagrams) is done in a way to aid learning, and I expect that this book will be the preferred text in courses in the subject for some time to come.

Advanced undergraduates will be able to follow the logical progression of subjects. Several special features in the book help: Exercises, an extensive and instructive glossary, historical insight, motivation, appendices (including key math topics, e.g., modular arithmetic and Hadamard transforms which perhaps may not be widely known), and circuit diagrams illustrating at the same time matrix factorization and the complexity of circuits.

Contents: 1. History and background, 2. Rudiments of quantum physics as it is needed, 3. Qubits and computer science rewritten in the form of quantum gates, 4. The key quantum algorithms (Shor, Grover, Simon) and the highpoints in the subject, 5. Entanglement, decoherence, error-correcting codes, Bell, dense coding, EPR, reversible computation, thermodynamic entropy, and more.

Highly recommended!

An errata for the book Approaching Quantum Computing has been available at http://www.cs.ucf.edu/~dcm since February 2004. Please contact the author (dcm@cs.ucf.edu) to signal any error you may find.