An Introduction to Quantum Computing Algorithms: (19 Progress in Computer Science and Applied Logic)

The purpose of this monograph is to provide the mathematically literate reader with an accessible introduction to the theory of quantum computing algorithms, one component of a fascinating and rapidly developing area which involves topics from physics, mathematics, and computer science. The author briefly describes the historical context of quantum computing and provides the motivation, notation, and assumptions appropriate for quantum statics, a non-dynamical, finite dimensional model of quantum mechanics. This model is then used to define and illustrate quantum logic gates and representative subroutines required for quantum algorithms. A discussion of the basic algorithms of Simon and of Deutsch and Jozsa sets the stage for the presentation of Grover's search algorithm and Shor's factoring algorithm, key algorithms which crystallized interest in the practicality of quantum computers. A group theoretic abstraction of Shor's algorithms completes the discussion of algorithms. The last third of the book briefly elaborates the need for error- correction capabilities and then traces the theory of quantum error- correcting codes from the earliest examples to an abstract formulation in Hilbert space. This text is a good self-contained introductory resource for newcomers to the field of quantum computing algorithms, as well as a useful self-study guide for the more specialized scientist, mathematician, graduate student, or engineer. Readers interested in following the ongoing developments of quantum algorithms will benefit particularly from this presentation of the notation and basic theory.

Table of Contents:
1 Quantum.- 2 Basics of Quantum Computation.- 3 Quantum Algorithms.- 4 Quantum Error-Correcting Codes.- Afterword.- References.

Review :
"Pittenger's book, as the title suggests, explains the mathematics at the basis of quantum computing and the fundamental algorithms, including Shor's factoring, Grover's search and error correction algorithms... Since quantum computing is a highly interdisciplinary science, the author has tried to capture the attention of a large variety of readers and he has mostly achieved this objective. The book can be used as a formal introductory text for graduate students as well as a fascinating, but still engaging resource for interested readers who are comfortable with linear algebra... Pittenger helps the reader into focusing attention on the algorithmic aspects rather than the formal content and uses examples as [an] integral part of the book, illustrating the substantial meaning of quantum theory applied to computing. He also proposes some exercises to stimulate an insightful reading... The bibliography is complete and the interested reader can improve the understanding of the book and of the entire matter by following the numerous references, acquiring in this way more tools for the comprehension of a subject of such complexity..." --SIGACT News "An Introduction to Quantum Computing Algorithms reflects its author's own experience in learning the mathematics and theoretical physics required for the subject, as he writes in the acknowledgements. It is generally written in a pleasant and informal style, with much motivation in between the mathematics... In just 150 pages this book manages to explain much of the core of quantum computing, and to explain it well." --Quantum Information and Computation (QIC) "If you have a general (fuzzy) background on quantum physics and on computer science, I recommend reading this book... It is well written, easy to read, with many illustrating examples, and many exercises." --Zentralblatt Math