An Introduction to Quantum Computing [Paperback]

Phillip Kaye (Author), Raymond Laflamme (Author), Michele Mosca (Author)

Book Description

ISBN-10: 019857049X | ISBN-13: 978-0198570493 | Publication Date: January 18, 2007 | Edition: 1

This concise, accessible text provides a thorough introduction to quantum computing - an exciting emergent field at the interface of the computer, engineering, mathematical and physical sciences. Aimed at advanced undergraduate and beginning graduate students in these disciplines, the text is technically detailed and is clearly illustrated throughout with diagrams and exercises. Some prior knowledge of linear algebra is assumed, including vector spaces and inner products. However, prior familiarity with topics such as tensor products and spectral decomposition is not required, as the necessary material is reviewed in the text.

Editorial Reviews

Review

"The book is very accessible and the authors do an excellent job breaking up Shor's factoring algorithm into pieces that students can easily digest." Jonathan R. Friedman, Physics Today

"A reasonably brief and very accessible introductory graduate or senior undergraduate textbook."--Mathematical Reviews

About the Author

Phillip Ronald Kaye was born in Toronto, and raised in Waterloo, Ontario, Canada. In 1995 Phil was accepted to the Faculty of Engineering at the University of Waterloo with an entrance scholarship. He completed his undergraduate degree in Systems Design Engineering in 2000 and was awarded the George Dufault Medal for Excellence in Communication at his convocation. During the Summer months following his undergraduate convocation, Phil worked as an encryption software developer at Research in Motion (RIM), where he continued to work on a part-time basis during his graduate studies. Phil did his Master's degree in the department of Combinatorics and Optimization at Waterloo. His Master's thesis was entitled 'Quantum Networks for Concentrating Entanglement, and a Logical Characterization of the Computational Complexity Class BPP.' Phil is currently a PhD student at the School of Computer Science at the University of Waterloo. Raymond Laflamme completed his undergraduate studies in Physics at Universit� Laval. He then moved to Cambridge, UK, where he took Part III of the Mathematical Tripos before doing a PhD in the Department of Applied Mathematics and Theoretical Physics (DAMTP) under the direction of Professor Stephen Hawking. Following posts at UBC, Cambridge and Los Alamos National Laboratory, Raymond moved to the University of Waterloo in 2001 as a Canada Research Chair in Quantum Information. Raymond is a recipient of Ontario's Premier Research Award and a Director of the Quantum Information program of the Canadian Institute for Advanced Research. He was named the Ivey Foundation Fellow of the Canadian Institute for Advanced Research (CIAR) in September of 2005. Michele Mosca obtained a DPhil in quantum computer algorithms in 1999 at the University of Oxford. Since then he has been a faculty member in Mathematics at St. Jerome's University and in the Combinatorics and Optimization department of the Faculty of Mathematics, University of Waterloo, and a member of the Centre for Applied Cryptographic Research. He holds a Premier's Research Excellence Award (2000-2005), is the Canada Research Chair in Quantum Computation (since January 2002), and is a CIAR scholar (since September 2003). He is a co-founder and the Deputy Director of the Institute for Quantum Computing, and a founding member of the Perimeter Institute for Theoretical Physics.

Product Details

• Paperback: 288 pages
• Publisher: Oxford University Press, USA; 1 edition (January 18, 2007)
• Language: English
• ISBN-10: 019857049X
• ISBN-13: 978-0198570493
• Product Dimensions: 9.1 x 6 x 0.6 inches
• Shipping Weight: 15.5 ounces (View shipping rates and policies)
• Average Customer Review: 4.5 out of 5 stars  See all reviews (6 customer reviews)
• Amazon Best Sellers Rank: #735,464 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

26 of 27 people found the following review helpful:

5.0 out of 5 stars Terrific choice for engineers interested in quantum computing, July 14, 2007

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calvinnme - See all my reviews
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This review is from: An Introduction to Quantum Computing (Paperback)

This book is geared for the reader who has an undergraduate education in a technical field and who has a solid background in linear algebra, including vector spaces and inner products. Prior familiarity with topics such as eigendecomposition and more advanced mathematical topics is not required. The book reviews all of the necessary additional material. There are some places in the book where group theory is referred to, but these sections of the book are self-contained so that the reader can skip them if needed. It is a very accessible introduction to a complex subject that is fairly detailed and complete. Exercises are integrated into the body of the text. Each exercise is designed to illustrate a particular concept, fill in the details of a calculation or proof, or to show how concepts in the book can be generalized or extended. The following is a brief overview of the book:

1. Introduction and Background - Presents some fundamental notions of computation theory and quantum physics that will form the basis of what follows.

2. Linear Algebra and the Dirac Notation - Familiarizes the reader with the algebraic notation used in quantum mechanics, reminds the reader of some basic facts about complex vector spaces, and introduces some notions that may not have been covered in an elementary linear algebra course.

3. Qubits and the Framework of quantum Mechanics - Introduces the framework of quantum mechanics as it pertains to the types of systems that are considered in the book. Here the author also introduces the notion of a quantum bit or "qubit", which is a fundamental concept in quantum computing.

4. A Quantum Model of Computation - The circuit model of classical computation can be generalized to a model of quantum circuits. In such a model you have logical qubits carried along "wires" and quantum gates that act on the qubits. For convenience, the discussion is limited to unitary quantum gates.

5. Superdense Coding and Quantum Teleportation - Looks at our first protocols for quantum information. Examines two communication protocols that can be implemented using the tools which can be implemented using the tools developed in previous chapters. These protocols are known as superdense coding and quantum teleportation. Both of these are inherently quantum - there are no classical protocols that behave in the same way as these.

6. Introductory Quantum Algorithms - Describes some of the early quantum algorithms that are simple and illustrate the main ingredients behind the more useful and powerful quantum algorithms described in subsequent chapters. Since quantum algorithms share some features with classical probabilistic algorithms, the chapter starts with a comparison of the two algorithmic paradigms.

7. Algorithms with Superpolynomial Speed-Up - Examines one of two main classes of algorithms: quantum algorithms that solve problems with a complexity that is superpolynomially less than the complexity of the best-known classical algorithm for the same problem. That is, the complexity of the best-known classical algorithm cannot be bounded above by any poynomial in the complexity of the quantum algorithm. The chapter starts off by studying the problem of quantum phase estimation, which leads naturally to the Quantum Fourier Transform (QFT).

8. Algorithms Based on Amplitude Amplification - Discusses a broadly applicable quantum algorithm - quantum search - that provides a polynomial speed-up over the best-known classical algorithms for a wide class of important problems.

9. Quantum Computational Complexity Theory and Lower Bounds - Quantum computers seem to be more powerful than classical computers for certain problems. However, there are limits on the power of quantum computers. Since a classical computer can simulate a quantum one, a quantum computer can only compute the same set of functions that a classical computer can. This chapter examines this and some related issues.

10. Quantum Error Correction - Quantum computers are more susceptible to errors than classical digital computers because quantum mechanical systems are more delicate and more difficult to control. If large-scale quantum computers are to be possible, a theory of quantum error correction is needed. This is the issue discussed in this chapter.

Overall, I found this book well suited to self-study, particularly for someone with an engineering background. Highly recommended.

13 of 15 people found the following review helpful:

5.0 out of 5 stars Great book, June 8, 2007

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C. Chiang - See all my reviews
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This review is from: An Introduction to Quantum Computing (Paperback)

For a beginner like me, I think this is a great book. I used to spend lots of time on N+C book but still got confused.

This introduction to Quantum computing book has lots of illustrations explaining how things are done step by step inside those complicated algorithms. If you study on your own with this book, there should be no problem. Then you can go back to review N+C's book and things would be much more clear.

1 of 1 people found the following review helpful:

2.0 out of 5 stars Nice introduction, but somewhat disappointing towards the end, May 30, 2011

By 

Andreas Müller - See all my reviews

This review is from: An Introduction to Quantum Computing (Paperback)

The book certainly gives a nice and gentle introduction. But about half through it, I become more and more disappointed:
- It is often not clear which theorems and statements are proved and what is merely cited from the literature. This isn't a problem at the beginning, but becomes a source of confusion in the second half of the book.
- There is a large bibliography, but as far as I could see, it is very seldom referenced where it would make most sense.
- Some statements are really careless. Many algorithms talk about registers without even specifying them. E.g. Simon's algorithm.