Quantum Computation and Quantum Information

by Michael A. Nielsen, Isaac Chuang, Issac L Chuang, et al.

Book Overview

One of the most cited books in physics of all time, Quantum Computation and Quantum Information remains the best textbook in this exciting field of science. This 10th anniversary edition includes an introduction from the authors setting the work in context. This comprehensive textbook describes such remarkable effects as fast quantum algorithms, quantum teleportation, quantum cryptography and quantum error-correction. Quantum mechanics and computer...

• Format: Hardcover
• Language: English
• ISBN: 1107002176
• ISBN13: 9781107002173
• Release Date: January 2011
• Publisher: Cambridge University Press
• Length: 702 Pages
• Weight: 3.50 lbs.
• Dimensions: 1.6" x 7.0" x 9.8"

Customer Reviews

A book that repays study

My first acquaintance with this book came from a copy which I ordered through interlibrary loan after seeing favorable comments on the internet. The loan period was only two weeks, so I wasn't able to study this 600-page book in detail. But I learned quite a bit just by skimming it. After I saw that it was a book that would repay study, I purchased it. The first chapter of 58 pages nicely introduces many of the important ideas, leaving the more difficult details to later chapters. For example, I learned about quantum teleportation, which I had never understood from popular accounts. I read it from cover to cover and was able to follow almost all of it in detail. Since I read it as someone learning this material for the first time, I'll review it from a student's perspective. A much longer review discussing technical issues is available on my web site. Chapter 2 gives a nice summary of basic quantum mechanics. It includes an introduction to necessary concepts from abstract linear algebra, including important specific applications (e.g., the Schmidt decomposition) which are not likely to be covered even in advanced linear algebra courses. The third chapter gives an introduction to computer science concepts. This gives a conceptual framework within which to present the ideas of quantum computation. More material is included here than is necessary to understand the rest of the book. Readers may find it efficient to skim this chapter initially and return for more detail when necessary. The next three chapters present the essentials of quantum circuits, the quantum Fourier transform, and quantum search algorithms. Here there is perhaps room for a little improvement. I thought that important details were sometimes omitted from the exposition, and I occasionally had to go to the original literature to understand the ideas. Also, there is a bad misuse of the "Big-O" notation throughout these chapters, startling in a book so generally carefully written. Sophisticated readers will take this in stride, but it might demoralize beginners. For details, see the longer review on my web site. The mathematics of quantum computation is easy compared to the problems of physically realizing it. Chapter 7 gives an extensive discussion of these problems and various proposals for overcoming them. This concludes the "quantum computation" section of the book, which is a little more than half of the 600-odd pages. The rest deals with quantum information theory. This is presented in less detail than the quantum computation chapters, and demands more from the reader. A summary of classical information theory is included, with sketches of proofs of important results. I found this very helpful in refreshing my memory of Khinchin's book on information theory, which I read decades ago. Some of the more complicated proofs are only sketched. I didn't get as much from the quantum information section of the book as from the quantum computation section. I thi

An essential text

Despite its age, I keep coming back to this text for the careful prose and knowledgeable authors; so much so that I am ordering the hardback edition, having worn out the binding of the paperback edition. It is both a book to learn from and one to refer to later. It will eventually be outdated, but I don't see this as having happened yet. Although a large book, it is not bulked out like some, containing a lot of useful and relevant material. Perhaps not the text for those setting out from a 'cold start', but then a great follow up to 'The Quest for Quantum Computing" by Julian Brown. Not overtly rigorous, which is to its credit, as the concepts remain clear as a result. Certainly an essential text, where the prose does not get in the way. A very readable book about a very exciting subject, that is sure to deliver to the determined reader.

Great reference text - hard to learn from for the first time

This book has found its many uses as a reference. In particular the citations helped me locate key papers that I needed to work toward my research project. If you want to do research in this area than I recommend you add this text to your collection without question, however if you are trying to teach yourself quantum mechanics (like I did) I can suggest several other books that will help you along your quest. This book lacks worked examples, I recommend the worked problems text: (Problems & Solutions in Quantum Computing & Quantum Information, ISBN: 9812387900) This book also skips over many `simple' concepts as expected for the depth of coverage. The kindest introduction to quantum computing out of the dozen books on my shelf is: (Approaching Quantum Computing, Dan C. Marinescu, Gabriela M. Marinescu , ISBN: 013145224X). There are now many texts on the subject of quantum computing, but there is a reason why this text is citied hundreds of times by the top people in this field. For a research project you must get this book, if you are teaching a class it might be wise to mention this book and refer students to another text. I think that the text (Explorations in Quantum Computing, ISBN: 038794768X) is good in the amount of material covered, but does not go into depth on key points -- It could be argued that the Mathematica simulation files more than compensate for this. I have not had a chance to read the Gruska text (Quantum Computing, ISBN: 0077095030) since it is out of print for the time being. I hear a new addition is on its way and I am interested in reading that book. I would say that this text will remain a classic but the material is not easy for me to grasp. The book is hard, but quantum computing is hard so this is expected. I could live without the other texts on my shelf, but I need NC. If you do buy this book search for the "Quantum Computing Tutorial by Mark Oskin", an Assistant Professor at the University of Washington. His notes were designed as a guide for his students using the NC text, and they will help you get through some key examples. I downloaded the file: quantum-notes.pdf but it is also free in latex for professors.

Interdisciplinary!

Classical computation follows the model of A. Turing,-- strings of bits, i.e., 0s and 1s; a mathematical model, now called the Turing mashine. Analogues based instead on two-level quantum systems were suggested in the 1980ties by R.P. Feynman and D. Deutsch. But it wasn't until Peter Shor's qubit-factoring algorithm in the mid 1990ties that the subject really took off, and really caught the attention of the math community. That there is a polynomial factoring algorithm shook the encryption community as well, for obvious reasons. New elements of thinking in the quantum realm, and not part of the classical framework, include superposition of (quantum) states, and (quantum) coherence. This makes a drastic change in the whole theoretical framework when one passes from the classical notion of bit-registers to that of qubit-registers. In passing from logic gates to quantum gates(unitary matrices), the concept of switching networks changes. It introduces new challenges, and new truely exciting opportunities. It is not easy for authors to make everyone happy;-- this is especially so in a new field,--one which has grabbed headlines, and one which is at the same time interdisiplinary. In this case, the authors succeed as well as anyone, I believe.-- This lovely book covers several of the appropriate areas of physics (quantum theory, (some) experiment...), of computer science (the mathematical side of the subject), and of math (operators in Hilbert space, and the theory of algorithms);-- each member of the particular scientific specialty has very definite ideas of his/her own subject,-- and that of the others. Nonetheless, in this readers opinion, the two authors did a great job;-- they explain math to the physics community,-- and they sucessfully teach quantum theory and theoretical CS to mathematicians. The book is suitable for grad students: has lots of great exercises, but it could perhaps have used some more worked examples. (Fortunately they can be found in other books on quantum computation.) The Nielsen-Chuang book is most certainly a great entry for students into this exciting new subject. There are other books,-- but they, for the most part, take a more narrow view. The material in Nielsen-Chuang is timeless,-- and I expect the book will also be popular ten years from now.

Good for Research and Self-Study

I think that this book is excellent for self-study, and does provide a significant level of rigour. I believe that the authors do a significantly good job defining their terms and making sure the reader is "with them." For example, just a few lines up from Equation 5.36 on page 226, in fact immediately after the start of Section 5.3.1, the authors make the comment, "For positive integers x and N, x This is admittedly rather a specific example, but it illustrates the point: the authors have a well-developed sense of logical flow, and such flow makes it much easier to follow what is rather a difficult subject. The subject is difficult because it spans such a huge variety of disciplines. My advice is to take courses in mathematics: linear algebra (easily the most important of all the classes), abstract algebra, discrete mathematics, advanced calculus, number theory; in physics: classical mechanics, quantum mechanics, electricity and magnetism; electrical engineering: linear circuits, digital logic, microprocessors; and in computer science: algorithms and data structures, cryptography. Then I think you would have an adequate background to understand this top-notch, advanced book.