Rating: 
Summary: Physics Today review
Review: A positive review of this book was in the November 2001 issue of Physics Today (...) Excerpts:
"Michael Nielsen and Isaac L. Ike Chuang have produced a highly readable, thorough, and timely survey of the field of theoretical quantum information science. Their Quantum Computation and Quantum Information is probably destined to become a standard text for researchers in this still emerging, rapidly developing field." "The book is divided into three sections, dealing respectively with fundamental concepts, quantum computation, and quantum information. The authors rightly choose to examine key issues in depth rather than attempt a mile-wide, inch-deep, catholic approach. They concentrate on the development of an understanding of quantum information theory, of what a quantum computer can do and why it will be powerful, rather than on how such a device can be constructed. Descriptions of experiments are confined to a single chapter that serves to whet the appetite and direct the reader to other sources." "In a work of this size, minor errors are inevitable. The authors are maintaining a web site with errata (...)."
Rating:
Summary: Interdisciplinary!
Review: 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.
Rating: 
Summary: Follow on from previous review
Review: Despite one reader's view. I am not an idiot. I agree that on page 226 the majority of the relevant definitions are present. So to some extent I stand corrected. The review I wrote was written while I was intensively studying the book in preparation for teaching a course involving quantum computation. I found the informal mix of discussion in the text and formal statements unclear at times. I would have preferrred informal discussion accompanied by highly formal statements (a la a mathematics text) of theorems etc. Then one wouldn't have to scan pages of text to find all the relevant definitions.
To come back to page 226. To make the definitions really water-tight one needs to say:
0 gte xy(modN) lte N-1
(lte and gte means less than or equal to and greater than or equal to respectively)
This is because
xy (mod N) = Nk + xy where k is any integer. However ket(z) where z gte N makes no physical sense.
This illustrates the subtle difference between mathematics and physics. Physics requires many restrictions (e.g. that physical variables are real valued) that mathematics doesn't require.
Note I have with hindsight and using the book over several years raised my star rating for the book to 4. I do not think books should be given 5 star rating just because they are the best currently written on the subject. For me the star rating is an absolute scale.
I would recommend the author's adopt the convention of collecting all definitions and theorems in boxes (so the busy reader can look there for the formal stuff) and not have to scan through lots of informal discussion to find all the definitions.
My apologies for incorrectness but I did find the book very difficult (and all my students did too) on first reading. It took me a long time of figuring things out to realise "Ah. That's what they meant"!
I think if readers accuse people of being idiots the least they can do is provide their name!
Rating:
Summary: The Reader Review by Julian Miller is INCORRECT!
Review: Dr. Julian Miller is either an idiot and obviously didn't read the book carefully at all. On page 226 just above the equation Miller talks about it says "For positive integers x and N, x < N, with no common factors, ..." and goes on to clearly define EVERYTHING. I read this book and I disagree 100% with that review and have just proved to you that the reviewer was completely wrong and just didn't read the book carefully on page 226. I had no trouble understanding the topics in this book and don't have PhD in anything, just a Bachelors in Physics and took a couple graduate courses. Everything was very clear in this book to me and I think it is a great book. Don't believe what that reviewers said, if he/she had just read the book more carefully he/she would notice that everything is defined. I bet that reviewer wasn't reading the book carefully at all and was just skipping sections and jumping around from page to page, skimming over certain paragraphs. It's a great book and it's the first one I encountered that was helpful enough to allow me to really make sense of this subject.
Rating:
Summary: The Reader Review by Julian Miller is INCORRECT!
Review: Dr. Julian Miller is either an idiot and obviously didn't read the book carefully at all. On page 226 just above the equation Miller talks about it says "For positive integers x and N, x < N, with no common factors, ..." and goes on to clearly define EVERYTHING. I read this book and I disagree 100% with that review and have just proved to you that the reviewer was completely wrong and just didn't read the book carefully on page 226. I had no trouble understanding the topics in this book and don't have PhD in anything, just a Bachelors in Physics and took a couple graduate courses. Everything was very clear in this book to me and I think it is a great book. Don't believe what that reviewers said, if he/she had just read the book more carefully he/she would notice that everything is defined. I bet that reviewer wasn't reading the book carefully at all and was just skipping sections and jumping around from page to page, skimming over certain paragraphs. It's a great book and it's the first one I encountered that was helpful enough to allow me to really make sense of this subject.
Rating: 
Summary: Good for reference, poor for teaching,self-study
Review: I am actually teaching a course involving Quantum Computing. I am using this book because it is better than other books I have seen. However that still doesn't mean this is a good book! I have a BSc in Physics and a PhD in mathematics and I work in a Computer Science Department so one would expect that it would be relatively easy to follow this text. However often nothing could be further from the truth! The book appears to be VERY hastily written with certian passages being absolutely impregnable to understanding. The authors often appear to have forgotten to define all their terms, so some arguments are as difficult to decipher as the Rosetta Stone. I give an example: page 226 equation 5.36 they define a unitary transformation U|y> -> |xy(modN)>. They talk about y and its relation to N (I presume that x and N are integers) but NOWHERE do they define what values x can take. So in principle x could be bigger than N. it is easy to demonstrate that some values of x give an operator that is not unitary. This isn't allowed so therefore it implies that x has some restrictions placed upon it. WHAT ARE THOSE RESTRICIONS? WHY DO THE AUTHORS NOT STATE THEM? The above example is just an illustration of the main fault of the book: Extremely sloppy definitions of many things (or absent definitions). They cultivate an air of rigour but it is all a sham. Verdict: Be prepared to spend a phenomenal amount of time on this book if you are going to use it for teaching. You will have to fill in many gaps and consult many research papers to make sense of it. BTW: there are no worked examples and exercises that often are incredibly difficult (presumably because the authors have omitted many definitions)
Rating:
Summary: Needs solutions to problems!
Review: I have over 3 dozen books on the subject and this is by far the clearest. I believe this book to be extremely well written and much clearer than other texts. In addition, the circuit notation used in the text is BY far easier than what is found in a text on Quantum Physics. Also, the way things are stated about general Quantum Theory is so much kinder and more logical than in any other text I have read, both saying the same things only this text explains this painful subject in a nice clean way. In any case, I believe this to be the best book on the subject. I also recommend Explorations in Quantum Computing (Williams, Clearwater), it is useful since it has many Mathematica Workbooks to simulate Quantum Circuits and that related. Really you need to read many books to understand this subject, but Nielsen and Chuang make a good foundation. I do agree that this book could be better, as could all texts, but being the best book in a very complicated new area of study is worthy of 5 stars. Simply, this is the best book on the subject that I have seen. If you are trying to teach yourself this material from any book chances are you will fail, but if you must I would get this one first and then the Williams book. Regards.
Rating:
Summary: Good for Research and Self-Study
Review: 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 < N, with no common factors,...". Now I would assume that Equation 5.36 would reference these same variables, and thus the restriction would still apply. 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.
Rating:
Summary: Excellent for startup and self-study on QC
Review: I'm an undergraduate student in Computer Science, doing my Diploma (BS/MS) thesis on Quantum Computing and Algorithms. One year has passed since I bought this book and I must say that Nielsen and Chuang did an excellent job! The book is outstanding in way of a global approach to the subject. If you are computer scientist, mathematician or physicist and you want some startup information, this is the book you are looking for! Although, the book doesn't assume that you have appropriate background on mathematics or computer science, it will be good that you have some affiliation with linear algebra, tensor calculus and basic computational complexity concepts. The book is excellent for self study and research, containing many exercises. If you want to get into Quantum computing, this could be your first option including some lectures by: Vazirani on Berkeley, Preskill on Calteh and Short Course on Quantum Computing (AMS). If you are an advanced undergraduate or graduate student, I will prefer Classical and Quantum Computing (AMS) by Kitaev, Shen and Vyalyi. This book will give you mathematical approach on computational complexity-classical computing (first 50 pages), which is needed to continue and understand further concepts of quantum complexity classes and quantum algorithms. Currently, I'm using both books, Kitaev's and Chuang's, and this is an excellent combination. Lot's of mathematics and ideas is covered by these books. Chuang's and Nielsen's book is something what is worth to have in your library because it represents an information treasure not only on quantum computing but also on quantum information processing experiments and quantum cryptology.
Rating:
Summary: Good Book !
Review: It is a well written book which clearly explains the essentials of quantum information theory. I highly recommend it to anybody interested in learning this field or using this as a text book. -Farhan Massachusetts Institute of Technology (MIT) Cambridge, MA
| 
