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Quantum Computation & Quantum Information
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This text is the first comprehensive introduction to the main ideas and techniques of the field of quantum computation and quantum information. Michael Nielsen and Isaac Chuang ask the question: what are the ultimate physical limits to computation and communication? They describe in detail such remarkable effects as fast quantum algorithms, quantum teleportation, quantum cryptography and quantum errorcorrection. A wealth of accompanying figures and exercises illustrate and develop the material in more depth. The authors describe what a quantum computer is, how it can be used to solve problems faster than familiar classical computers, and the realworld implementation of quantum computers. The book concludes with an indepth treatment of quantum information, explaining how quantum states can be used to perform remarkable feats of communication, together with a discussion of how it is possible to protect quantum states against the effects of noise.
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  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 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 twolevel quantum systems were suggested in the 1980ties 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 bitregisters to that of qubitregisters. 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 NielsenChuang 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 NielsenChuang is timeless, and I expect the book will also be popular ten years from now.
Good for reference, poor for teaching,selfstudy
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 Uy> > 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)
Decoherence, entanglement and information protection in complex quantum systems A. Sarfati, G. Kurizki, S. Pellegrin, Vladimir M. Akulin 
Principles of Quantum Computation and Information. Basic Concepts Giuliano Benenti, Giuliano Strini, Giulio Casati 



