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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)
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