I like the idea, but I must admit that (with my background of a mathematics researcher, but almost completely ignorant of quantum physics and quantum physicists' notations) it is rather difficult to understand. In particular the bra-ket notation (which to me is already difficult due to its breaking the obvious way to match parentheses, but this might just require some time) seems to be used inconsistently across the paper (I believe that different authors wrote about the different algorithms, and the variations are rather evident and unhelpful). There are some formulas of which I cannot make any sense (last example I found: in the definition of QFT inside Shor's algorithm, the k inside the ket ranges from 0 to N-1, while according to the introduction it should range on all the combinations of a certain number of qubits).

Also, some authors seem to take for granted some concepts (such as the properties of the quantum gates) that are not explained anywhere and not obvious to me.

Still, an interesting read.