This is a gross oversimplification. For the true version see here
Now, I got to the bottom of page 6 and my maths failed me: I can't follow the expansion, but I expect that the reviewers of Physica A or where ever the gentleman who wrote this sends it off to will be able to check. I do follow the principle of the proof though and it's pretty intuitive to me, for what that's worth.
Anyway, I can't say I give a hoot what the majority or minority think - and nor should anyone else. Read the paper for yourself and make up your mind.
* The author thanks Al Aho, Dan Boneh, P ́eter Ga ́cs, Zvi Galil, Fred Green, Steve Homer, Leonid Levin, Dick Lipton, Ashwin Maran, Albert Meyer, Ken Regan, Ron Rivest, Peter Shor, Mike Sipser, Les Valiant, and Ben Young for insightful comments. He also thanks Eric Bach for inspiring discus- sions on some of the number theoretic estimates, and we hope to report some further improvements soon [7]. A similar result can be proved for Shor’s algorithm computing Discrete Logarithm, and will be reported later.
1. Shor's algorithm won't work on the very noisy quantum computer we have for the near and intermediate future.
2. Shor's algorithm won't work on a hypothetical error corrected future quantum computer.
Claim 1 is pretty convincing proved in the paper. Claim 2 is not. The author puts forward some arguments for claim 2 in the introduction and conclusions but explicitly states that he does not prove it.
I think the point of view that the person you're replying to is talking about is claim 2. There are pretty good reasons to believe that claim 2 is false in my opinion, in particular we have threshold theorems for quantum error correction which should "save the day" for quantum computing.
