The Hooft thing is that there are limits on computation due to the process of the universe and that if a classical computer that was at the plank scale, runs at plankian speed (help help I am using terms I can't understand!!!) and covered the whole of the universe couldn't do it from the beginning of time to heat death... then nor can an arbitrary QC. Shores algorithm does factors in (log n)^3 maybe we'll find that there are physical limits on the scale of QC which hold it below hundreds of millions of qbits where a plankian computer could be synthesised, and/or it may be that such a computer can't run at high clock speeds, and because of this BQP algorithms can't be run on problems that are not allowed in the sense that they somehow solve the universe.
I don't think anyone has any reason to believe this is true in an engineering sense but there is every reason to believe that large QC will be very, very difficult in an engineering sense and I think that the people building one do expect to run into problems of this sort eventually, but at the moment they are delighted to find that they are able to do things at the lower end that will create devices that are going to be transformational for reasoning about some components of the physical universe - for example simulation of the interactions of very large molecules - maybe mapping seconds of a virus interacting with a cell membrane using months of QC ?
The mentioning of quantum computers is very interesting in the following sense: If one were able to build a sufficiently large quantum computer, this would provide strong evidence that the (at the moment rather hypothetical) theory whether quantum mechanics is rather an emergent phenomen by a deterministic process (cellular automaton)
> https://arxiv.org/abs/1405.1548
which the Nobel laureate Gerard 't Hooft worked on for the last years is probably wrong. To quote p. 79-80:
"Such scaled classical computers can of course not be built, so that this quantum computer will still be allowed to perform computational miracles, but factoring a number with millions of digits into its prime factors will not be possible – unless fundamentally improved classical algorithms turn out to exist. If engineers ever succeed in making such quantum computers, it seems to me that the CAT is falsified; no classical theory can explain quantum mechanics."
On the other hand, if we seriously get into trouble building a sufficiently large quantum computer (despite our best efforts), this would at least to me provide evidence that 't Hooft is on something - since that this is a prediction that his Cellular Automaton Interpretation of Quantum Mechanics provides.