[sweezyjeezy]

The paper also shows that the proposed QC strategy for calculating energy levels - where you start with a guess and then optimise - may not lead to exponential speedup on a large class of important chemicals, because just coming up with an appropriate initial guess has no polynomial time algorithm at present. So it's not clear for what class of chemicals this would even theoretically become a tractable calculation.

[marcosdumay]

Yes, that applies to the chemicals that we currently have very good heuristics to guide the optimization, in a process that is usually validated empirically afterwards because of it's not perfect reliability.

At the same time, it doesn't go to lengths to discuss how the heuristics needed for the quantum computer are much more general and self-validating (if it converges, it converges).

But then, nobody knows if the classical algorithms will improve enough so that when we actually get quantum computers they will still be needed. That's the article's point... What is not different from the RSA one from my post.