They claim that "The projected performance of this new experimental quantum simulator eclipses the current maximum capacity of any known computer by an astonishing 10 to the power of 80. That is 1 followed by 80 zeros, in other words 80 orders of magnitude, a truly mind-boggling scale." Is this even remotely credible? Or is this applicable to some specific category of computation?
Some specific category. In general, the best we know how to do is a square-root speed up, which would only be applicable here if the number of possible solutions were 10^160.
(Specific categories do appear to have marvelous exponential speed-ups, such as factoring.)
From briefly skimming the abstract, it appears to be analogous to a hard-wired circuit built to execute a specific calculation. i.e. It is not a programmable quantum computer. This is similar to the sort of thing D-Wave has been doing, although likely for a different purpose.
The speed-up figure is plausible, but only for the specific single algorithm this quantum circuit implements.
