In my "crackpot index", item 20 says:
20 points for naming something after yourself. (E.g., talking about the "The Evans Field Equation" when your name happens to be Evans.)
In the original paper they do not give it any name: https://people.csail.mit.edu/rivest/Rsapaper.pdf
Shor's algorithm is part of BQP. Is the JVC algorithm part of BQP, even though it utilizes classical components? I think so.
I believe that the precomputational step is the leading factor in the algorithm's time complexity, so it isn't technically a lower complexity than Shor's. If I had to speculate, there will be another class in quantum computational complexity theory that accommodates precomputation utilizing classical computing.
I welcome the work, and after a quick scroll through the original paper, I think there is a great amount of additional research that could be done in this computational complexity class.
The JVG algorithm is not a high quality example of this or really anything else. If you think of it as “classical advice”, then it fails, because the advice depends on the input and not just the size of the input. If you think of it as precomputation, it’s useless, because the precomputation involved already fully solves the discrete log problem. And the JVG paper doesn’t even explain how to run their circuit at respectable sizes without the sheer size of the circuit making the algorithm fail.
It’s a bit like saying that one could optimize Stockfish to run 1000x faster by giving it an endgame table covering all 16-or-fewer-piece-positions. Sure, maybe you could, but you also already solved chess by the time you finish making that table.
People get taken by the theoretical coolness and ultimate utility of the idea, and assume it's just a matter of clever ideas and engineering to make it a reality. At some point, it becomes mandatory to work on it because the win would be so big it would make them famous and win all sorts of prizes and adulation.
QC is far earlier than "linear regression" because linear regression worked right away when it was invented (reinvented multiple times, I think). Instead, with QC we have: an amazing theory based on our current understanding of physics, and the ability to build lab machines that exploit the theory, and some immediate applications were a powerful enough quantum computer built. On the other side, making one that beats a real computer for anything other than toy challenges is a huge engineering challenge, and every time somebody comes up with a QC that does something interesting, it spurs the classical computing folks to improve their results, which can be immediately applied on any number of off-the-shelf systems.
As an engineer, I care about where the curve bends. If your 'supremacy' algorithm fails the moment you step out of the 'demo sandbox,' it's not a solution—it's a nerd-snipe. I'd much rather see 10 years of incremental work on error correction than 10 minutes of hype over a flawed paper.