alt Hacker NewsWhile I think the idea that claiming one can "precompute the xr mod N’s on a classical computer" sounds impractical there are a subset of problems where this might be valid. According to computational complexity theory, there's a class of algorithms called BQP (bounded-error quantum polynomial time).
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.
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JVC isn't BQP. it's exp time (I.e. worse than factoring without a quantum computer at all). it takes the only step of shors algorithm that is faster to run on a quantum computer and moves it to a classical computer
There is a genuinely interesting complexity class called BQP/poly, which is pronounced something like “bounded-error quantum polynomial time with classical advice” (add some more syllables for a complete pronunciation).
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.