alt Hacker NewsWell the author saysin that paragraph:
> In layman’s terms, I do not consider the “Exp-Minus-Log” function to be the continuous analog of the Boolean NAND gate or the universal quantum CCNOT/CSWAP gates.
But is there actually a combination of NANDs that find the roots of an arbitrary quintic? I always thought the answer was no but admittedly this is above my math level.
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Combinations of the NAND gate can express any Boolean function. The Toffoli (CCNOT) or Fredkin (CSWAP) can express any reversible Boolean function, which is important in quantum computing where all gates must be unitary (and therefore reversible). The posited analog is that EML would be the "universal operator" for continuous functions.
Solving polynomials over finite fields is trivial. Just try all combinations.
Yes, NAND gates can implement root finding algorithms for arbitrary polynomials. For example a variant of Newton’s method can be used (there are also better algorithms for circuits specifically).
This can be done in polynomial time as well.
This is fairly obvious if you think about that your computer can do the same thing and it’s just a fancy circuit.