If a Fourier Transform can be computed from something in which Quantum Bits are implemented by some underlying physical system, then is there anything self-existing in Nature which could be used to (or does in actuality) implement a Fourier Transform?
Now, I don't know the answer to that.
Something not occuring naturally in Nature is a Prism, and a Prism splits light, and that's sort of, kind of analogous to what a Fourier Transform does, although, perhaps there's a limited range of frequencies at which the effect is applicable...
So now the next question is, is there anything in Nature, that is, naturally occurring, which acts like a Prism does?
Although, perhaps we're not looking for something that necessarily splits light, perhaps we're looking for something that splits other electromagnetic radiation, that is, waves of some sort...
Also, maybe there's some kind of naturally occuring shape of rock that could be used to "split" ocean waves into one or more component parts... while perhaps not a true Fourier Transform, it might be a step in the right direction for conceptualization purposes...
Anyway, just thinking aloud... It would be interesting to know all of the systems, both natural and man-made, which are capable of Fourier Transforms -- or even just splitting waves of different sorts into component parts...