Quantum circuit for the fast Fourier transform
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Quantum circuit for the fast Fourier transform
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Re: Quantum circuit for the fast Fourier transform
#2This brings up an interesting question...
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...
Re: Quantum circuit for the fast Fourier transform
#3This brings up an interesting question... 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 tha…
Ears
Re: Quantum circuit for the fast Fourier transform
#4What effect do yall think this could have on AI? There is literature describing performance advantages of using Fourier transform space for convolutional neural networks
Re: Quantum circuit for the fast Fourier transform
#5This brings up an interesting question... 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 tha…
Ears
A cochlea? Yes, that does occur naturally, and it does work to allow us to hear different frequencies of sound...
So, now the next question is, could we prove that a cochlea implements a Fourier Transformation? Note that this Fourier Transform isn't applicable to all frequencies, that is, our ears cannot hear vibrations beyond a certain high pitch, so if a Fourier Transformation could be proved, we could almost think of this as a Fourier Transformation inside of a specific range of frequencies...
But anyway, an interesting observation!
Re: Quantum circuit for the fast Fourier transform
#6What effect do yall think this could have on AI? There is literature describing performance advantages of using Fourier transform space for convolutional neural networks
For those interested there is a cool relationship between a convolution and a Fourier transform:
https://en.wikipedia.org/wiki/Convolution_theorem
Re: Quantum circuit for the fast Fourier transform
#7Earlier quoted context omitted.
Ears
A cochlea? Yes, that does occur naturally, and it does work to allow us to hear different frequencies of sound... So, now the next question is, could we prove that a cochlea implements a Fourier Transformation? Note that this Fourier Transform isn't applicable to all frequencies, that is, our ears cannot hear vibrations beyond a certain high pitch, so if a Fourier Transformation could be proved, we could almost think…
We know how it works, and it's a simple version of a Fourier transform. The cochlea has hairs of different lengths that vibrate according to the contribution of the sine wave that corresponds to the resonant frequency of that hair's length. By the time neurons get involved at all, it's already a signal of the frequency domain over time.
Re: Quantum circuit for the fast Fourier transform
#8This brings up an interesting question... 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 tha…
Great question!
Prisms and diffraction pattern gratings split light according to the frequency of the photons (colours) in the input. That's a Fourier transform in a certain sense, and you'd use that to make a spectral analyzer. But what about the Fourier transform of an image, according to the frequency components of objects in the image? Like fence posts at a regular spacing, and such?
Well you might be excited to learn that optical lenses actually compute the Fourier transform of their input image:
http://web.mit.edu/2.710/Fall06/2.710-wk10-a-sl.pdf (the ideal thin lens as a Fourier transform engine, PDF)
Re: Quantum circuit for the fast Fourier transform
#9This brings up an interesting question... 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 tha…
Your average water droplet acts as a dispersive element (a prism). Dispersive elements can act as temporal Fourier transforms. Lenses act as spatial Fourier transforms. Going further, any mechanical device that exhibits resonance can be claimed to act as a Fourier transform (but that starts sounding meaninglessly vague).
Re: Quantum circuit for the fast Fourier transform
#10This brings up an interesting question... 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 tha…
Great question! Prisms and diffraction pattern gratings split light according to the frequency of the photons (colours) in the input. That's a Fourier transform in a certain sense, and you'd use that to make a spectral analyzer. But what about the Fourier transform of an image, according to the frequency components of objects in the image? Like fence posts at a regular spacing, and such? Well you might be excited to…
Great link, thank you very much!
Also (since I didn't know what a "thin lens" was prior to reading this (I never studied Optics)) I Googled it, and found the Wikipedia page for it:
https://en.wikipedia.org/wiki/Thin_lens
>"In optics, a thin lens is a lens with a thickness (distance along the optical axis between the two surfaces of the lens) that is negligible compared to the radii of curvature of the lens surfaces. Lenses whose thickness is not negligible are sometimes called thick lenses.
The thin lens approximation ignores optical effects due to the thickness of lenses and simplifies ray tracing calculations."
Which makes me wonder if there's a link between Fourier Transformations and Ray Tracing, and if so, how does it express itself?
Although, that's probably going seriously off-topic for this HN article!
Anyway, thanks again for the link/info!