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I'm interested in better understanding the ultimate limits on how fast quantum and classical logic gates can be performed. Based on principles like the time-energy uncertainty relationship, there should be minimum times required to enact state changes and operations.

I'd be interested in a high-level conceptual explanation and pointers to good review papers on this topic. The goal is to better understand these ultimate limits on computational speed at a qualitative level.

Any insights would be greatly appreciated.

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There's something called the Margolus-Levitin Theorem. Roughly speaking, this says that the time required to transition between two orthogonal states using a transition of strength $E$ is $$ \delta t=\frac{\pi}{2E}. $$ So you could very reasonably take this as a limit on each logic gate, and $E$ is some parameter that you can play with (there will be physical limits, but not much in the way of a priori limits, to my knowledge.

If you want to go really fundamental, you could make the following estimate:

  • what is we make 1 bit of information as small as possible? The limit is that if you made it too small, it would turn into a black hole. How big is that? There's something called the Bekenstein–Hawking entropy, which relates the entropy (i.e. information storage) to the area of the black hole. Assume it's a sphere, and you have a minimum size of a bit.
  • If you're going to compute with that bit, you at least need time for light to travel across the bit. This gives you a minium time for a logic operation. (It's crazy small!)
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  • $\begingroup$ Thanks for your help! $\endgroup$ Commented Aug 1, 2023 at 13:13

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