What are the theoretical minimum times for quantum and classical logic gates?

Question

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.

Answer 1

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!)