If you compute reversibly you need use special logic gates to not throw any bits away during the computation, like the Toffoli gate. All your operations need to have the same number of input and output bits and needs to be able to run forwards and backwards. Effectively you set or zero no bits during the entire computation that can't be losslessly reversed.
If you structure your computation this way you can do it adiabatically.
You still however need to expend energy when you set all the bits your program requires for execution when you start a computation.
Wait, so does this imply (ignoring the time requirements) that you could do NP calculations with a feasible amount of energy, because the inputs and outputs are small?
Combine that with something that uses time dilation to make it go fast (from our frame of reference) and you'd be giving even hypothetical quantum computers a silver medal.
I think a longer runtime for a terminating program will require more state to be kept. Every step needs to keep extra reversibility information.
So I don't think this gives any edge on NP.
I suspect that even if you waited for the universe to cool down a lot by waiting aeons and then performed computations arbitrarily slowly you'd still be limited by your starting energy (maximum bits you can write to start with).
Although maybe using random bits might help somehow?
> time dilation to make it go fast (from our frame of reference)
The only way to do that is that we move to a place from which the computer processes appear accelerated, e.g. into a strong gravity well. That isn't very useful, because we do not have such a well nearby, as only very dense hypothetical objects can provide it (e.g. black holes), and it would not be compatible with life to move there.
You misunderstand. The problem with using time dilation is that you can only make the clock go slower, not faster. If you wanted to exploit time dilation to get a computer result faster (in subjective time), you don't send the computer to an exotic locale, you go there yourself, while you leave the computer to do work in normal space.
Time dilation means the object in the gravity well is experiencing time at a slower rate than us humans outside. That is the opposite condition we want: us slow, computer fast.
Not unless you can isolate the computer from environmental noise exponentially well. Otherwise you'll need to spend exponential energy on entropy removal / error correction (e.g. keeping the dilution fridge running).
If you're going to use time dilation so you can wait for the computer to calculate, it's hard to imagine a setup where the power needs of the computer are more than a rounding error in comparison.
If you're using time dilation the power needs of the computer (in terms of how much fuel you need) are proportional to the rate time passes inside. If the goal is to get the ratio way up there, the power consumption gets important.
Especially if you're using the velocity-based method and have to accelerate the fuel.
My analogy probably isn’t perfect but isn’t this how an abacus or a slide rule works? You expend energy to set the values for computation but the act of computing and then reading them expends no energy.
Suppose you put the abacus sideways, such that setting a bead requires working against gravity, but then returning the bead to the original position gives you that energy back?
If you compute reversibly you need use special logic gates to not throw any bits away during the computation, like the Toffoli gate. All your operations need to have the same number of input and output bits and needs to be able to run forwards and backwards. Effectively you set or zero no bits during the entire computation that can't be losslessly reversed.
If you structure your computation this way you can do it adiabatically.
You still however need to expend energy when you set all the bits your program requires for execution when you start a computation.