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This only holds because the system returns its raw (a, b) inputs unchanged. It doesn't seem like a useful property. Of course we can "reverse any function" if we store the inputs! Reversing here just means yielding back the inputs.
ok, the Landauer limit defines the minimum energy for a bit flip but I don't see how a Toffoli gate would require less energy for a bit flip let alone come into the region of the Landauer limit. Could someone with more knowledge enlighten us (or at least me)?
> any Boolean function can be computed reversibly This only holds because the system returns its raw (a, b) inputs unchanged. It doesn't seem like a useful property. Of course we can "reverse any function" if we store the inputs! Reversing here just means yielding back the inputs.
Not quite I think - the example gate they give has (a,b,c) as input and it doesn't return c. So it's not yielding all the inputs back.
Furthermore: if you always returned all the inputs, and also computed other values, the outputs from the gates would be strictly increasing in size, so you wouldn't be able to use a finite set of gates to build a computer of arbitrary size.
[1] https://en.wikipedia.org/wiki/Janus_(time-reversible_computi...
ok, the Landauer limit defines the minimum energy for a bit flip but I don't see how a Toffoli gate would require less energy for a bit flip let alone come into the region of the Landauer limit. Could someone with more knowledge enlighten us (or at least me)?
Obviously, implementing one as a CMOS gate wouldn't be enough. Reversible gates would be very different. AFAIR they need to have a fan-out of one - you can't just wire an output to two inputs without losing reversibility.
There is a programming language that is reversible: Janus [1]. You could write a (lossless) data compression algorithm in this language, and if run in reverse this would uncompress. In theory you could do all types of computation, but the "output" (when run forward) would need to contain the old state. With reversible computing, there is no erased information. Landauer's principle links information theory with thermo…
ok, the Landauer limit defines the minimum energy for a bit flip but I don't see how a Toffoli gate would require less energy for a bit flip let alone come into the region of the Landauer limit. Could someone with more knowledge enlighten us (or at least me)?
A reversible gate doesn't involve any such erasure and therefore Landauer's principle doesn't apply to it.
What will happen in practice if you do an entirely reversible computation is that you end up with the data you care about and a giant pile of scratch memory that you're going to need to zero out if you ever want to reuse it. Or perhaps you rewind the computation all the way back to the beginning to unscratch the scratch memory but you're going to at least need to pay to copy the output somewhere.
> any Boolean function can be computed reversibly This only holds because the system returns its raw (a, b) inputs unchanged. It doesn't seem like a useful property. Of course we can "reverse any function" if we store the inputs! Reversing here just means yielding back the inputs.
> Reversing here just means yielding back the inputs. Not quite I think - the example gate they give has (a,b,c) as input and it doesn't return c. So it's not yielding all the inputs back. Furthermore: if you always returned all the inputs, and also computed other values, the outputs from the gates would be strictly increasing in size, so you wouldn't be able to use a finite set of gates to build a computer of arbitr…
> Furthermore [this doesn't scale].
Precisely.
https://en.wikipedia.org/wiki/Toffoli_gate has better details.
Earlier quoted context omitted.
> Reversing here just means yielding back the inputs. Not quite I think - the example gate they give has (a,b,c) as input and it doesn't return c. So it's not yielding all the inputs back. Furthermore: if you always returned all the inputs, and also computed other values, the outputs from the gates would be strictly increasing in size, so you wouldn't be able to use a finite set of gates to build a computer of arbitr…
c is the constant 1. You don't need to store that. > Furthermore [this doesn't scale]. Precisely. https://en.wikipedia.org/wiki/Toffoli_gate has better details.