[gnramires]

Interesting, I suppose you'd use reversible logic for the computation? I think non-reversibility is relatively common in computing, but surely a significant fraction of operations could be made using reversible logic. Fourier transforms are a good example. Sorting a simple example of an operation destroying information (log2(n!) roughly ~ n log2(n) bits). Algorithms would need to be redesigned significantly I suppose if it ever came to reversible computing being energy advantageous.

[bee_rider]

You could also think of reversible blocks. For example, if you had an half-adder, you each constituent gate could be thought of as doing something like erasing in normal operation. If instead the half-adder was reversible, and you perform the operation, save the outputs, reverse it, and then erase the inputs, at least you only have to pay the Landauer tax on the input bits (rather than each intermediary bit). The bigger the block, the more you save.

[orlp]

All of quantum computing is done with strictly reversible logic. But this is not a reduction of power. The Toffoli gate is an example of a reversible 3-bit logic gate that is universal. You can transform any classical circuit into a reversible one using this gate.

The trick? You have some input/output wires in your circuit that start with initial value 0 or 1, and some that end up in a 'garbage' state. You don't care about what they end up with, they strictly exist to maintain reversibility.

As an concrete example, the binary operator a OR b is not reversible - it destroys information. But if we make it a three-in three-out operator f(a, b, c) -> (a, b, c XOR (a OR b)), then it is reversible. Here f is it's own inverse, because applying it twice you'd end up with c XOR (a or b) XOR (a or b) = c.

Yet if you start with c in an initial 0 state, you can now compute the binary OR of two variables a, b in a reversible manner.