It's not too difficult to cool a system down to the temperature of the
cosmic background radiation. All you need to do is build a radiator in
interstellar space with a very large surface area, and connect it with the
system you're trying to cool with some high thermal-conductance material.
However, even at the cosmic background temperature of T=3K, erasing a bit
still costs a minimum of k*T*ln 2 = 2.87e-23 J. What is needed is a way to
efficiently cool a system down to near absolute zero. I think the only way
to do it is with black holes.
Black holes emit Hawking radiation at a temperature of
T=h*c^3/(16*pi*G*M). With the mass of the sun, the temperature of a black
hole would be about 10^-8 K. At this temperature, erasing a bit costs only
about 10^-31 J. If you build an insulating shell outside the event horizon
of a black hole, everything inside the shell would eventually cool down to
the temperature of the black hole. However, it would not be necessary to
build a complete shell around a black hole in order to take advantage of
its low temperature. For example you can simply point the radiators of
your black hole orbiter toward the black hole and insulate the side facing
away from the black hole.
If it's true that the only efficient way to cool material down to near
absolute zero is with black holes, we should expect all sufficiently
advanced civilizations to live near them. However testing this prediction
may be difficult to test since they would have virtually no radiation
signatures.