Can we make a Maxwell's Demon using Quantum Computers?

Question

Although I'm reasonably sure that quantum computing advances will not lead to the ability to construct a machine that globally violates the 2nd law of thermodynamics, it feels like a difficult position to defend when I see things like this:

http://www.flickr.com/photos/jurvetson/8054771535

(summary: an alternative to Moore's law that predicts basically unbounded growth is computing ability)

There's a proviso with this, while quantum computers could solve problems that would take a classical computer almost forever, it can't solve all problems. Wikipedia helped clarify this for me:

(BQP are problems solvable by quantum computers with polynomial time)

This image is to say, although quantum computers could solve every computing problem we have now and more, there are things it can't solve. But is THIS the reason we couldn't make a quantum computer into a Maxwell's Demon?

My biggest problem with a 10,000 Qubit computer is the internal memory. The Landauer limit dictates that any given memory transition must expend at least $k T \ln 2$ of energy to make the transition, otherwise it then violates the 2nd law. What is the "internal memory" analog to such a massively powerful quantum computer? Would it also be subject to this limit, or would the internal states, never actually existing in a way, circumvent it?

So let me narrow the question, looking at the idea of Maxwell' Demon:

Let's formalize this to say that we have some observable vector $\vec{y}$, that we get from sensors in the $A$ gas. We then take that information, process it, and apply the information to a decision vector $\vec{u}$, which in the above image is a single Boolean open/shut decision. What is the reason that we can not build this with a quantum supercomputer? My guesses are:

1. The internal memory switches would use energy, increasing global entropy (seems to violate the claims of quantum computing)
2. The particular type of problem can't be solved by quantum computers with sufficient efficiency (implying there exists a set of problems that could violate the 2nd law if solved with polynomial time)
3. The problem is irrelevant of both memory and processing capability, as the sensors and the control input themselves require too much energy (seems this would trash certain explanations I've heard for why various Maxwell's Demons wouldn't work, in fact, it would seem to flagrantly ignore the principle behind the Landauer limit)

As you can see, none of my explanations are consistent. Is the universe big enough for both superpowerful quantum computers and the 2nd law?

Answer 1

Quantum computer performs unitary, reversible operation so it is not a subject to Landauer's principle until the reading the final result.

Still operation of Maxwell's demon cannot be reversible, as it needs to conduct measurements.

Answer 2

If you make a Maxwell's Demon using a quantum computer, you may find that it is actually a heat engine operating on the difference in temperature between the system and the quantum computer's memory. (For you to analyze it this way, it might help assume a very small energy difference between a 0 bit in memory and a 1 bit.)

As soon as the memory fills up (in thermodynamic terms, reaches the same temperature as the system), the Maxwell's Demon will stop working.

Answer 3

The energy of quantum systems encodes redundant information. If a quantum computer were used to to emulate a vast number of physical systems this might be possible.