# How to cool your (quantum) beer

Everybody has a fridge. Maybe not an Eskimo, but I have heard that Eskimos actually use fridges to make sure that their foodstuffs are not always completely frozen. I have never personally met an Eskimo to verify this, but anyway everybody has a fridge, and everybody enjoys a nice cold beverage every now and then. Including physicists.

Now, as physicists are wont to do, they start to think: What if you have a quantum beer?

Suppose said beer is a qubit. This is the smallest possible beer since a qubit only has 2 discrete energy states. What is the smallest self contained refrigerator that, in principle, can be constructed?

This was a question that was tackled by Linden et. al. (See link). Their answer: a single atom that can occupy at least 3 discrete energy states. Or alternatively, if you construct your fridge out of qubits, then the answer is 2 qubits which collectively occupy a grand total of 4 possible energy states.

How does it work? Well, technicalities aside, it really is pretty simple. Consider the case where the fridge is made out of 2 qubits. Suppose when a qubit is occupying its lowest energy (ground) state, we label the state 0 and say the qubit is in the state 0. If the qubit is occupying its excited state (the only other energy level), then we say it is in state 1.If you have 3 qubits, then we can describe them compactly in the following way: 000 means all 3 qubits are in the lowest energy state, 001 means only the 3rd qubit is excited, and so on.

All you then need to do is to arrange an interaction between the qubits (or in physics nomenclature, introduce an interacting Hamiltonian) which transfers a 3 qubit state from an energy configuration of 101 to 010. If your quantum beer is the first qubit, then if you start at state 1, you will end in state 0. This means basically that the qubit becomes less energetic and therefore cooler. The problem is that such an interaction between 101<–>010 typically go both ways, which causes the state of your beer to go from 1->0 (cooling) and from 0->1 (heating) with equal measure, messing up the cooling process. This is where a little bit of ingenuity becomes necessary. By putting part of the fridge at a different (higher) temperature, and tweaking the energy levels of the qubits appropriately, you can make the beer and fridge system more likely to find itself in the 101 configuration than the 010 configuration. This means that your beer is more likely to go from 1->0 than from 0->1, and wala! you have a 2 qubit fridge and a nice chill qubit beer.

And that’s pretty cool.