This seems to be a good week for talking about quantum memories and distributing qubits. The thing about working with quantum states, though, is that you don't have much room to avoid messing it up. And, afterwards, figuring out when you've made a mistake is difficult. Once you make a measurement on a quantum system, there is no going back to its original state.

To get around this uncertainty, you have to find some way to increase your confidence that the operation you performed has actually turned out as expected. One option for this is called entanglement distillation. And entanglement distillation is exactly what a group in the Netherlands has recently demonstrated.

Impure diamonds are the best diamonds

This is a story about generating entangled quantum states in different locations. To understand how the researchers can do that, we need to see how a qubit state can be encoded in a bit of diamond. Most diamonds have a certain amount of nitrogen. The bonding between the carbon and the nitrogen leaves a rather unhappy electron. It is still bound to carbon, but the electron doesn't really want to be. So it floats around in between the carbon and the nitrogen atom.

This electron has its own set of states. Two low-lying states can be addressed by microwaves; these serve as the one and zero states. They can be set and measured by hitting the electron with a laser and looking for a photon in response. The ease of manipulation and measurement makes this an excellent qubit for computation.

The nitrogen vacancies in diamond have an advantage that comes from another impurity: an isotope of carbon. Most carbon has a nucleus with six protons and six neutrons. But one in every 100,000 carbon atoms has an extra neutron. Like the spare electron, the extra neutron creates a set of energy levels within the nucleus that can be used as a qubit. The nuclear qubit has the advantage of having a nice long lifetime, while transferring quantum states between the nuclear qubit and the electron qubit is reasonably straightforward. That makes the nuclear qubit a great memory.

The upshot is that diamonds with a bit of nitrogen have a whole lot of randomly located qubits that are excellent for computation and communication (the electrons), and nearby there are isotopes of carbon that provide a natural memory (the heavier carbon isotope).

Entangle them qubits

If you want to perform a computation involving more than a single qubit (say, two qubits), then you have to entangle them. To do this, two of the nitrogen vacancies are hit with laser light: each nitrogen vacancy may or may not emit a photon. The (potential) photons are mixed on a partially reflective mirror and sent to a pair of photodetectors. If a detector clicks, then a photon has been detected, and it should be impossible to tell from which nitrogen vacancy it came. This lack of knowledge is what entangles the two qubits.

Unfortunately, no experiment is perfect. So a test for entanglement would reveal that the qubits are barely entangled. And this is a problem because quantum computing relies on having good entanglement.

To improve matters, the trick is to use a second set of entangled qubits to strengthen the entanglement of the first two. To achieve this, the researchers make use of the built-in memory in the carbon of the diamond crystals. After entangling the two computational qubits, they transfer both states to their respective memories. Now, the two memory qubits are entangled with each other, although the entanglement is still rather low-quality.

The next step is to entangle the computational qubits again. Now, we have two memory qubits that are poorly entangled and two computational qubits that are poorly entangled. All you have to do is turn this into a single pair of entangled qubits. This is done by performing operations on the memory qubits, but only conditionally. The condition depends on the state of the computational qubit. This is followed by a measurement on the computational qubit, which completes the process.

You can think of the process like this: we have four qubits, entangled in pairs. That means their states are correlated, but, because of the way the experiment is set up, the correlation is not perfect. However, now we use the correlation between the computational qubits to perform an operation on the memory qubits, which increases the correlation between the memory qubits.

A well-distilled qubit

The researchers in the Netherlands showed that this worked by measuring the state fidelity, which is basically a measure of the probability of finding the qubit in the state that it was set to. In the ideal case, this is unity: you always measure the state as what you set it to. For a single pair of entangled qubits, the fidelity was less than 50 percent. However, that increased to around 60 to 70 percent when a second entangled pair was used to improve the entanglement.

I should note that 60 to 70 percent is nowhere near enough to be useful. However, this is after only a single attempt to improve the entanglement. In principle, another pair of entangled communication qubits can be used to distill some more.

This is useful for quantum key distribution, where you want to progressively move a qubit state through a chain of well-separated qubits. However, we should remember that all of these qubits are scattered randomly through diamond crystals. It is not a small task to go through, find a few that have reasonable characteristics (like a 13C atom nearby), then deposit electrodes and position optics to access those qubits without interference from neighboring, unwanted, nitrogen vacancy centers.

So, I can see this working as a communication node, but not as a computational node. However, there are ways to create grids of nitrogen vacancies. This could overcome some of the challenges of using nitrogen vacancies and expand the sorts of things you can do with them.

Science, 2017, DOI: 10.1126/science.aan0070 (About DOIs).