Quantum Computing in Diamond

Two weeks ago, now, I promised some peer=reviewed physics blogging, to compensate for the "screechy monkey" nonsense. Of course, I got distracted by other things, but I've been sitting on this paper for a while now, and I really need to get it off my desk.

The paper in question is "Quantum Register Based on Individual Electronic and Nuclear Spin Qubits in Diamond," by the group of Misha Lukin at Harvard, published in Science last June. It's a clever idea for a way to do quantum computing using individual nuclear spins in a diamond matrix. I really like this idea, not least because it has the potential to someday turn up as a fantastic mcguffin in a SF story-- some haples thief steals a diamond, only to learn that it's a special quantum computing diamond holding secrets that powerful people will kill to recover, that sort of thing. Will Smith can be in the movie.

The central idea here is to use nuclear spins in diamond as the qubits for a quantum computer. This seems like a really promising idea, as nuclear spins do a great job of meeting the criteria for a useful quantum computing system: they provide nice two-level systems with exceptionally long lifetimes, and they're insulated from a lot of perturbations that would otherwise cause problems for a quantum bit. Better yet, you can use nuclear magnetic resonance techniques to manipulate the spins, giving you the control you need to do qubit operations.

Nuclear spins in a solid matrix of some sort give you almost everything you could want in a quantum computer. They're readily scalable, they can be individually addressable, they have long lifetimes, and people have decades of experience of manipulating spins with NMR. There's only one catch: reading the state of individual spins with NMR is really incredibly difficult.

The signal generated by one spin flipping back and forth in an NMR machine is too small to detect easily and reliably. This doesn't matter for a normal NMR machine, because you can throw in a sample containing billions or trillions of identical molecules, all of which will do the same thing in unison, thus amplifying the signal. That's no good for a quantum computer, though, because in a quantum computer, you need a way to accurately measure the state of each individual qubit-- if you can't do that, you can't get the result of your computation out.

What Lukin and co-workers have done is to come up with a scheme where they can measure the state of individual carbon-13 nuclei using lasers.

The basic idea is this: when you have a chunk of diamond crystal, it consists mostly of carbon-12 atoms, which have no nuclear spin, and thus aren't useful for NMR or as qubits. Every now and then, though, you'll find an individual atom of carbon-13 (about 1% of the total), which does have a nuclear spin that can be used as a qubit.

In a real diamond crystal, you'll also find what are called "nitrogen vacancy centers," which are basically places where a carbon atom has gone missing, and a nitrogen atom has taken its place. These act sort of like atoms embedded within the solid diamond crystal-- where most of the crystal contains electrons that are shared between atoms and occupy broad bands, electrons in the nitrogen vacancy centers have well-defined discrete states. These include a pair of low-energy states that can be coupled with microwaves, and also some higher-lying states that can be excited with lasers (green light, at 532 nm).

This structure allows Lukin and company to manipulate and probe the state of these nitrogen vacancies in much the same manner as the people using ion traps do-- they set their laser frequency so that atoms in one of the two low states-- called "|0>" in the usual jargon-- will readily absorb light, and produce detectable fluorescence, while the other state-- "|1>" will not absorb light. They can drive the electrons back and forth between |0> and |1> states with pulses of microwaves, and measure the state by shining in the green laser-- if the electrons absorb and re-emit light, the system was in |0>, if not, it was in |1>.

This is all very nice, but the meat of this paper comes in when you combine the nitrogen vacancies with the carbon-13 atoms. The nuclear spin of a carbon-13 atom produces a tiny magnetic field. If a carbon-13 atom happens to be near one of the nitrogen vacancies, that magnetic field is enough to cause a shift in the energy levels of the electrons (through what's known as the "hyperfine interaction"), a shift that depends on both the state of the electron and th state of the spin. The |0> electron state is unaffected, while the |1> state shifts up in energy if the nuclear spin is up, and down if the nuclear spin is down.

This gives Lukin and company a way to make selective measurements of the state of the spins. They prepare an electron in |0>, then tune their microwave source to a frequency that will transfer the electron to |1> only if the nuclear spin of a nearby carbon-13 atom is down. After some time, they check the state of the electron by shining in the green laser, and what they measure tells them the state of the nuclear spin-- if the electron is still in |0>, then the nuclear spin is up; if it's moved to |1>, the nuclear spin is down.

They can also use this mechanism to map the electron state onto the nuclear spin, which they demonstrate by preparing the spin in a "down" state, using microwave pulses to put the electron into a superposition of |0> and |1>, then mapping the electron state onto the nuclear spin. Then they wait some time, map the state back onto the electron, and read it out. By tracking the evolution, they can show that indeed, the superposition was transferred over, and it behaves in the expected manner.

The bulk of the paper is taken up with demonstrating the quantum coherence properties of the various states. They demonstrate that they can write a number of different superposition states onto the nuclear spins, and that they oscillate between states in the usual manner (Figure 2 in the paper). They also demonstrate that optical probing and manipulation of the electrons does not affect the evolution of the nuclear state, by preparing a superposition, letting it evolve for a while, hitting the electron with a pulse of light, then mapping the nuclear state back and checking its behavior (Figure 3). They don't see any significant degradation of the signal for light pulses that are more than sufficient to do anything they would need to do to the electrons during a calculation.

Finally, they demonstrate some interaction between nearby nuclear spin qubits, showing a modulation of the oscillation due to other nearby spins (Figure 4). This is critical for quantum information, as you need to be able to entangle different qubits together in order to do quantum computation.

I should stress that this is very much a proof-of-principle experiment. They haven't done any quantum gate operations, let alone factored any numbers. All they are doing here is demonstrating that they can use electron states at nitrogen vacancies to detect and manipulate the states of nuclear spins in diamond. These are essential tools for doing quantum information experiments, but they're still a long way off.

Still, they have a scheme for building a quantum computer out of diamond. And really, you don't get much cooler than that.

Dutt, M.V., Childress, L., Jiang, L., Togan, E., Maze, J., Jelezko, F., Zibrov, A.S., Hemmer, P.R., Lukin, M.D. (2007). Quantum Register Based on Individual Electronic and Nuclear Spin Qubits in Diamond. Science, 316(5829), 1312-1316. DOI: 10.1126/science.1139831