Quantum Computing Candidates: Liquid State NMR

Continuing the series of descriptions of candidate technologies for making a quantum computer (previous entries covered optical lattices and ion traps), we come to one that's a little controversial. It's the only remaining candidate I can describe off the top of my head without doing some more background reading, though, so I will plunge ahead boldly...

Liquid state Nuclear Magnetic Resonance (NMR) was first suggested as a technology for quantum information processing in 1997, and some demonstration experiments followed very quickly, as there's relatively little infrastructure required. The significance of these results was a topic of much heated discussion (see here for the rapid onset of dissent), and at least one near fight at a conference. Bulk liquid NMR has kind of faded in the years since, for reasons that will become clear in a little bit.

What's the system Liquid state NMR, or bulk liquid NMR, uses, well, large numbers of molecules in a liquid. These molecules are placed in an NMR apparatus, which serves to both manipulate the qubits and measure their state. Lots of different molecules have been used-- one of the early demonstrations went for cute points by using caffeine, leading to endless news stories about computing based on coffee.

What's the qubit? The "0" and "1" states are the spin-up and spin-down states of nuclei within a molecule. Atomic nuclei are made up of protons and neutrons, which have a property called "spin," which isn't really a physical rotation, but is mathematically very similar. When the right sort of atoms are placed in a strong magnetic field, there will be two possible energy states for the nucleus-- a state in which the "spin" axis points along the magnetic field, and a state in which the "spin" axis points opposite the magnetic field. These have slightly different energies, and serve as the "0" and "1" states for the quantum computer.

Each molecule in the sample is its own "quantum register," containing as many qubits as there are nuclei in the molecule. They all do the same "computation" in parallel.

How do you manipulate the qubits? The nuclear spins can be measured and manipulated through Nuclear Magnetic Resonance. If you put the sample of molecules in a strong magnetic field, and irradiate them with microwaves, you can drive transitions between "0" and "1." If you have a very large sample of molecules, all doing the same thing, you can detect the change in the microwave intensity due to absorption and emission of microwaves by the molecules, and use that to determine the exact quantum state.

As any chemist can tell you, the exact frequency at which a given nucleus absorbs or emits microwaves in an NMR machine depends on the environment of that nucleus. Different nuclei at different points in the molecule will resonate at different frequencies. This means you can very easily address the nuclei individually, and flip whatever spin you like into whatever state you like.

How do you entangle the qubits? You can do entangling operations using the same NMR system of microwave pulses and so on. It's a little more complicated, but doesn't involve anything that skilled NMR operators don't already know how to do.

How do you read the result out? Again, it's the same NMR system. You use magnetic fields and microwave pulses for everything in this system.

Does it scale? This is where we hit the problem.

In the absolutely ideal Theorist World situation, where the experiments can be done at Absolute Zero, there's no reason why you couldn't make an arbitrarily large quantum computer doing NMR of bulk samples of molecules. It's tricky to construct a molecule with enough nuclei offering distinct frequencies, but that's not an absolute barrier.

The problem is, these experiments are never done at zero temperature. And when you include the effects of finite temperature, it turns out that the signal you get decays exponentially with every bit you add.

It's a little tricky to see why, but it has to do with the problem of "initialization," one of the criteria for evaluating quantum computers. You need to be able to start your system in some known state-- "0000000...." is ideal, but any arbitrary sequence would work, as long as you know what it is.

The problem with bulk NMR quantum computation is that your signal depends on having large numbers of identical molecules, all doing the same thing. At zero temperature, you're all set, because every nucleus in every molecule will be in the lowest energy state-- call that "0" and you're good to go.

At non-zero temperature, though, the nuclei will be distributed between "0" and "1" states in numbers that depend on the temperature, and the energy difference between the molecules. The energy difference is tiny, though, so the split is nearly 50-50, with only a tiny excess in the lower energy state-- 50.0000001% versus 49.9999999%, or even smaller.

You can "initialize" your sample by selecting out those molecules that happen to be in the "0000...." state. If you're dealing with only one qubit (just "0"), that's half the sample. If you're using two qubits ("00"), that's a quarter of the sample. Three qubits is an eighth, and you can see where this is going. The signal gets very small, very quickly.

People have used liquid NMR systems to do some demonstration computations-- up to seven qubits in some cases. It's extremely unlikely to be useful for anything practical, though, where "practical" means "cracking codes that the NSA would care about."

(There are some other highly technical arguments about what's really going on in these systems, and whether the experiments to date really "count." I'm not up on the details of this particular fight, but it generated a great deal of heat back in 1999-2001, and may still be contentious for all I know.)

What about decoherence? Decoherence is one of the features that make NMR-based systems attractive. Nuclei are pretty robust, as quantum systems go-- they're buried way down in the nucleus of the atom, shielded by the electron clouds from most of the effects that would disrupt your computation. To the best of my knowledge, decoherence isn't a major problem for bulk liquid NMR.

Summary: The liquid NMR system has a lot of nice features, chief among them being the low overhead. If you've got an NMR machine and a cup of coffee, you've got what you need to do basic quantum information experiments. The scaling problem is a show-stopper, though, so while NMR experiments may provide a useful test bed for some quantum ideas, I don't believe anybody's really pushing them as the basis for practical computing systems.

If they were running for president, they would be: Ralph Nader. They really shook up the field about ten years ago, but they've faded back since then.