Back of the Envelope

Every once in a while I'm forcibly reminded that although I have a Ph.D., I am not a theorist, such as when I attempted to make sense out of this article at NewScientist.com:

ATTEMPTS to build quantum computers could run up against a fundamental limit on how long useful information can persist inside them. Exceed the limit and information could just leak away, making computation impossible.

...The entire [Quantum Computer] system is delicate: during a computation the qubits have to be isolated from their environment, because any outside disturbance can cause "decoherence" and spoil the calculations.

Coherence is harder to maintain in larger qubits containing more particles, because there is more potential for interaction with the surroundings. To try and limit this effect, researchers are pursuing ways of making microscopic qubits...

But physicists Jasper van Wezel, Jeroen van den Brink and Jan Zaanen of Leiden University in the Netherlands have shown that efforts to engineer quantum computers around ever-smaller qubits may face significant obstacles. "We have proven that there is a universal decoherence rate for qubits," says van den Brink. This means that quantum information will inevitably be lost after a certain time, even without any external disturbance. Rather than remaining in a superposition of two states, a qubit will spontaneously collapse into one state or another (Physical Review Letters, vol 94, p 230401). "When we discovered this we were stunned," says van den Brink.

Worryingly, the time limit for decoherence seems to grow shorter as systems get smaller. Zaanen says that for some of the most promising qubit technologies the limit would be about 1 second. It's not a problem at the moment, he says, because researchers are fighting to get coherence times up to around a microsecond. "But this fundamental limit is getting within reach."

Not being satisfied with the news report, I read the paper. Upon doing that, I realized that it is very much a theoretical paper, and I'm not sure I feel qualified to comment on it. I did notice a couple of things in the paper that don't really fit with the article, however, which means that either I am misreading the paper (quite possible), the article got it wrong, or the authors of the paper are missing something. Anyway, rather than attempt to Fisk the paper (again, I'm not qualified to do that), I'll just pose the questions I have about it. The paper can be found here, but only if you or your organization has an account with APS. However, there is an older version of it available to everyone here.

1. The calculations in the paper begin with the assumption that the qubit is entangled to the measurement device, and calculates the decoherence time (the time it takes for the qubit to lose its information) from there. However, the measurement schemes which I'm most familiar with do their best not to entangle the measurement device to the qubit until it's time to perform the measurement. As the measurement is performed at the end, after all the calculations are done, I don't see why this would limit the coherence time of the qubit while it's performing the calculations, which is where the coherence time is most critical. If that's the case, then the article is highly misleading. However, it may be that the measurement device represented in the paper is not literally the device performing measurements, but is rather representative of the environment, which is effectively measuring the qubit.


2. The New Scientist article says, "the time limit for decoherence seems to grow shorter as systems get smaller." In the paper, this is because the coherence time is inversely proportional to the N variable, which is the number of atoms. However, this brings me to my second problem, as N is not the number of atoms in the qubit, but in the measurement device. The measurement device can be much, much bigger than the qubit storing the data, so it's not obvious to me that a smaller qubit (an ion in a trap, for instance) should have worse decoherence than a larger one (a superconducting ring), should they use the same measurement device (a SQUID magnetometer, for instance). Of course, this may go back to my first question, and whether the measurement device is really the measurement device or rather the environment seen by the qubit, this being itself. (Yes, the qubit is its own environment, in the sense that the physical system has a lot more quantum states than those purposely used to store data, and losing data into these states is just as bad as losing data to the world at large.)


3. Nowhere in the decoherence equation does a coupling parameter appear. The coupling between the measurement device and the qubit is controllable in most quantum computation schemes, and if they're really talking about a measurement device, it seems to me that this should be taken into account. I think, reading the paper, that the coupling parameter is supposed to cancel out, but I find that hard to believe, and I'm not sure if I'm reading the paper correctly.


4. The paper doesn't address the question of quantum error correction. A fundamental time limit on quantum coherence time doesn't matter if quantum error correction can still be performed (which requires the coherence time to be 10⁴ times as long as the operation time), which can extend the coherence time of the device indefinitely. One second should be plenty of time for most quantum computation schemes to implement error correction. Is there something in this fundamental limit which prevents this?


5. Finally, I want to know whether this fundamental coherence time limit can be applied to NMR. NMR quantum computers, though limited in size, have demonstrated quantum coherence greater than the one second limit at room temperature. Admittedly, there is some question of whether NMR is real quantum computing, but I'd like to see the authors address this and how their analysis applies, or why it does not, in this case.

So there're five questions I don't know the answer to.Maybe I should ask a real theorist, such as Ben Schumacher, what he thinks.