Here's something you might be familiar with: a performance ends, the audience begins to applaud, and the sound becomes thunderous and continuous. But in your immediate neighborhood, everyone seems to be clapping at the same moment.

This synchronization is common in the classical world. Attach a few grandfather clocks to a wall and over the course of the day, their pendulums will start to swing in sync. In things like pendulums, the oscillators are not perfect—they lose energy over time. That energy is transmitted through vibrations to neighboring pendulums, where it is absorbed. The mutual emission and absorption of vibrations slowly brings the two pendulums into sync with each other.

Does synchronization work in a quantum system and, if so, how? This is the question a pair of researchers from Switzerland set out to answer.

Happy swinging

Why does synchronization work in the first place? Well, an oscillator, like a swing, has a frequency that is given by its construction: the mass and length of the rope set a preferred frequency. Phase is also a property of an oscillator. The phase describes where in an oscillation the swing is. So as the swing swings, the frequency stays constant and the amplitude of the oscillation stays constant, but the phase constantly changes.

Synchronization works because a swing has no preferred phase. Essentially, if I set a swing going now, it will have some phase. I could also set the swing going a bit later, and it would have a different phase. The swing doesn’t care.

Two swings on the same cross bar will exchange energy. When a swing absorbs energy, it speeds up slightly so the phase advances a bit more than expected. When it emits energy, it slows down. When the two swings are out of phase, the swing that is behind will absorb energy from its partner. This slows the swing that is ahead and speeds the swing that is behind until they are in sync. Once in sync, every time a swing gets a little ahead, it gives up some energy and the other swing gets a little boost to hold them together.

Spinning out of control

If we add a dash of quantum mechanics, things get more complicated. First, the thing that is swinging is not a physical object. We are not talking about an electron moving about. Instead, we are talking about probabilities that are swinging.

In particular, we are talking about spin, which is the intrinsic angular momentum of particles like electrons. Angular momentum is a spatial property—it has an orientation in space. In the smallest possible quantum system, in any given orientation, the spin can take on one of two possible values (plus or minus a half).

Being quantum particles, though, they can also be in a state that is both plus a half and minus a half at the same time. This is called a superposition state. When we measure the state, the spin makes a random decision and returns either a plus half or a minus half. The random decision is determined by the relative probabilities of the two states.

The thing that oscillates is that relative probability.

If we try to drive that oscillation with some force, will the spin synchronize with the driving force? No. You can drive the oscillation, but the phase of a two-state qubit is fixed. The spin can absorb or emit energy, but this does not change the phase of the oscillation. This is also true if two spins are exchanging energy: they do not have the freedom required to adjust their phases and synchronize.

But if you add an extra state so that the spin values are +1, 0, and -1, the possibility of energy exchange opens up. The oscillation we're interested in might be between the 0 and -1 states. But the phase evolution can be slowed by adding in a small detour via the +1 state. Likewise, phase evolution can be sped up by driving the system away from the 0 state (so that it cannot go to state 1). This allows the oscillation between the 0 and -1 state to be synchronized to an outside signal.

This only happens if the probability of absorbing (or emitting) energy to transfer between the +1 and 0 states is quite different from the probability of absorbing or emitting energy to transfer between the 0 and -1 states. In other words, the system needs some asymmetry to it as well.

No extra spin here

The paper is theoretical, but it's theory with implications. Quantum computing is reliant on controlling and understanding the phase evolution of superposition states. In particular, error correction schemes use lots of (quantum) hardware to correct for the fact that we do not have full control over phase evolution.

This paper does not directly solve that problem, but it does show that there might be a different approach that requires less computational hardware to reduce the accumulation of errors. Indeed, even if it can’t be used for error correction (and I don’t believe it can), it is yet another tool that we can use to control quantum states. And at the moment, we need every tool we can get our hands on.

Physical Review Letters, 2018, DOI: 10.1103/PhysRevLett.121.053601. (About DOIs).