Although I write a lot about quantum computing, I've not really paid much attention to performing quantum computations with silicon-based qubits. Luckily Stephanie Simmons from Simon Fraser University in Canada helped me catch up.

The idea with silicon-based quantum computers is that impurities form the basis of a qubits. If you drop a single phosphorous atom into a silicon crystal, it replaces a silicon atom. But it has one proton and one electron more than the surrounding atoms. That single proton and electron behave like their own little artificial atom, one that looks a lot like hydrogen.

A good qubit needs to have certain properties: well-defined states that are long lived, the ability to create superpositions of states, and the ability to entangle and couple different qubits. Now, I don't want to delve into the meaning of any of these particular properties. But suffice to say that phosphorous in silicon does very well at several of these aspects, but it's not very good for coupling multiple qubits.

According to Simmons, the problem with coupling qubits in silicon is due to precision. The obvious way to couple two qubits is to simply place them such that their wavefunctions overlap. Then, if you control that overlap, you control how the two qubits couple. If phosphorus in silicon were truly like hydrogen, this would be simple, because the lowest two energy levels of hydrogen are slowly decaying waves with spherical symmetry. But here, the wavefunction is broken up by the surrounding silicon lattice, which turns into a more complicated structure (if I drew the picture correctly, it has hexagonal symmetry).

If a phosphorous atom is misplaced by one atomic lattice position, it goes from being strongly coupled to the neighboring qubit to being very weakly coupled to the neighboring qubit. This is not a situation you want to be in.

The alternative, favored by Simmons, is to couple qubits through optical signals. But, here phosphorus makes life very painful. The wavelength has to match the transition energies of the hydrogen-like atom. These turn out to require shorter wavelengths than microwaves, but much longer than infrared light. Yes, phosphorus puts you right in what we call the Terahertz gap—a spectral location avoided by all respectable physicists. Although it is still technically possible to do work at these wavelengths, it would be much better to find a different way of coupling.

Simmons' response to this problem was to ditch phosphorous. She replaced phosphorous with selenium, which produces, with a bit of manipulation, a hydrogen-like atom that can be manipulated using wavelengths of about three micrometers. This is still not convienent, but a wavelength of 3µm can be produced by a high-quality laser.

It turns out that selenium works very well. The coherence times and state lifetimes are good enough to use. And it seems that one of the problems that often plagues solid state systems—vibrations of the crystal disrupting the atomic states—do not seem to cause problems (though Simmons cautions that this is still not thoroughly tested).

Even better, the influence of the silicon lattice, which is so disastrous for coupling, acts to break up the energetic states into a series that seem to have very good properties for a qubit. By choosing the right combinations of these substates, you can put a qubit into a protected state that will live for a long time, put it in a different state to perform operations on it, or couple it to a neighboring qubit. It's like being able to switch the mode you're working in.

So far, though, Simmons has only achieved the first step: a single qubit that seems to behave very well. But she has excellent reasons to be optimistic about her approach. As she points out, working in silicon gives her access to a whole bunch of tricks, and she's not just referring to all the mature process technology that is used to make devices. Silicon is also used to make photonic crystal devices. These are structures that confine and guide light at very short length scales. Her qubits can be placed at the center of these light guides, giving her lots of opportunity to explore different ways of controlling her quantum circuits.

For example, one possibility is to use the splitting in the quantum states to produce entanglement between the wavelength of light that interrogated a qubit and the qubit's state. This can then be used to transfer that entanglement from the light to another qubit. But—and this might even be more exciting—with a photonic circuit involved, the path that the light takes will also be entangled with the qubit state, so entanglement between large numbers of qubits might be possible.

This is all very exciting stuff, and I look forward to seeing the future developments.

This talk was presented at Physics@FOM, Veldhove, 2017