Chapman Lecture: Using Topology to Build a Better Qubit

Yesterday, we hosted Prof. Charlie Marcus of the Niels Bohr Institute and Microsoft for our annual Chapman Lecture on Nanotechnology.   He gave a very fun, engaging talk about the story of Majorana fermions as a possible platform for topological quantum computing. 

Charlie used quipu to introduce the idea of topology as a way to store information, and made a very nice heuristic argument about how topology encodes information in a global rather than a local sense.  That is, if you have a big, loose tangle of string on the ground, and you do local measurements of little bits of the string, you really can't tell whether it's actually tied in a knot (topologically nontrivial) or just lying in a heap.  This hints at the idea that local interactions (measurements, perturbations) can't necessarily disrupt the topological state of a quantum system.

The talk was given a bit of a historical narrative flow, pointing out that while there had been a lot of breathless prose written about the long search for Majoranas, etc., in fact the timeline was actually rather compressed.  In 2001, Alexei Kitaev proposed a possible way of creating effective Majorana fermions, particles that encode topological information,  using semiconductor nanowires coupled to a (non-existent) p-wave superconductor.   In this scheme, Majorana quasiparticles localize at the ends of the wire.  You can get some feel for the concept by imagining string leading off from the ends of the wire, say downward through the substrate and off into space.  If you could sweep the Majoranas around each other somehow, the history of that wrapping would be encoded in the braiding of the strings, and even if the quasiparticles end up back where they started, there is a difference in the braiding depending on the history of the motion of the quasiparticles.   Theorists got very excited a bout the braiding concept and published lots of ideas, including how one might do quantum computing operations by this kind of braiding.

In 2010, other theorists pointed out that it should be possible to implement the Majoranas in much more accessible materials - InAs semiconductor nanowires and conventional s-wave superconductors, for example.  One experimental feature that could be sought would be a peak in the conductance of a superconductor/nanowire/superconductor device, right at zero voltage, that should turn on above a threshold magnetic field (in the plane of the wire).  That's really what jumpstarted the experimental action.  Fast forward a couple of years, and you have a paper that got a ton of attention, reporting the appearance of such a peak.  I pointed out at the time that that peak alone is not proof, but it's suggestive.  You have to be very careful, though, because other physics can mimic some aspects of the expected Majorana signature in the data.

A big advance was the recent success in growing epitaxial Al on the InAs wires.  Having atomically precise lattice registry between the semiconductor and the aluminum appears to improve the contacts significantly.   Note that this can be done in 2d as well, opening up the possibility of many investigations into proximity-induced superconductivity in gate-able semiconductor devices.  This has enabled some borrowing of techniques from other quantum computing approaches (transmons).

The main take-aways from the talk:

• Experimental progress has actually been quite rapid, once a realistic material system was identified.
• While many things point to these platforms as really having Majorana quasiparticles, the true unambiguous proof in the form of some demonstration of non-Abelian statistics hasn't happened yet.  Getting close.
• Like many solid-state endeavors before, the true enabling advances here have come from high quality materials growth.
• If this does work, scale-up may actually be do-able, since this does rely on planar semiconductor fabrication for the most part, and topological qubits may have a better ratio of physical qubits to logical qubits than other approaches.
• Charlie Marcus remains an energetic, engaging speaker, something I first learned when I worked as the TA for the class he was teaching 24 years ago.