By Dr. Andre Saraiva, UNSW

Measuring electric currents through a specially designed semiconductor device, researchers from the Manfra group at Purdue University measured directly an important topological quantity: the braiding statistics of anyons. This is a long sought-after scientific milestone for demonstrating the principles behind topological quantum computers. What are anyons? Well, make yourself a cup of tea, because this might take a minute.  

While all materials are made from the same subatomic particles – protons, neutrons and electrons – these particles can swarm together and act collectively as a new effective particle, called quasiparticle. Traditionally, both fundamental particles and quasiparticles will get their wavefunction affected when they are swapped around each other, either changing their sign or remaining unchanged. The former are called fermions (electrons, protons and neutrons are fermions), while the latter are called bosons (photons, phonons, excitons, etc). 

Anyons are exotic quasiparticles that gain some arbitrary complex phase when they are swapped. Well, at least that was the theory so far. Theorists have been evoking anyons for a long time to describe currents in semiconductors under intense magnetic fields (called fractional Hall effect). But so far, all evidence that these fractional Hall states were indeed anyons was indirect. 

The attempts to directly detect the braiding phase of anyons involved confining these Hall states in a small region –anyons naturally circulate by the edges, such that their relative phase will change as they swirl around each other. To measure this phase from interference effects, all electromagnetic interactions must remain very weak so that they do not create a traditional dynamical phase. But the repulsion of the electrons in the middle of the confinement region is already sufficient to disturb the edge states. The charging energy of these devices already completely washes out any braiding effects. 

The high sensitivity Fabry-Perot interferometer demonstrated by Nakamura and colleagues overcame these difficulties and showed well defined phase slips in the conductivity as controlled by magnetic field and gate voltages. This is an important confirmation that the topological property associated to braiding these particles have measurable effects.  

So, what’s next? 

These anyons are not yet of the type that can be used in quantum computing. To perform computations by braiding topological states, it is necessary that these particles follow a non-abelian statistics, which means that the order with which they are braided has an impact in the resulting phase. Particles with this prospect have only recently been indirectly detected, and the type of interferometers that harbour such particles are far more complex and still in their infancy. Microsoft, the giant force behind a lot of the worldwide effort in the direction of topological quantum computing, including this study, will still have to conquer a few more milestones before the anticipated topological protection of qubits is demonstrated. 

Dr. Saraiva has worked for over a decade providing theoretical solutions to problems in silicon spin quantum computation, as well as other quantum technologies. He works on MOS Silicon Quantum Dot research and commercially-oriented projects at the University of New South Wales (UNSW).

September 11, 2020