Non-Abelian topological order is a special quantum state of matter with unique properties. One of the major features is that its quasiparticles (or more simply, excitations) can “remember” the order in which they are exchanged or switched around. These special quasiparticles are called “non-Abelian anyons”.

Imagine you have a bunch of coins, but instead of being heads or tails, they can be both at the same time (weird, right?). Now imagine these special coins have a memory – if you swap their positions in a certain way, they “remember” the order they were swapped into. That’s kind of what’s happening here with non-Abelian topological order and its special particles called anyons.

Non-Abelian anyons are very promising for building powerful quantum computers that can resist errors. However, even after lots of effort, non-Abelian topological order and its associated anyons have remained difficult to actually create and control in real systems.

In this new study, the researchers were able to realize non-Abelian topological order in a quantum processor. Specifically, they programmed a trapped-ion quantum computer made by Quantinuum to generate the ground state of a non-Abelian topological state called the D4 state. This ground state function, which describes the exotic quantum properties of the system, was created with very high accuracy.

By cleverly moving the non-Abelian anyons around in the quantum state, the researchers detected signatures of the anyons’ special ability to retain the memory of past manipulations. This demonstrates inherently non-Abelian braiding statistics.

Furthermore, by tunnelling the anyons in different patterns, they generated all the possible ground states of this non-Abelian state, as well as an excited state with a single anyon present. This illustrates the strange and counterintuitive nature of non-Abelian anyons.

Overall, this work is a major advance towards harnessing non-Abelian anyons for quantum information processing. The ability to accurately generate and manipulate non-Abelian topological states on a real controllable quantum device opens new possibilities for research and applications.