"Non-Abelian codes are a dark horse in the race to quantum error correction," said Henrik Dreyer, managing director and scientific lead at Quantinuum's Munich office and a co-author. "In this work we show the first universal gate set in a non-Abelian code, which demonstrates that fault-tolerant computations can in principle be done without resorting to magic state distillation or cultivation, which are the most expensive operations in standard quantum error correction codes."

Bottom line: anyon-based codes could slash one of quantum computing's biggest overheads.

How are these anyons different from ordinary qubits?

A normal qubit stores information in two basic states, plus quantum mixtures of them. Non-Abelian anyons don't exist as ordinary particles. Engineers build them inside quantum circuits by entangling many qubits into a single collective state that behaves like a brand-new particle with its own unusual rules.

"The way I think about these codes is they're creating little universes — alternative universes, but ones that reflect some of the properties of our own," Verresen said.

Each anyon carries an internal state that changes when one anyon loops around another, a move called braiding. The order of those loops matters, hence the name "non-Abelian." Because information lives spread across many entangled qubits, it gains some natural defense against small disturbances.

The upshot: a single hardware trick delivers both computation and a layer of protection.

Why wasn't braiding alone enough?

In 2024, a team that included Verresen created anyons tied to a symmetry group called D4 — the rotations and reflections that leave a square unchanged. They proved the particles existed and could be moved around. They also hit a wall.

"In that work, we didn't demonstrate that those emergent forces were enough to do quantum computation," Verresen said. "That particular universe we created was not powerful enough."

For the new study, the team switched to S3, the symmetry of an equilateral triangle, and built the matching anyons on the H2 processor. S3 brings enough structure for universal computation, but only if braiding teams with a second move: fusion, bringing two anyons together and measuring the result.

The deeper idea dates to 2003, when Carlos Mochon proposed it in his Caltech PhD thesis under John Preskill. Two decades of theory and hardware progress turned that math into a working experiment.

What's next?

The latest run skipped active error correction. The team focused on confirming each building block worked and that the magic state matched theory. "So far, we've ignored the question of error correction. Here, it's more like a proof of principle," Verresen said.

Next stop: weave these operations into a full fault-tolerant setup. Verresen is already collaborating with PME colleagues on ways to stabilize non-Abelian quantum memories.

The takeaway: the method works on paper and on hardware, but the road to a large-scale fault-tolerant machine still runs through the unglamorous work of stitching every piece together.