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The coat of arms of Italy’s aristocratic House of Borromeo contains an unsettling symbol: an arrangement of three interlocking rings that that cannot be pulled apart but doesn’t contain any linked pairs.

That same three-way linkage is an unmistakable signature of one of the most coveted phenomena in quantum physics — and it has now been observed for the first time. Researchers have used a quantum computer to create virtual particles and move them around so that their paths formed a Borromean-ring pattern.

The exotic particles are called non-Abelian anyons, or nonabelions for short, and their Borromean rings exist only as information inside the quantum computer. But their linking properties could help to make quantum computers less error-prone, or more ‘fault-tolerant’ — a key step to making them outperform even the best conventional computers. The results, revealed in a preprint on 9 May^{1}, were obtained on a machine at Quantinuum, a quantum-computing company in Broomfield, Colorado, that formed as the result of a merger between the quantum computing unit of Honeywell and a start-up based in Cambridge, UK.

“This is the credible path to fault-tolerant quantum computing,” says Tony Uttley, Quantinuum’s president and chief operating officer.

Other researchers are less optimistic about the virtual nonabelions’ potential to revolutionize quantum computing, but creating them is seen as an achievement in itself. “There is enormous mathematical beauty in this type of physical system, and it’s incredible to see them realized for the first time, after a long time,” says Steven Simon, a theoretical physicist at the University of Oxford, UK.

## Basket-weave doughnut

In the experiment, Henrik Dreyer, a physicist at Quantinuum’s office in Munich, Germany, and his collaborators used the company’s most advanced machine, called H2, which has a chip that can produce electric fields to trap 32 ions of the element ytterbium above its surface. Each ion can encode a qubit, a unit of quantum computation that can be ‘0’ or ‘1’ like ordinary bits, but also a superposition of both states simultaneously.

Quantinuum’s approach has an advantage: compared with most other types of qubit, the ions in its trap can be moved around and brought to interact with each other, which is how quantum computers perform computations.

The physicists exploited this flexibility to create an unusually complex form of quantum entanglement, in which all 32 ions share the same quantum state. And by engineering those interactions, they created a virtual lattice of entanglement with the structure of a kagome — a pattern used in Japanese basket-weaving that resembles the repeated overlapping of six-pointed stars — folded to form a doughnut shape. The entangled states represented the lowest-energy states of a virtual 2D universe — essentially, the states that contain no particles at all. But with further manipulation, the kagome can be put in excited states. These correspond to the appearance of particles that should have the properties of nonabelions.

To prove that the excited states were nonabelions, the team performed a series of tests. The most conclusive one consisted of moving the excited states around to create virtual Borromean rings. The appearance of the pattern was confirmed by measurements of the state of the ions during and after the operation, Dreyer says.

“No two particles are taken around each other, but all together they are linked,” says Ashvin Vishwanath, a theoretical physicist at Harvard University in Cambridge, Massachusetts, and a co-author of the paper. “It’s really an amazing state of matter that we don’t have a very clear realization of in any other set-up.”

Michael Manfra, an experimental physicist at Purdue University in West Lafayette, Indiana, says that although the results are impressive, the Quantinuum machine does not truly create nonabelions, but merely simulates some of their properties. But the authors say that the particles’ behaviour satisfies the definition, and that for practical purposes they could still form a basis for quantum computing.

## Quantum pedigree

Like the Borromeo family, nonabelions come with a storied genealogy in both physics and mathematics, including work that has led to several Nobel prizes and Fields medals. Nonabelions are a type of anyon, a particle that can only exist in a 2D universe or in situations where matter is trapped in a 2D surface — for example at the interface of two solid materials.

Anyons defy one of physicists’ most cherished assumptions: that all particles belong to one of two categories, fermions or bosons. When two identical fermions switch positions, their quantum state, called the wavefunction, is flipped by 180 degrees (in a mathematical space called Hilbert space). But when bosons are switched, their wavefunction is unchanged.

When two anyons are switched, on the other hand, neither of these two options applies. Instead, for standard, ‘Abelian’ anyons, the wavefunction is shifted by a certain angle, different from fermions’ 180 degrees. Non-Abelian anyons respond by changing their quantum state in a more complex way — which is crucial because it should enable them to perform quantum computations that are non-Abelian, meaning that the calculations produce different outcomes if performed in a different order.

## Topological robustness

Nonabelions could also offer an advantage over most other ways of doing quantum computing. Ordinarily, the information in an individual qubit tends to degrade quickly, producing errors — something that has limited progress towards useful quantum computing. Physicists have developed various error-correction schemes that would require encoding a qubit in the collective quantum state of many atoms, potentially thousands.

But nonabelions should make that task a lot easier, because the paths they trace when they are looped around one another should be robust to errors. Perturbations such as magnetic disturbances might slightly move the paths around without changing the qualitative nature of their linking, called their topology.

The concept of nonabelions and their potential as ‘topological qubits’ was first proposed 20 years ago by theoretical physicist Alexei Kitaev, now at the California Institute of Technology in Pasadena^{2}. Physicists including Manfra have been aiming to create states of matter that naturally contain nonabelions and can therefore serve as the platform for topological qubits. Microsoft has made topological qubits its preferred approach to developing a quantum computer.

Vishwanath says that the nonabelions in Quantinuum’s machine are an important initial step. “To get into that game — to be even a contender for a topological quantum computer — the first step you need to take is to create such a state,” he says.

Simon says that the virtual nonabelion approach could be useful for quantum computations, but that it remains to be seen whether it will be more efficient than other error-correction schemes — some of which are also topologically inspired. The physical anyons that both Manfra and Microsoft are working on would be topologically robust out of the box. Dreyer says that, at the moment, it is still unclear how efficient his team’s nonabelions will turn out to be.

*This article is reproduced with permission and was first published on May 9, 2023.*

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