Physicists create long-sought topological quantum states


09 May 2023

Exotic particles called nonabelions could fix quantum computers’ error problem.

by Davide Castelvecchi

borromean rings .jpeg
Borromean rings depicted in a church in Florence, Italy. If any one of the three rings is removed, the other two are no longer joined.Credit: Raphael Salzedo/Alamy

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 May1, 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.

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.

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.

The strange topology that is reshaping physics

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.

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 Pasadena2. 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.


  1. Iqbal, M. et al. Preprint at (2023).
  2. Kitaev, A. Y. Ann. Phys. 303, 2–30 (2003).

Nonabelions observed in quantum computer could make them less prone to errors

by Bob Yirka

Creating and controlling non-Abelian wavefunctions. (a) We entangle 27 ions to create the ground and excited states of a Hamiltonian with D4 topological order on a kagome lattice with periodic boundary conditions. (b) Its excitations go beyond Abelian anyons, whose spacetime braiding depends only on pairwise linking, as exemplified by the e- and m-anyons of the toric code. (c) We create and control non-Abelian anyons mR,G,B which can detect Borromean ring braiding via anyon interferometry. Credit: arXiv (2023). DOI: 10.48550/arxiv.2305.03766

In a development that could make quantum computers less prone to errors, a team of physicists from Quantinuum, California Institute of Technology and Harvard University has created a signature of non-Abelian anyons (nonabelions) in a special type of quantum computer. The team has published their results on the arXiv preprint server.

As scientists work to design and build a truly useful quantum computer, one of the difficulties is trying to account for errors that creep in. In this new effort, the researchers have looked to anyons for help.

Anyons are quasiparticles that exist in two dimensions. They are not true particles, but instead exist as vibrations that act like particles—certain groups of them are called nonabelions. Prior research has found that nonabelions have a unique and useful property—they remember some of their own history. This property makes them potentially useful for creating less error-prone quantum computers. But creating, manipulating and doing useful things with them in a quantum computer is challenging. In this new work, the team have come close by creating a physical simulation of nonabelions in action.

The research involved building a quantum computer based on a chip that produces electric fields that can trap ytterbium ions, which are then used to represent qubits. In their design, the trapped ions could be moved around, allowing them to interact if desired. They used this characteristic to entangle 32 ions in a lattice in the form of a kagome, all of which shared the same quantum state. Additional manipulation put the kagome in an excited state that allowed for simulating particles with properties of nonabelions.

The team then tested their machine to ensure the simulated nonabelions performed just as real ones would do under the same conditions—one such test involved moving the nonabelions to create Borromean rings—and that, the team suggests, showed that they might be used to overcome the need for much of the error correction normally involved in quantum computers.

More information: Mohsin Iqbal et al, Creation of Non-Abelian Topological Order and Anyons on a Trapped-Ion Processor, arXiv (2023). DOI: 10.48550/arxiv.2305.03766


The 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 particles’ behaviour satisfies the definition, and that for practical purposes they could still form a workable basis for quantum computing.