Physicists create long-sought topological quantum states

by The Insights

The coat of arms of the Italian aristocratic House of Borromeo contains a disturbing symbol: an arrangement of three interlocking rings that cannot be separated but contain no linked pairs.

This same three-way link is an unmistakable signature of one of the most coveted phenomena in quantum physics – and it has now been observed for the first time. The researchers used a quantum computer to create virtual particles and move them so that their trajectories formed a Borromean ring pattern.

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 binding properties could help make quantum computers less error-prone or more “fault-tolerant,” a key step in making them perform better than the best conventional computers. The results, revealed in a preprint on May 91were obtained on a machine from Quantinuum, a quantum computing company in Broomfield, Colorado, which formed as a result of a merger between Honeywell’s quantum computing unit and a start-up based in Cambridge, UK.

“This is the credible path to fault-tolerant quantum computing,” said Tony Uttley, President and COO of Quantinuum.

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

braided donut

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

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

Physicists have exploited this flexibility to create an unusually complex form of quantum entanglement, in which all 32 ions share the same quantum state. And in designing these interactions, they created a virtual web of entanglement with the structure of a kagome – a pattern used in Japanese basketry that resembles the repeated overlapping of six-pointed stars – folded to form a donut shape. Entangled states represented the lowest energy states of a 2D virtual universe – essentially, states that contain no particles. But with other manipulations, the kagome can be put into excited states. These correspond to the appearance of particles which should have the properties of non-abelions.

To prove that the excited states were non-abelions, the team performed a series of tests. The most conclusive was to move the excited states 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, says Dreyer.

“There are no two particles caught around each other, but all together they are bound,” says Ashvin Vishwanath, theoretical physicist at Harvard University in Cambridge, Massachusetts, and co-author of the item. “It really is an amazing state of matter that we don’t have a very clear realization of in any other configuration.”

Michael Manfra, an experimental physicist at Purdue University in West Lafayette, Indiana, says that while the results are impressive, the Quantinuum machine doesn’t actually create non-abelions, but merely simulates some of their properties. But the authors say that particle behavior satisfies the definition and that, for practical purposes, they could still provide a basis for quantum computing.

Quantum Pedigree

Like the Borromeo family, nonabelions have a rich ancestry in 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 challenges one of physicists’ most cherished assumptions: that all particles belong to one of two categories, fermions or bosons. When two identical fermions change position, their quantum state, called the wave function, is reversed by 180 degrees (in a mathematical space called Hilbert space). But when the bosons are switched, their wave function remains unchanged.

When two anyons are exchanged, on the other hand, neither of these two options applies. Instead, for standard “abelian” anyons, the wave function is shifted by some angle, different from the 180 degrees of the fermions. Non-abelian anyons respond by changing their quantum state in more complex ways – which is crucial as this should allow them to perform non-abelian quantum computations, meaning that the computations produce different results if performed in a different order.

Topological robustness

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

But nonabelions should make this task much easier, since the paths they make when looped around each other should be robust to errors. Disturbances such as magnetic disturbances could shift paths slightly without altering the qualitative nature of their linkage, 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 sought to create states of matter that naturally contain non-abelions and can therefore serve as a platform for topological qubits. Microsoft has made topological qubits its preferred approach to developing a quantum computer.

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

Simon says the virtual non-abelion approach could be useful for quantum computations, but it remains to be seen whether it will be more efficient than other error-correction schemes – some of which are also topology-inspired. . The physical anyons that Manfra and Microsoft are working on would be topologically robust out of the box. Dreyer says that, at this time, it’s still unclear how effective his team’s non-abelions will be.

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

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