A possible path to fault-tolerant quantum computing

Amazing stuff! Mind boggling!

"The coat of arms of Italy’s aristocratic House of Borromeo contains an unsettling symbol: an arrangement of three interlocking rings 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. ...

Nonabelions are a type of anyon, a particle that can exist only 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. ..."

From the abstract:

"Non-Abelian topological order (TO) is a coveted state of matter with remarkable properties, including quasiparticles that can remember the sequence in which they are exchanged. These anyonic excitations are promising building blocks of fault-tolerant quantum computers. However, despite extensive efforts, non-Abelian TO and its excitations have remained elusive, unlike the simpler quasiparticles or defects in Abelian TO. In this work, we present the first unambiguous realization of non-Abelian TO and demonstrate control of its anyons. Using an adaptive circuit on Quantinuum's H2 trapped-ion quantum processor, we create the ground state wavefunction of D4 TO on a kagome lattice of 27 qubits, with fidelity per site exceeding 98.4%. By creating and moving anyons along Borromean rings in spacetime, anyon interferometry detects an intrinsically non-Abelian braiding process. Furthermore, tunneling non-Abelions around a torus creates all 22 ground states, as well as an excited state with a single anyon -- a peculiar feature of non-Abelian TO. This work illustrates the counterintuitive nature of non-Abelions and enables their study in quantum devices."

Physicists create long-sought topological quantum states Exotic particles called nonabelions could fix quantum computers’ error problem.

Creation of Non-Abelian Topological Order and Anyons on a Trapped-Ion Processor (open access)

Confusing? 😊