Our intuition tells us that it is impossible to see if two objects of the same type have been switched back and forth, and that is the case for all particles observed to date. Until now.

Non-Abelian ions—the only particles predicted to break this rule—have been sought after for their fascinating properties and potential to revolutionize quantum computing. Microsoft and others have chosen this approach for their quantum computing efforts. But after decades of researchers’ efforts in the field, observing non-Abelian humans and their strange behavior has proven challenging.

A Paper Published on preprint server *arXiv* Last October and published *Nature *Today, researchers at Google Quantum AI announced the first observation of strange non-Abelian behavior using one of their superconducting quantum processors.

They also demonstrated how this phenomenon can be used to perform quantum calculations. Earlier this week, quantum computing company Quantinuum published another study on the topic, which complements Google’s initial findings. These new results open a new path toward topological quantum computation, in which operations are achieved by wrapping any non-Abelian around like strings in a braid.

Trond I. Andersson, a Google Quantum AI team member and first author of the manuscript, says, „The first observation of strange non-Abelian behavior highlights the kind of exciting phenomena we can now access with quantum computers.”

You are shown two identical objects and asked to close your eyes. Open them again and you see the same two items. How to determine if they have been replaced? Intuition suggests that there is no way to tell if the objects are really the same.

Quantum mechanics supports this intuition, but only in the three-dimensional world we are familiar with. If homogeneous objects are constrained to move only in a two-dimensional plane, sometimes our intuition fails and quantum mechanics allows something strange: anyone who is non-Abelian retains a kind of memory—being able to tell when two of them exist. Served exactly the same though.

This „memory” of non-Abelian ions can be thought of as a continuous line in space-time: the particle is called the „world line”. When two non-Abelians interchange, their world lines wrap around each other. Fold them in the right way, and the resulting knots and braids form the basic functions of a topological quantum computer.

The team began by preparing their superconducting qubits in a complex quantum state best represented as a checkerboard — a structure familiar to the Google team recently. proved a milestone in quantum error correction Using this system. In a checkerboard arrangement, related—but less useful—particles called abelian ions can emerge.

To realize anything non-Abelian, the researchers stretched and verified the quantum state of their qubits, transforming the verified form into oddly shaped polygons. Certain vertices in these polygons hosted non-Abelian yans. Using a Ethics Created by Eun-Ah Kim and former postdoc Yuri Lenski at Cornell University, the group can move anyone who isn’t Abelian.

In a series of experiments, the Google researchers observed the behavior of these non-Abelians and how they interacted with any more ordinary Abelians. Interweaving the two types of particles together produced strange phenomena – the particles mysteriously disappeared, reappeared, and changed shape from one type to the other.

More importantly, the team noticed a peculiarity of the non-Abelian ones: when two of them were switched, it caused a measurable change in the quantum state of their system—a remarkable phenomenon never seen before.

Finally, the team demonstrated how non-Abelian entanglement can be used in quantum computations. By combining several other non-Abelian states, they were able to create the well-known quantum entangled state known as the Greenberger-Horn-Zeilinger (GHZ) state.

At the heart of the approach Microsoft has chosen for their quantum computing effort is the physics of non-Abelian particles. As they try to engineer material systems that intrinsically host these molecules, the Google team has now shown that the same kind of physics can be realized in their superconducting processors.

This week quantum computing company Quantinuum published an impressive complementary study that demonstrated non-Abelian entanglement, in this case using a trapped-ion quantum processor. Anderson is excited to see other quantum computing groups looking at non-Abelian entanglement. He says, „It will be very interesting to see how any non-Ephelion works in quantum computing in the future, and could their strange behavior be the key to fault-tolerant topology quantum computing?”

**More information:**

Google Quantum et al., Non-Abelian entanglement of graph vertices in a superconducting process, *Nature* (2023) DOI: 10.1038/s41586-023-05954-4

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* *„Oddany rozwiązywacz problemów. Przyjazny hipsterom praktykant bekonu. Miłośnik kawy. Nieuleczalny introwertyk. Student.