Google Quantum AI braids non-Abelian people for the first time

Our intuition tells us that it’s impossible to tell whether two identical objects have been swapped back and forth, and for all the particles observed to date, that is the case. Until now.

Non-Abelian anyons – the only particles expected to violate this rule – have been sought after for their attractive features and potential to revolutionize quantum computing by making operations more noise-resistant. Microsoft and others have chosen this approach for their quantum computing endeavors. But after decades of effort by researchers in the field, observing any non-Abelians and their strange behavior has proven challenging, to say the least.

In a paper posted on the Arxiv.org preprint server last October and published in the Natural Today, researchers at Google Quantum AI announced that they have used one of their superconducting quantum processors to observe the strange behavior of non-Abelian people for the first time. They also demonstrate how this phenomenon can be used to perform quantum computations. Earlier this week quantum computing company Quantinuum released another study on the topic, complementing Google’s initial findings. This new result opens a new pathway to topological quantum computation, in which operations are accomplished by wrapping non-Abelian anyons around each other like strings in a braid.

Google Quantum AI team member and first author of the manuscript, Trond I. Andersen said, “Observing the strange behavior of non-Abelian people for the first time really sheds light on the kinds of interesting phenomena we can now access with quantum computers.”

Imagine that you are shown two identical objects and then asked to close your eyes. Open it again, and you see the same two objects. How can you determine if they have been exchanged? Intuition tells us that if the objects are completely identical, there’s no way of knowing.

Quantum mechanics supports this intuition, but only in the three-dimensional world we know. If identical objects were limited to moving only in a two-dimensional plane, on occasion, our intuition could fail and quantum mechanics allowed something strange: non-Abelians retain some sort of memory — it is possible to tell when two of them have exchanged, even if true -completely identical.

These non-Abelian anyon “memories” can be thought of as continuous lines in space-time: so-called “worldlines” of particles. When two non-Abelian people are exchanged, their world lines wrap around one another. Wrap them in the right way, and the resulting knots and braids form the basic operations of a topological quantum computer.

The team started by setting up their superconducting qubit in an entangled quantum a state well-represented as a chessboard — a familiar configuration to the Google team, more recently demonstrated a milestone in quantum error correction use this setting. In a checkerboard setting, a related—but less useful—particle called Abelian anyons can appear.

To realize non-Abelian anyons, the researchers expanded and compressed their qubit quantum states to turn the checkerboard patterns into oddly shaped polygons. Certain vertices in this polygon host non-Abelian anyons. Using a protocol developed by Eun-Ah Kim at Cornell University and former postdoctoral Yuri Lensky, the team could then move non-Abelians anywhere by continuously changing the shape of the lattice and shifting the locations of non-Abelian vertices.

In a series of experiments, researchers at Google looked at the behavior of these non-Abelians and how they interacted with more ordinary Abelians. Woven two types of particles around each other produces a strange phenomenon – particles mysteriously disappear, reappear, and change shape from one type to another as they twist and collide with each other. Most importantly, the team observed a distinctive feature of non-Abelian anyons: when two of them are swapped, it causes a measurable change in the quantum state of their system — a striking phenomenon that had never been observed before.

Finally, the team demonstrated how non-Abelian anyon entanglements could be used in quantum computation. By braiding several non-Abelian anyons together, they were able to create the famous quantum entangled state called the Greenberger-Horne-Zeilinger (GHZ) state.

Non-Abelian particle physics is also at the core of Microsoft’s preferred approach to their quantum computing endeavours. While they are trying to engineer material systems that intrinsically host all of this, the Google team has now shown that the same kind of physics can be realized on their superconducting processors.

This week quantum computing company Quantinuum released an impressive complementary study that also demonstrates non-Abelian braiding, in this case using an ion-trapped quantum processor. Andersen is thrilled to see other quantum computing groups observing non-Abelian entanglements as well. He said, “It will be very interesting to see how non-Abelians are employed in quantum computing in the future, and whether their strange behavior could hold the key to fault-tolerant topological quantum computing.”