The math that explains why a donut is indeed the same shape as a coffee cup but not a wastebasket could be the key to making quantum computers viable. Two teams of researchers have used topology, an age-old field of mathematics, and a new type of quasi-particle to come up with an error-correction technique for quantum computers that could leave others developed to date in the trash.

Error correction systems are essential for quantum computers, because the unprotected quantum bit (qubit) is such a perennially delicate thing, often a single particle or quantum state that it is forever at the mercy of thermal or random noise in the system. And since qubits are typically quantum interconnected with each other, to use the jargon, qubits are typically entangled, knocking just one or two out of order can affect the entire system.

The hunt for the best quantum error correction systems today takes many forms. Prototypes, techniques, and inventions that eliminate quantum errors regularly emerge from labs, startups, and aspiring quantum computing giants around the world. But a new development exploits a long-elusive quasiparticle whose behaviors could be bent to meet the perennially finicky qubit’s most pressing needs. Two companies, Google’s Quantum AI unit and Broomfield, Colorado-based startup Quantinuum, are battling over the discovery rights to a quantum entity called a non-abelian anyon.

## New states of matter to solve old problems

Non-Abelian anions exist in two-dimensional spaces, as surfaces or planar material such as graphene, and exhibit a peculiar kind of individuality enforced by the laws of quantum physics. Unlike completely interchangeable particles such as electrons and photons, non-Abelian anions can be made distinguishable enough from each other to trace distinct trajectories, potentially tying knots and twists around each other in the process. (Topology is the study of, among other things, these same kinks and twists. That’s why the non-Abelian anyone is a creature of what’s called topological quantum computing.)

We used qubit entanglement to create an environment where these anyons could be created, says Tony Uttley, president and COO of Quantinuums. It’s a quantum state of matter that we can now create inside a quantum computer.

The interesting feature of this new generation of quasiparticles, says Pedram Roushan of Google Quantum AI, is the combination of their accessibility to quantum logic operations and their relative invulnerability to thermal and ambient noise. This combination, he says, was recognized in the very first proposal for topological quantum computing, in 1997 by Russian-born physicist Alexei Kitaev.

At that time, Kitaev realized that non-Abelian anyons could run any quantum computer algorithm. And now that two separate groups have created quasi-particles in nature, each team is eager to develop their own suite of quantum computational tools around these new quasi-particles.

The Quantinuums H2 quantum computer chip features 32 qubits made up of individual ytterbium ions within an electromagnetic trap. Quantinuum

We used qubit entanglement to create an environment where these anyons could be created, says Tony Uttley, president and COO of Quantinuums. It’s a quantum state of matter that we can now create inside a quantum computer.

The interesting feature of this new generation of quasiparticles, says Pedram Roushan of Google Quantum AI, is the combination of their accessibility to quantum logic operations and their relative invulnerability to thermal and ambient noise. This combination, he says, was recognized in the very first proposal for topological quantum computing, in 1997 by Russian-born physicist Alexei Kitaev.

At that time, Kitaev realized that non-Abelian anyons could run any quantum computer algorithm. And now that two separate groups have created quasi-particles in nature, each team is eager to develop their own suite of quantum computational tools around these new quasi-particles.

The nice idea is that if you have two particles, you can move them around each other keeping them apart, protecting them from interactions that could collapse their delicate quantum states, Roushan says. The magic is that when these particles do a particular braid, these protected pieces can actually flip.

## What does a topological quantum computer look like?

Quantinuum, along with collaborators from Harvard and Stanford universities, uploaded an article to Arxiv’s preprint server last month announcing their creation of non-Abelian anions in the company’s H2 quantum computer, each of whose 32 qubits are single ions of ytterbium inside an electromagnetic trap. That trap sits inside an ultra-high vacuum chamber about the size of a basketball, Uttley says.

Meanwhile, the Google Quantum AI team and an international consortium of contributors have published a paper on *Nature**this month after first uploading it to the Arxiv server last October. This group also reported the creation of non-abelian Anyons of different types.*

The Google team made its non-Abelian anyon discovery on a quantum computer built around superconducting qubits that are made up of Josephson junctions and other circuit elements such as inductors and capacitors.

Google’s Quantum AI team has begun to imagine how topological quantum computing can twist and wrap qubits around each other. Google quantum AI

Qubits are essentially inductor-capacitor oscillators, says Trond Andersen, a member of the Google Quantum AI team of qubits in the Google system. But they are made with Josephson joints. And the beauty of them is that when we cool them down, we can see the quantized levels of this oscillator. And those quantized levels are what we use as zeros and ones.

Chetan Nayak, an expert on non-abelian anions and topological error correction, Microsoft Research in Santa Barbara, California, confirmed the importance of the new research. He described Quantinuum’s work as an impressive scientific demonstration that validates Microsoft’s long-standing belief that error-proof topological qubit design is the way to deliver large-scale quantum computing.

And as the electron hole is to the day-to-day operations of semiconductors and CPUs, at least according to these researchers, the new quasiparticle could be the necessary bridge towards a kind of topologically protected entanglement that can begin to fulfill the outsized promise of quantum computing.

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