Mathematicians have found a way to transform an unproductive quantum computing approach by reviving a class of previously discarded particles.
Quantum computers can solve problems beyond the capabilities of classical computers by using principles like superposition. This means a quantum bit, or qubit, can represent both 0 and 1 simultaneously, similar to the famous thought experiment of a cat being both dead and alive. But qubits are extremely fragile. Interactions with the environment can easily disrupt their quantum states. Their fragility makes it difficult to build stable quantum computers.
Ising anyons exist only in two-dimensional systems. They are at the heart of topological quantum computing. It means that anyons store information not in the particles themselves, but in how they loop or braid around one another. That braiding can encode and process information in ways that are far more resistant to environmental noise.
But there’s been a major limitation. “The only problem with Ising anyons is that they are not universal,” Aaron Lauda, a professor of physics and mathematics at the University of Southern California, told Live Science. “It’s like when you have a keyboard and it only has half the keys.”
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That’s where the overlooked math comes in. The team revisited a class of theories called “non-semisimple topological quantum field theory,” is used to study symmetry in mathematical objects.
“This is a key idea in particle physics,” Lauda said. “You’re able to predict new particles that people didn’t know about just by understanding the symmetry of what happens.”
In this theory, each particle has a quantum dimension — a number that reflects how much “weight,” or influence, it has in the system. If the number is zero, the particle is usually discarded.
“The key idea of these new non-semisimple versions is that you keep those particles, which originally had zero weight,” Lauda told Live Science. “And you come up with a new way of measuring the weight. There are some properties that it has to satisfy, and figure out how to make that number not be zero.”
The neglected pieces, reinterpreted as particles, filled in the missing capabilities of Ising anyons. The team showed that with just one neglecton added to the system, the particle becomes capable of universal computation just through braiding.
Why do Ising anyons matter?
To see why anyons matter at all, it helps to understand their peculiar behavior in two dimensions.
In three dimensions, particles like bosons and fermions can loop around each other. But those loops can be undone, like slipping a string over or under another. In two dimensions, by contrast, there’s no “over” or “under.” That means when anyons move around one another, the paths can’t be untangled, giving rise to fundamentally new physics.
“The way to think about it,” Lauda explained, “is if I start with a state zero and I wrap it around, does it stay in a state zero or some multiple of that? Or does it create a zero and a one? Am I able to mix them and create these superpositions that I need to do quantum computation?”
The key with Ising anyons is to be able to create superpositions. Because these operations depend on the overall shape of the braiding path, rather than on precise locations, they’re naturally shielded from many kinds of noise.
The finding doesn’t mean we’ll have topological quantum computers tomorrow. But it suggests that rather than inventing entirely new materials or exotic particles, researchers may just need to look at familiar systems through a new mathematical lens.
