A Forgotten Math Idea Could Supercharge Quantum Computers
Scientists have revived an ignored area of math to envision a path toward stable quantum computing
Aaron Lauda has been exploring an area of mathematics that most physicists have seen little use for, wondering if it might have practical applications. In a twist even he didn’t expect, it turns out that this kind of math could be the key to overcoming a long-standing obstacle in quantum computing—and maybe even for understanding the quantum world in a whole new way.
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Unlike ordinary qubits, which store information in the state of a single particle, store it in the arrangement of several particles—which is a global property, not a local one, making them far more robust.
Take, for example, braided hair. The type and number of braids that a person has are global properties that remain the same regardless of how they shake their head. In contrast, the position of an individual hair strand is a local property that can shift with the slightest movement.
In our three-dimensional world, swapping two particles is like weaving one string over or under the other. You can always unweave them back to their original structure. When you swap particles in two dimensions, however, you cannot go over or under; you have to make the strings go through each other, which permanently changes the structure of the strings.
Because of this property, swapping two anyons can completely transform the state of a system. These swaps can be repeated among multiple anyons—a process called anyon braiding. The final state depends on the order in which the swaps, or braids, are formed, much like the way the pattern of a braid depends on the sequence of its strands.
Theoretically, many types of anyons exist. One variety, called Ising anyons, “are our best chance for quantum computing in real systems,” Lauda says. “However, by themselves, they are not universal for quantum computation.”
Picture a qubit as a number on a calculator display and the quantum gates as the buttons on the calculator. A nonuniversal computer is like a calculator that only has buttons for doubling or halving. You can reach plenty of numbers—but not all of them, which limits your computing power. A universal quantum computer would be able to reach all numbers.
It’s a shift that evokes the early days of imaginary numbers, which are numbers built on negative square roots. They were originally just a mathematical trick with no physical meaning—until Erwin Schrödinger used them in the wave equation that became a cornerstone of quantum mechanics. “This is similar,” says Eric Rowell, a mathematician at Texas A&M University, who was not involved in the work. “It’s like there’s another door we hadn’t pursued because we couldn’t see it as physical. Maybe it needs to be opened now.”
The catch is that adding a neglecton risks pushing everything into unphysical territory, in which probabilities stop adding up the way they should. “There’s this much larger theory,” Lauda says, “and sitting inside it, there’s a place where everything physically makes sense.” It’s like when you wander off the map in a video game—the game starts glitching, you can walk through walls, and all the rules break down. The trick is to build an algorithm that keeps the player safely inside the map. That job fell to Lauda’s graduate student, Filippo Iulianelli, who reworked an algorithm he’d encountered in a recent class.
The next hurdle is finding a real-world version of this system; the neglecton remains entirely hypothetical for now. Lauda is optimistic. In the 1930s physicists used mathematical symmetries to predict the existence of a strange subatomic particle—the meson—years before experiments confirmed it. “We’re not claiming we’re in the same situation,” he says, “but our work gives experimentalists a target to look for in the same systems that are realizing Ising anyons.”
Shawn Cui, a mathematician at Purdue University who peer-reviewed the new paper, calls the research “very exciting theoretical progress” and hopes to see studies exploring physical systems where such anyons might emerge. Rowell agrees, and he suggests that the neglecton could arise from some interaction between an Ising system and its environment. “Maybe there’s just a little bit of extra engineering needed to construct this neglecton,” he says.
For Lauda, the implementation is only part of the excitement. “My goal is to make as compelling a case as possible to other researchers that the nonsemisimple framework is not just valid but an exciting approach to better understanding quantum theory,” he says. The neglecton is unlikely to be neglected for much longer.
Ananya Palivela is a science writer with a background in physics. She enjoys turning complex ideas in physics and science history into engaging stories.
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