Mathematicians have found ways to transform an unproductive quantum computing approach by reviving previously discarded classes of particles.
Quantum computers can solve problems that go beyond the capabilities of classical computers by using principles such as superposition. This means that Quantum Bit, or qubit, can represent both 0 and 1 at the same time, similar to the famous thought experiments of dead and surviving cats. However, Qubits is extremely vulnerable. Interaction with the environment can easily disrupt quantum states. These vulnerabilities make it difficult to build a stable quantum computer.
Now, in a new study published in the journal Nature Communications, mathematicians have shown that when paired with a mathematical element previously thrown out as unrelated, a type of quasiparticle called Ising Anyon can help overcome its vulnerability. They named the revived component “Neglecton.”
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Anyons exist only in two-dimensional systems. They are at the heart of topological quantum computing. That means that anyons store information in a way that loops or braids with each other, not in the particles themselves. The braiding allows information to be encoded and processed in a way that is much more resistant to environmental noise.
However, there were major restrictions. “The only problem with Ising Anyons is that they are not universal,” Aaron Lauda, professor of physics and mathematics at the University of Southern California, told Live Science. “It’s like when you have a keyboard and only half of the keys.”
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That’s an overlooked mathematical event. The team revisited a class of theory called “non-blood topological quantum field theory.” It is used to study the symmetry of mathematical objects.
“This is an important idea in particle physics,” Lauda said. “You can predict new particles that people just understand the symmetry of what happens.”
In this theory, each particle has a quantum size. This is a number that reflects the “weight” or effect that is present in the system. If the number is zero, the particles are usually discarded.
“The key idea for these new non-semisul pull versions is to hold particles that were originally weighing zero,” Lauda told Live Science. “And you come up with a new way to measure weight. There are some properties that it needs to meet and you need to understand how to avoid zeroing that number.”
The neglected pieces reinterpreted as particles are filled with Anyons’ lacking capabilities. The team showed that adding only one neglectone to the system would allow for universal calculations by braiding alone.
Why is it important?
It helps you understand unique behaviour in two dimensions to see why anyons are important.
Three dimensions allow particles such as bosons and fermions to loop with each other. However, these loops can be reverted, such as by sliding the string above or below other strings. In contrast, in the two dimensions there is no “over” or “under”. In other words, when anysons move around each other, they can’t solve the path, resulting in a fundamentally new physics.
“How to think about it,” explained Lauda, “If you start with zero state and wrap it around it, will it stay in a state zero or a multiple of it? Or will you create a zero?
The key to Ising Anyons is that you can create overlaps. These operations are naturally protected from many types of noise, as they depend on the overall shape of the braided path rather than the exact location.
This discovery does not mean that tomorrow we have topological quantum computers. But it suggests that researchers may need to look at familiar systems through new mathematical lenses rather than inventing entirely new materials or exotic particles.
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