Although quantum computers have the potential to solve problems beyond the reach of supercomputers, current qubits are highly susceptible to environmental interference, leading to rapid error accumulation. Topological quantum computing is regarded as a promising solution to this challenge, as it protects quantum information by encoding it in the geometric properties of exotic particles. Aaron Lauda, professor at the USC Dornsife College of Letters, Arts and Sciences, explains: "Ising anyons are one of the leading candidates for building topological quantum computers, but they alone cannot perform all the operations required for a universal quantum computer."

Computing with Ising anyons relies on "braiding," the physical movement of anyons to execute quantum logic. However, this braiding supports only a limited set of operations, insufficient for universal quantum computing. In a study published in Nature Communications, a USC-led team demonstrated a new approach that makes Ising anyons universal by introducing a new type of anyon—the "negliganyon."

The name "negliganyon" reflects both its previously overlooked status and its newly discovered importance. This anyon emerges naturally from a broader mathematical framework, providing the missing element in the computational toolkit. The research team used non-semisimple topological quantum field theory, retaining the "trace-zero" objects traditionally discarded in standard models, thereby revealing the existence of the negliganyon. When combined with Ising anyons, universal computation can be achieved solely through braiding.

Facing the mathematical challenges introduced by the non-semisimple framework, the Lauda team designed a quantum encoding that isolates mathematical irregularities from actual computations. Lauda likened it to: "Designing a quantum computer in a house with unstable rooms—we ensure all computations take place in structurally sound areas." This breakthrough shows that abstract mathematics can solve concrete engineering problems in unexpected ways, opening a new chapter in quantum information science.

The research opens new directions both theoretically and practically. The team is working to extend the framework to other parameter values and clarify the role of unitarity in non-semisimple TQFTs. Experimentally, they aim to identify material platforms where negliganyons may appear and develop protocols to translate braiding methods into realizable quantum operations.