Quantum computers have the potential to solve problems far beyond the reach of today's fastest supercomputers. But today's machines are notoriously fragile. The quantum bits, or "qubits," that store and process information are easily disrupted by their environment, leading to errors that quickly accumulate.
One of the most promising approaches to overcoming this challenge is topological quantum computing, which aims to protect quantum information by encoding it in the geometric properties of exotic particles called anyons. These particles, predicted to exist in certain two-dimensional materials, are expected to be far more resistant to noise and interference than conventional qubits.
"Among the leading candidates for building such a computer are Ising anyons, which are already being intensely investigated in condensed matter labs due to their potential realization in exotic systems like the fractional quantum Hall state and topological superconductors," said Aaron Lauda, professor of mathematics, physics and astronomy at the USC Dornsife College of Letters, Arts and Sciences and the study's senior author. "On their own, Ising anyons can't perform all the operations needed for a general-purpose quantum computer. The computations they support rely on 'braiding,' physically moving anyons around one another to carry out quantum logic. For Ising anyons, this braiding only enables a limited set of operations known as Clifford gates, which fall short of the full power required for universal quantum computing."
But in a new study published in Nature Communications, a team of mathematicians and physicists led by USC researchers has demonstrated a surprising workaround. By adding a single new type of anyon, which was previously discarded in traditional approaches to topological quantum computation, the team shows that Ising anyons can be made universal, capable of performing any quantum computation through braiding alone. The team dubbed these rescued particles "neglectons," a name that reflects both their overlooked status and their newfound importance. This new anyon emerges naturally from a broader mathematical framework and provides exactly the missing ingredient needed to complete the computational toolkit.
From mathematical trash to quantum treasure
The key lies in a new class of mathematical theories called non-semisimple topological quantum field theories (TQFTs). These extend the standard "semisimple" frameworks that physicists typically use to describe anyons. Traditional models simplify the underlying math by discarding objects with so-called "quantum trace zero," effectively declaring them useless.
"But those discarded objects turn out to be the missing piece," Lauda explained. "It's like finding treasure in what everyone else thought was mathematical garbage."
The new framework retains these neglected components and reveals the new type of anyon - the neglecton - which, when combined with Ising anyons, allows for universal computation using braiding alone. Crucially, only one neglecton is needed, and it remains stationary while the computation is performed by braiding Ising anyons around it.
A house with unstable rooms
The discovery wasn't without its mathematical challenges. The non-semisimple framework introduces irregularities that violate unitarity, a fundamental principle ensuring that quantum mechanics preserve probability. Most physicists would have seen this as a fatal flaw.
But Lauda's team found an elegant workaround. They designed their quantum encoding to isolate these mathematical irregularities away from the actual computation. "Think of it like designing a quantum computer in a house with some unstable rooms," Lauda explained. "Instead of fixing every room, you ensure all of your computing happens in the structurally sound areas while keeping the problematic spaces off-limits.
"We've effectively quarantined the strange parts of the theory," Lauda said. "By carefully designing where the quantum information lives, we make sure it stays in the parts of the theory that behave properly, so the computation works even if the global structure is mathematically unusual."
From pure math to quantum reality
The breakthrough illustrates how abstract mathematics can solve concrete engineering problems in unexpected ways.
"By embracing mathematical structures that were previously considered useless, we unlocked a whole new chapter for quantum information science," Lauda said.
The research opens new directions both in theory and in practice. Mathematically, the team is working to extend their framework to other parameter values and to clarify the role of unitarity in non-semisimple TQFTs. On the experimental side, they aim to identify specific material platforms where the stationary neglecton could arise and to develop protocols that translate their braiding-based approach into realizable quantum operations.
"What's particularly exciting is that this work moves us closer to universal quantum computing with particles we already know how to create," Lauda said. "The math gives a clear target: If experimentalists can find a way to realize this extra stationary anyon, it could unlock the full power of Ising-based systems."
About the study: In addition to Lauda, other authors include the study's first author, Filippo Iulianelli, and Sung Kim of USC, and Joshua Sussan of Medgar Evers College of The City University of New York.
The study was supported by National Science Foundation (NSF) Grants (DMS-1902092, DMS-2200419, DMS-2401375), Army Research Office (W911NF-20-1-0075), Simons Foundation Collaboration Grant on New Structures in Low-Dimensional Topology, Simons Foundation Travel Support Grant, NSF Graduate Research Fellowship (DGE- 1842487) and PSC CUNY Enhanced Award (66685-00 54).
