Researchers demonstrated that braiding and fusing particles known as non-Abelian anyons can perform every operation required by a quantum computer.
A quantum computer becomes broadly useful only when it can perform any computation rather than a limited set of specialized tasks. Physicists have now demonstrated that unusual quantum objects called non-Abelian anyons can provide that versatility by supporting the full range of operations required for universal quantum computing.
Researchers from the University of Chicago Pritzker School of Molecular Engineering (UChicago PME), Harvard, Stony Brook University and Quantinuum constructed and tested a complete computational toolkit based on non-Abelian anyons. Their experiments offer the first demonstration that this approach can support universal quantum operations.
“We demonstrated a so-called universal gate set—meaning that if you store information in these emergent versions of quarks, and you move them around, you can do any quantum computation you might want to do,” said Ruben Verresen, assistant professor of molecular engineering at UChicago PME and a co-author of the new study published in Nature.
The method could support both general-purpose quantum computing and more reliable machines. Quantum computers ordinarily protect information by distributing it across many physical qubits through error correction. However, those codes usually cannot perform every required operation directly on the protected information.
Engineers often overcome that limitation with specially prepared resources called “magic states.” Producing them requires a demanding distillation process that can consume a substantial portion of a quantum computer’s available qubits. The findings indicate that non-Abelian anyons may provide a way around that expensive step.
“Non-Abelian codes are a dark horse in the race to quantum error correction,” said Henrik Dreyer, managing director and scientific lead at Quantinuum’s Munich office and a co-author of the study. “In this work we show the first universal gate set in a non-Abelian code, which demonstrates that fault-tolerant computations can in principle be done without resorting to magic state distillation or cultivation, which are the most expensive operations in standard quantum error correction codes.”
Anyons combine computation with protection
A conventional qubit represents information as a zero, a one, or a quantum combination of both. Non-Abelian anyons work differently. They are not independent particles found in nature. Instead, researchers produce them with quantum circuits that bind many ordinary qubits into a shared entangled state that behaves like a new type of particle governed by its own rules.
“The way I think about these codes is they’re creating little universes—alternative universes, but ones that reflect some of the properties of our own,” Verresen said.
Each non-Abelian anyon has an internal state that changes when it is moved, or braided, around another anyon. The sequence of those movements affects the result (that’s what non-Abelian means), allowing the anyons to represent and manipulate information in ways unavailable to ordinary particles.
Their information is also distributed across many entangled qubits instead of being stored at one vulnerable location. That makes the resulting state more resistant to the minor disturbances that often disrupt conventional qubits. The same braiding process that protects the information can also perform a computational gate.
The first anyons were not universal
In 2024, researchers including Verresen used a Quantinuum trapped-ion computer to create anyons based on a mathematical symmetry known as D4 — the rotations and reflections that leave a square unchanged — in the first hardware demonstration of this type of non-Abelian order. However, moving those anyons around one another could not produce every operation needed for universal computing.
“In that work, we didn’t demonstrate that those emergent forces were enough to do quantum computation,” said Verresen. “That particular universe we created was not powerful enough.”
Braiding and fusion complete the toolkit
For the latest work, the researchers selected a different symmetry known as S3—the rotations and mirror-image flips that leave an equilateral triangle unchanged—and created the corresponding anyons on Quantinuum’s H2 trapped-ion processor by entangling 54 qubits.
S3 had the mathematical properties needed for universal computing, but braiding alone was still insufficient. The researchers also needed fusion, a process in which two anyons are brought together, and the result is read as a measurement.
An emergent quark moves around an obstacle and, through this braiding process, gradually changing its internal color label. Because there are three possible colors (R, B, and G) this degree of freedom forms a qutrit. Slightly altering the path does not change the result, which gives a sense of the stability of the braiding process. Credit: University of Chicago
Carlos Mochon, then a student of John Preskill at Caltech, proposed this theoretical strategy in 2003. Translating the idea into a workable procedure on real quantum hardware required additional theoretical development and experimental testing.
The researchers paired the anyons to encode “topological qutrits,” units that store three possible levels of quantum information rather than the two available to ordinary qubits. They then combined braiding and fusion in different ways to demonstrate three essential operations: one entangling gate produced through braiding and two distinct measurements produced through fusion.
Together, those operations can in principle generate any quantum operation, including calculations that braiding by itself could not reach. Beyond their possible role in computing, the resulting quantum states may also help physicists investigate fundamental properties of matter.
“It is gratifying to see ideas we have spent our PhD work thinking about realized in the lab, and it has been made possible by remarkable advances in quantum hardware over the past few years,” said Anasuya Lyons and Chiu Fan Bowen Lo, graduate students at Harvard University in the group of Ashvin Vishwanath who helped lead the work.
The researchers also prepared a magic state directly from the non-Abelian anyons using topological operations — sidestepping the costly distillation procedure commonly required in other quantum systems.
Error correction remains the next test
The researchers did not perform active error correction in these experiments. Instead, they evaluated the separate computational components, confirmed that they functioned as intended, and verified that the resulting magic state agreed with theoretical predictions.
“So far, we’ve ignored the question of error correction. Here, it’s more like a proof of principle,” Verresen said.
The next challenge is to combine the method with active error correction. Doing so could eventually establish non-Abelian anyons as a practical basis for large-scale, fault-tolerant quantum computers. Verresen is already working with other UChicago PME researchers on techniques for stabilizing non-Abelian quantum memories.
Reference: “Universal gates from braiding and fusing anyons on quantum hardware” by Chiu Fan Bowen Lo, Anasuya Lyons, Dan Gresh, Michael Mills, Peter E. Siegfried, Maxwell D. Urmey, Nathanan Tantivasadakarn, Henrik Dreyer, Ashvin Vishwanath, Ruben Verresen and Mohsin Iqbal, 15 July 2026, Nature.
DOI: 10.1038/s41586-026-10709-y
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