A practical quantum computer must eventually be able to handle any type of quantum algorithm, much like a conventional laptop can run many different kinds of software. Achieving this level of general-purpose flexibility has long been one of the ultimate goals of quantum information science. Now, an international team of researchers has demonstrated a new way to reach that level of operational versatility using unusual quantum objects known as non-Abelian anyons, marking a significant milestone in the ongoing development of fault-tolerant quantum machines.
Scientists from the University of Chicago Pritzker School of Molecular Engineering (UChicago PME), Harvard University, Stony Brook University, and Quantinuum have successfully created and tested a full set of operations based on these exotic quasiparticles. Their experimental results, published in the journal Nature, provide the first empirical demonstration that this topological approach can support the broad and diverse range of operations required for universal quantum computing.
"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.
A Possible Shortcut Around Costly Quantum Error Correction
Beyond helping scientists engineer a more versatile general-purpose quantum computer, this new strategy could offer a considerably more efficient pathway toward building reliable, scalable quantum machines.
Because quantum computers are notoriously fragile and extremely vulnerable to environmental noise, researchers typically protect sensitive information by distributing it across many physical qubits. While these error correction methods can successfully preserve stored data, they usually do not provide every single operation needed to perform universal quantum computation directly on that protected information.
To bridge this operational gap, engineers often have to rely on specially prepared resources known as "magic states." Producing these states generally requires an intensive, computationally demanding purification process called distillation, which can consume a frustratingly large fraction of a quantum computer’s available qubits and computational overhead. The newly reported results suggest that non-Abelian anyons may offer an elegant and efficient way around that expensive step altogether.
"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."
Why Non-Abelian Anyons Are Different
Ordinary qubits encode information using two basic computational states, along with complex quantum combinations—known as superposition—of those states. Non-Abelian anyons, however, operate in a fundamentally different and more robust way.
These anyons do not appear as ordinary, standalone elementary particles in the natural vacuum of our universe. Instead, scientists create them inside complex quantum circuits by entangling many conventional qubits together into a collective state that behaves as though it were an entirely new type of particle governed by its own unusual mathematical 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 explained.
Each non-Abelian anyon carries a hidden internal state that dynamically changes when one anyon is physically or logically moved around another in a process known as braiding. Crucially, the precise chronological sequence of those braiding operations matters—which is the defining characteristic of non-Abelian statistics—allowing quantum information to be safely encoded and manipulated in ways that are entirely unavailable to ordinary particles.
Because this information is spread nonlocal across many mutually entangled qubits rather than being stored in a single, vulnerable physical location, it is naturally protected from some of the small, localized disturbances that frequently disrupt conventional qubits. Furthermore, the very act of braiding the anyons performs computational operations on the data.
Why Braiding Alone Was Not Enough
The path to this breakthrough has been incremental. In 2024, a research team that included Verresen utilized a Quantinuum trapped-ion quantum computer to successfully create anyons associated with a mathematical symmetry group called D4—representing the rotations and reflections that leave a geometric square completely unchanged. That experiment successfully demonstrated this form of non-Abelian order on programmable quantum hardware for the very first time.
While that prior experiment proved that these unusual quasiparticles could indeed be created and manipulated in a laboratory setting, researchers quickly realized that braiding them alone was insufficient to carry out every single operation required for universal quantum computing.
"In that work, we didn’t demonstrate that those emergent forces were enough to do quantum computation," Verresen noted. "That particular universe we created was not powerful enough."
Fusion Unlocks Universal Quantum Operations
To overcome the limitations of the D4 symmetry model for the new study, the researchers shifted their focus to another mathematical symmetry known as S3—the rotations and mirror-image flips that leave an equilateral triangle unchanged. They successfully generated the corresponding anyons on Quantinuum’s H2 trapped-ion processor using a total of 54 entangled qubits.
The S3 system possessed the specific topological properties needed to unlock universal quantum computation, but this capability only emerged when braiding was combined with an additional, distinct operation called fusion. During the fusion process, two anyons are brought closely together and the resulting combined state is measured.
The underlying conceptual framework for this approach was originally proposed theoretically back in 2003 by Carlos Mochon, who was then a student working under prominent theoretical physicist John Preskill at the California Institute of Technology. Translating that decades-old theoretical concept into a functioning experiment that could actually run on modern, noisy quantum hardware, however, required extensive additional theoretical refinement and experimental engineering.
For the experiment, the researchers utilized pairs of anyons to encode what they call "topological qutrits," which can store three possible discrete levels of quantum information instead of the standard two levels utilized by traditional qubits.
By cleverly combining different braiding and fusion operations, the research team demonstrated three essential computational tools: one entangling gate produced exclusively through braiding, and two different types of measurements created through fusion. Together, this comprehensive suite of operations can in principle produce any arbitrary quantum operation, including specialized computational routines that braiding alone could never achieve.
Beyond their clear potential applications in advanced quantum computing hardware, these unusual topological quantum states could also provide physicists with a powerful experimental platform to investigate fundamental, hard-to-reach aspects of theoretical physics.
"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 working within the research group of Ashvin Vishwanath, who helped lead the collaborative project.
Toward Fault-Tolerant Quantum Computers
As part of their investigation, the researchers also demonstrated that non-Abelian anyons could directly produce a magic state utilizing pure topological operations—thereby entirely sidestepping the costly and cumbersome distillation process that plagues most conventional quantum architecture designs.
It is worth noting that the current experiment did not yet incorporate active quantum error correction. Instead, the research team deliberately focused their efforts on testing the fundamental individual building blocks of the method and confirming that they could successfully generate a magic state that was fully consistent with theoretical expectations.
"So far, we’ve ignored the question of error correction. Here, it’s more like a proof of principle," Verresen said.
The next major milestone for the field will involve combining these newly demonstrated operations with active, real-time error correction protocols. If that ambitious goal can be successfully achieved, non-Abelian anyons could eventually serve as a robust, practical foundation for large-scale, fault-tolerant quantum computers. Toward that end, Verresen is already actively collaborating with other researchers at UChicago PME to develop innovative new techniques aimed at stabilizing non-Abelian quantum memories.