Physicists at Shanxi University in Taiyuan, China, have demonstrated the first experimental observation of non-adiabatic non-Abelian braiding using quantum matter waves. The achievement, published July 3 in Nature Communications, opens a fast paradigm for braiding operations that could have implications for topological quantum computing and fundamental tests of quantum mechanics.
Think of braiding like interweaving strands of a rope. In the quantum world, “braiding” refers to the process of moving quantum particles around one another in space-time. The order in which you perform these moves matters, a property technically called non-commutative, or non-Abelian, braiding. Multiply A by B and you get one result; multiply B by A and you get a different one.
Previous experimental demonstrations of non-Abelian braiding, in acoustic and photonic systems, relied on adiabatic processes, meaning the operations had to be performed slowly to maintain the system in its instantaneous ground state. This built-in speed limit made the approach impractical for fast quantum operations. The Shanxi team has shown that non-Abelian braiding can be performed non-adiabatically, quickly, without sacrificing the topological protection that makes braiding attractive in the first place.
The Experiment
The researchers used an ultra-cold Bose-Einstein condensate (BEC), a cloud of atoms cooled to near absolute zero, where they collectively occupy the same quantum state, as their experimental platform. Rather than braiding physical particles in space, they encoded the braid “strands” in the momentum states of the BEC. Laser-driven couplings between different momentum components realized the braiding operations.
To verify that the braiding was genuinely non-Abelian, the team applied different sequences of holonomic operations to the same initial momentum state and observed distinct final outcomes. This is the hallmark of non-commutative algebra: if the braid group were Abelian, the order of operations would not matter, and the final state would be the same regardless of sequence. It was not.
The operations were generated via non-adiabatic non-Abelian holonomies, geometric phases accumulated along closed paths in state space, that do not require slow, adiabatic evolution. The approach works for both classical and quantum wave systems, the authors note, making it broadly applicable.
Why It Matters
Non-Abelian braiding has long been pursued as a route to topological quantum computing, where quantum information is stored in the braiding history of particles and is inherently protected from local noise. The catch has always been speed: adiabatic braiding is inherently slow, limiting its practical utility.
The Shanxi team’s demonstration suggests that the speed limit is not fundamental. “We show that non-Abelian braiding can be performed non-adiabatically, opening a fast paradigm applicable to both classical and quantum wave systems,” the authors write. The braiding operations were used to prepare, transfer, and distribute momentum quantum superposition states, directly demonstrating utility for quantum control.
The authors, Jin Xie and Bo-Wen Guan (equal contribution), Jiang Zhang, Chenhao Wang, Lantuan Xiao, Suotang Jia, and corresponding authors Yanting Zhao and Feng Mei, all at Shanxi University’s State Key Laboratory of Quantum Optics Technologies and Devices, report no competing interests.
Caveats
This is a proof-of-principle experiment in a BEC platform, not a working topological quantum computer. The braiding is demonstrated in momentum space rather than with anyon quasiparticles in a condensed matter system, which is the more commonly envisioned path for topological quantum computing. Whether the non-adiabatic approach can be translated to solid-state anyon systems, where practical topological qubits would likely live, remains an open question.
The paper also carries Nature Communications‘ standard “unedited manuscript” tag for early-release articles, though it has completed peer review as confirmed by the journal’s received (December 2025) and accepted (June 2026) dates.
Disclosure: Based on a peer-reviewed paper in Nature Communications, published July 3, 2026. DOI: 10.1038/s41467-026-75085-7. Open access under CC BY-NC-ND 4.0.