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arXiv:2608.12897

Observation of Time-Domain Braiding of Non-Abelian Anyons at $ν= 5/2$ State

Tomer Alkalay, Jinhong Park, Minseong Oh, Changki Hong, Jun-Young M. Lee, Priya Tiwari, Tapas Senapati, V. Umansky, Moty Heiblum, H. -S. Sim

Published Aug 13, 2026• 0 citations
arXivHTMLPDF

Abstract

Unlike elementary particles, which obey either bosonic or fermionic exchange statistics, certain quasiparticles, known as anyons, are predicted to exhibit Abelian or non-Abelian braiding statistics. While braiding Abelian anyons modifies the wavefunction by a 'statistical phase', braiding non-Abelian anyons implements a unitary transformation of the state within a degenerate subspace of states. Experimental evidence of non-Abelian braiding has thus far remained elusive. Here, we report a 'time-domain braiding' signature of non-Abelian anyons in the $ν= 5/2$ fractional quantum Hall state, by extending our previously demonstrated approach with Abelian anyons at $ν= 1/3$. Our approach is based on measurements of the current fluctuations arising from weak partitioning of a highly dilute one-dimensional edge mode. We independently probe the partition noise of the downstream charged mode and also that of the upstream neutral mode. These independent measurements agree with our theoretical predictions for 'time-domain braiding' of the downstream Abelian and the upstream non-Abelian anyons, respectively, in the 'particle-hole Pfaffian' topological order. Together, these results provide evidence for the presence of non-Abelian anyons.

DOI
10.48550/arxiv.2608.12897

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Observation of Time-Domain Braiding of Non-Abelian Anyons at ν=5/2ν= 5/2ν=5/2 State
Unlike elementary particles, which obey either bosonic or fermionic exchange statistics, certain quasiparticles, known as anyons, are predicted to exhibit Abelian or non-Abelian braiding statistics. While braiding Abelian anyons modifies the wavefunction by a 'statistical phase', braiding non-Abelian anyons implements a unitary transformation of the state within a degenerate subspace of states. Experimental evidence of non-Abelian braiding has thus far remained elusive. Here, we report a 'time-domain braiding' signature of non-Abelian anyons in the ν=5/2ν= 5/2ν=5/2 fractional quantum Hall state, by extending our previously demonstrated approach with Abelian anyons at ν=1/3ν= 1/3ν=1/3. Our approach is based on measurements of the current fluctuations arising from weak partitioning of a highly dilute one-dimensional edge mode. We independently probe the partition noise of the downstream charged mode and also that of the upstream neutral mode. These independent measurements agree with our theoretical predictions for 'time-domain braiding' of the downstream Abelian and the upstream non-Abelian anyons, respectively, in the 'particle-hole Pfaffian' topological order. Together, these results provide evidence for the presence of non-Abelian anyons.
On the edge of certain fractional quantum Hall states, e.g., at 2/3 and 5/2 filling, a local fractional excitation, occurring by anyon tunneling at a quantum point contact, is further fractionalized into counterpropagating charge and neutral (Abelian or non-Abelian) anyonic excitations. We propose a scheme to detect the braiding statistics of the charge and neutral anyons separately. It is the injection of a dilute beam of a target (charge or neutral) anyon to a Fabry-Perot interferometer. The monodromy of the target anyon is obtained by comparing the amplitude and phase of the interference current with a reference signal of the same setup but without the injection. Our proposal relies on braiding between anyons on the edge, and applies even in the presence of bulk-edge couplings.
The even-denominator fractional quantum Hall (FQH) states, understood as topological superconductors of composite fermions, are predicted to support elementary quasiparticles (QPs) or quasiholes (QHs) obeying non-Abelian braid statistics. Using the microscopic framework of parton theory, we investigate many experimentally observed paired composite-fermion states and find that their elementary QPs and QHs in general bind to form Abelian molecules, thus obscuring non-Abelian braid statistics. An exception is the ν=1/2ν=1/2ν=1/2 state in wide quantum wells, where our calculations show free QPs or QHs; we thus identify this state as an especially promising candidate for realizing and studying non-Abelian braid statistics. We also indicate how the study of such bound states can help reveal the topological structure of the state.
FINDING: Anyon braiding provides non-abelian statistics for topologically protected quantum computation, but the search results are mostly pedagogical videos and one unrelated ATLAS squark paper — no primary experimental data or new mathematical result is presented. | MATH: Anyons obey fractional statistics: braiding operator B B B acts on degenerate ground-state manifold with unitary representation ρ(B) \rho(B) ρ(B), where ρ(B1)ρ(B2)≠ρ(B2)ρ(B1) \rho(B_1)\rho(B_2) \neq \rho(B_2)\rho(B_1) ρ(B1​)ρ(B2​)=ρ(B2​)ρ(B1​) for non-abelian anyons. Exchange phase θ \theta θ generalizes Fermi (θ=π \theta=\pi θ=π) and Bose (θ=0 \theta=0 θ=0) to θ=2πs \theta = 2\pi s θ=2πs with s s s fractional (e.g., s=1/3,1/5 s=1/3, 1/5 s=1/3,1/5). Fibonacci anyon fusion rules: τ×τ=1+τ \tau \times \tau = 1 + \tau τ×τ=1+τ, with quantum dimension dτ=φ=(1+5)/2≈1.618 d_\tau = \varphi = (1+\sqrt{5})/2 \approx 1.618 dτ​=φ=(1+5​)/2≈1.618. | CONNECTION: **Strong.** The Fibonacci anyon quantum dimension is exactly the golden ratio φ=1.618 \varphi = 1.618 φ=1.618. Braid group Bn B_n Bn​ representations relate to Temperley–Lieb algebra with l Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Topological quantum computation has emerged as one of the most exciting approaches to constructing a fault-tolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are particles known as non-Abelian anyons, meaning that they obey non-Abelian braiding statistics. Quantum information is stored in states with multiple quasiparticles, which have a topological degeneracy. The unitary gate operations that are necessary for quantum computation are carried out by braiding quasiparticles and then measuring the multiquasiparticle states. The fault tolerance of a topological quantum computer arises from the nonlocal encoding of the quasiparticle states, which makes them immune to errors caused by local perturbations. To date, the only such topological states thought to have been found in nature are fractional quantum Hall states, most prominently the $\ensuremath{\nu}=5∕2$ state, although several other prospective candidates have been proposed in systems as disparate as ultracold atoms in optical lattices and thin-film superconductors. In this review article, current research in this field is described, focusing on the general theoretical concepts of non-Abelian statistics as it relates to topological quantum computation, on understanding non-Abelian quantum Hall states, on proposed experiments to detect non-Abelian anyons, and on proposed architectures for a topological quantum computer. Both the mathematical underpinnings of topological quantum computation and the physics of the subject are addressed, using the $\ensuremath{\nu}=5∕2$ fractional quantum Hall state as the archetype of a non-Abelian topological state enabling fault-tolerant quantum computation.
Abstract A collider where particles are injected onto a beam splitter from opposite sides has been used for identifying quantum statistics of identical particles. The collision leads to bunching of the particles for bosons and antibunching for fermions. In recent experiments, a collider was applied to a fractional quantum Hall regime hosting Abelian anyons. The observed negative cross-correlation of electrical currents cannot be understood with fermionic antibunching. Here we predict, based on a conformal field theory and a non-perturbative treatment of non-equilibrium anyon injection, that the collider provides a tool for observation of the braiding statistics of various Abelian and non-Abelian anyons. Its dominant process is not direct collision between injected anyons, contrary to common expectation, but braiding between injected anyons and an anyon excited at the collider. The dependence of the resulting negative cross-correlation on the injection currents distinguishes non-Abelian SU(2)k anyons, Ising anyons, and Abelian Laughlin anyons.
Abstract Quantum many-body systems with a non-Abelian topological order can host anyonic quasiparticles. It has been proposed that anyons could be used to encode and manipulate information in a topologically protected manner that is immune to local noise, with quantum gates performed by braiding and fusing anyons. Unfortunately, realizing non-Abelian topologically ordered states is challenging, and it was not until recently that the signatures of non-Abelian statistics were observed through digital quantum simulation approaches. However, not all forms of topological order can be used to realize universal quantum computation. Here we use a superconducting quantum processor to simulate non-Abelian topologically ordered states of the Fibonacci string-net model and demonstrate braidings of Fibonacci anyons featuring universal computational power. We demonstrate the non-trivial topological nature of the quantum states by measuring the topological entanglement entropy. In addition, we create two pairs of Fibonacci anyons and demonstrate their fusion rule and non-Abelian braiding statistics by applying unitary gates on the underlying physical qubits. Our results establish a digital approach to explore non-Abelian topological states and their associated braiding statistics with current noisy intermediate-scale quantum processors.