Non-Abelian anyons arise as exotic excitations in fractional quantum Hall (FQH) matter and have proved very elusive to realize in conventional platforms. In this work, we show that on a programmable quantum hardware platform, the more exotic FQH excitations are the less costly ones to prepare: clustered non-Abelian FQH states admit parallel quantum preparation circuits whose two-qubit depth is independent of system size, while constructing the more common Abelian Laughlin state requires a sequential circuit chain with linear depth. The centerpiece of this work is our new systematic framework for cataloging possible FQH states and preparing them on quantum circuits at unprecedented scale and variety. Our prepared parafermionic Read--Rezayi $\mathbb{Z}_3$ state holds depth 3 from 8 to 118 qubits, and full root sampling extends to a 154-qubit, 104-electron Read--Rezayi $\mathbb{Z}_4$ state. In all, our demonstrated 18-family catalog of prepared FQH states extends to all 156 qubits of an IBM Heron processor, limited only by existing hardware scale. Measurements on the prepared states recover the expected fractional quasihole charges, with the charge estimator exact in every symmetry-selected shot for the clustered states, and braiding data of the non-Abelian $e/4$ quasihole measured via interferometric extensions. Our work establishes a scalable route to studying FQH physics on quantum processors and opens new avenues for preparing and probing non-Abelian topological matter far beyond the reach of conventional platforms.Non-Abelian anyons arise as exotic excitations in fractional quantum Hall (FQH) matter and have proved very elusive to realize in conventional platforms. In this work, we show that on a programmable quantum hardware platform, the more exotic FQH excitations are the less costly ones to prepare: clustered non-Abelian FQH states admit parallel quantum preparation circuits whose two-qubit depth is independent of system size, while constructing the more common Abelian Laughlin state requires a sequential circuit chain with linear depth. The centerpiece of this work is our new systematic framework for cataloging possible FQH states and preparing them on quantum circuits at unprecedented scale and variety. Our prepared parafermionic Read--Rezayi $\mathbb{Z}_3$ state holds depth 3 from 8 to 118 qubits, and full root sampling extends to a 154-qubit, 104-electron Read--Rezayi $\mathbb{Z}_4$ state. In all, our demonstrated 18-family catalog of prepared FQH states extends to all 156 qubits of an IBM Heron processor, limited only by existing hardware scale. Measurements on the prepared states recover the expected fractional quasihole charges, with the charge estimator exact in every symmetry-selected shot for the clustered states, and braiding data of the non-Abelian $e/4$ quasihole measured via interferometric extensions. Our work establishes a scalable route to studying FQH physics on quantum processors and opens new avenues for preparing and probing non-Abelian topological matter far beyond the reach of conventional platforms.

cond-mat.str-elCross-listedarXiv:2608.05140Aug 6, 20260 citations

Probing non-Abelian statistics in ν=12/5 quantum Hall state

K. T. Law

The tunneling current and shot noise of the current between two fractional quantum hall (FQH) edges in the $\ensuremath{\nu}=12/5$ FQH state in an electronic Mach--Zehnder interferometer are studied. It is shown that the tunneling current and shot noise can be used to probe the existence of $k=3$ parafermion statistics in the $\ensuremath{\nu}=12/5$ FQH state. More specifically, the dependence of the current on the Aharonov--Bohm flux in the Read--Rezayi state is asymmetric under the change in the sign of the applied voltage. This property is absent in the Abelian--Laughlin states. Moreover, the Fano factor can exceed 12.7 electron charges in the $\ensuremath{\nu}=12/5$ FQH state. This number well exceeds the maximum possible Fano factor in all Laughlin states and the $\ensuremath{\nu}=5/2$ Moore--Read state, which was previously shown to be $e$ and $3.2e$ , respectively.The tunneling current and shot noise of the current between two fractional quantum hall (FQH) edges in the $\ensuremath{\nu}=12/5$ FQH state in an electronic Mach--Zehnder interferometer are studied. It is shown that the tunneling current and shot noise can be used to probe the existence of $k=3$ parafermion statistics in the $\ensuremath{\nu}=12/5$ FQH state. More specifically, the dependence of the current on the Aharonov--Bohm flux in the Read--Rezayi state is asymmetric under the change in the sign of the applied voltage. This property is absent in the Abelian--Laughlin states. Moreover, the Fano factor can exceed 12.7 electron charges in the $\ensuremath{\nu}=12/5$ FQH state. This number well exceeds the maximum possible Fano factor in all Laughlin states and the $\ensuremath{\nu}=5/2$ Moore--Read state, which was previously shown to be $e$ and $3.2e$, respectively.

arXiv:0707.3995Physical Review BMay 12, 200825 citations

Study of partially polarized fractional quantum Hall states

Moumita Indra, Debashis Das, Dwipesh Majumder

arXiv:1811.10314Physics Letters AAug 10, 20185 citations

\mathbb{Z}_3

state holds depth 3 from 8 to 118 qubits, and full root sampling extends to a 154-qubit, 104-electron Read--Rezayi

\mathbb{Z}_4

state. In all, our demonstrated 18-family catalog of prepared FQH states extends to all 156 qubits of an IBM Heron processor, limited only by existing hardware scale. Measurements on the prepared states recover the expected fractional quasihole charges, with the charge estimator exact in every symmetry-selected shot for the clustered states, and braiding data of the non-Abelian

e/4

quasihole measured via interferometric extensions. Our work establishes a scalable route to studying FQH physics on quantum processors and opens new avenues for preparing and probing non-Abelian topological matter far beyond the reach of conventional platforms.

k=3

parafermion statistics in the $\ensuremath{\nu}=12/5$ FQH state. More specifically, the dependence of the current on the Aharonov--Bohm flux in the Read--Rezayi state is asymmetric under the change in the sign of the applied voltage. This property is absent in the Abelian--Laughlin states. Moreover, the Fano factor can exceed 12.7 electron charges in the $\ensuremath{\nu}=12/5$ FQH state. This number well exceeds the maximum possible Fano factor in all Laughlin states and the $\ensuremath{\nu}=5/2$ Moore--Read state, which was previously shown to be

e

and

3.2e

, respectively.