Coupled atom-cavity arrays, such as those described by the Jaynes-Cummings-Hubbard model, have the potential to emulate a wide range of condensed-matter phenomena. In particular, the strongly correlated states of the fractional quantum Hall effect can be realized. At some filling fractions, the fraction quantum Hall effect has been shown to possess ground states with non-Abelian excitations. The most well studied of these states is the Pfaffian state of Moore and Read G. Moore and N. Read, Nucl. Phys. B 360, 362 (1991), which is the ground state of a Hall liquid with a three-body interaction. We show how an effective three-body interaction can be generated within the cavity QED framework, and that a Pfaffian-like ground state of these systems exists.Coupled atom-cavity arrays, such as those described by the Jaynes-Cummings-Hubbard model, have the potential to emulate a wide range of condensed-matter phenomena. In particular, the strongly correlated states of the fractional quantum Hall effect can be realized. At some filling fractions, the fraction quantum Hall effect has been shown to possess ground states with non-Abelian excitations. The most well studied of these states is the Pfaffian state of Moore and Read G. Moore and N. Read, Nucl. Phys. B 360, 362 (1991), which is the ground state of a Hall liquid with a three-body interaction. We show how an effective three-body interaction can be generated within the cavity QED framework, and that a Pfaffian-like ground state of these systems exists.

arXiv:1603.02348Physical Review AMay 19, 20165 citations

A fractional quantum Hall factory on quantum processors: constant-depth preparation of clustered non-Abelian states

Cheng Xu, Ching Hua Lee, Hong-Hao Tu +1 more

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

Fractional Quantum Hall Physics in Jaynes-Cummings-Hubbard Lattices

Andrew L. C. Hayward, A. Martin, Andrew D. Greentree

Jaynes-Cummings-Hubbard arrays provide unique opportunities for quantum emulation as they exhibit convenient state preparation and measurement, as well as in situ tuning of parameters. We show how to realize strongly correlated states of light in Jaynes-Cummings-Hubbard arrays under the introduction of an effective magnetic field. The effective field is realized by dynamic tuning of the cavity resonances. We demonstrate the existence of Laughlin-like fractional quantum Hall states by computing topological invariants, phase transitions between topologically distinct states, and Laughlin wave function overlap.Jaynes-Cummings-Hubbard arrays provide unique opportunities for quantum emulation as they exhibit convenient state preparation and measurement, as well as in situ tuning of parameters. We show how to realize strongly correlated states of light in Jaynes-Cummings-Hubbard arrays under the introduction of an effective magnetic field. The effective field is realized by dynamic tuning of the cavity resonances. We demonstrate the existence of Laughlin-like fractional quantum Hall states by computing topological invariants, phase transitions between topologically distinct states, and Laughlin wave function overlap.

arXiv:1202.5067Physical Review LettersJun 1, 201284 citations

Local models of fractional quantum Hall states in lattices and physical implementation

Anne E. B. Nielsen, Germán Sierra, J. I. Cirac

arXiv:1304.0717Nature CommunicationsNov 28, 2013100 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.