Deformed Fredkin model for the ν=5/2 Moore-Read state on thin cylinders
We propose a frustration-free model for the Moore-Read quantum Hall state on sufficiently thin cylinders with circumferences ≲7 magnetic lengths. While the Moore-Read Hamiltonian involves complicated long-range interactions between triplets of electrons in a Landau level, our effective model is a si...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2024-01-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.6.013105 |
| _version_ | 1797210312400699392 |
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| author | Cristian Voinea Songyang Pu Ammar Kirmani Pouyan Ghaemi Armin Rahmani Zlatko Papić |
| author_facet | Cristian Voinea Songyang Pu Ammar Kirmani Pouyan Ghaemi Armin Rahmani Zlatko Papić |
| author_sort | Cristian Voinea |
| collection | DOAJ |
| description | We propose a frustration-free model for the Moore-Read quantum Hall state on sufficiently thin cylinders with circumferences ≲7 magnetic lengths. While the Moore-Read Hamiltonian involves complicated long-range interactions between triplets of electrons in a Landau level, our effective model is a simpler one-dimensional chain of qubits with deformed Fredkin gates. We show that the ground state of the Fredkin model has high overlap with the Moore-Read wave function and accurately reproduces the latter's entanglement properties. Moreover, we demonstrate that the model captures the dynamical response of the Moore-Read state to a geometric quench, induced by suddenly changing the anisotropy of the system. We elucidate the underlying mechanism of the quench dynamics and show that it coincides with the linearized bimetric field theory. The minimal model introduced here can be directly implemented as a first step towards quantum simulation of the Moore-Read state, as we demonstrate by deriving an efficient circuit approximation to the ground state and implementing it on an IBM quantum processor. |
| first_indexed | 2024-04-24T10:08:36Z |
| format | Article |
| id | doaj.art-7000cbbbc9c540b89cb14532cb462f84 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:08:36Z |
| publishDate | 2024-01-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-7000cbbbc9c540b89cb14532cb462f842024-04-12T17:38:32ZengAmerican Physical SocietyPhysical Review Research2643-15642024-01-016101310510.1103/PhysRevResearch.6.013105Deformed Fredkin model for the ν=5/2 Moore-Read state on thin cylindersCristian VoineaSongyang PuAmmar KirmaniPouyan GhaemiArmin RahmaniZlatko PapićWe propose a frustration-free model for the Moore-Read quantum Hall state on sufficiently thin cylinders with circumferences ≲7 magnetic lengths. While the Moore-Read Hamiltonian involves complicated long-range interactions between triplets of electrons in a Landau level, our effective model is a simpler one-dimensional chain of qubits with deformed Fredkin gates. We show that the ground state of the Fredkin model has high overlap with the Moore-Read wave function and accurately reproduces the latter's entanglement properties. Moreover, we demonstrate that the model captures the dynamical response of the Moore-Read state to a geometric quench, induced by suddenly changing the anisotropy of the system. We elucidate the underlying mechanism of the quench dynamics and show that it coincides with the linearized bimetric field theory. The minimal model introduced here can be directly implemented as a first step towards quantum simulation of the Moore-Read state, as we demonstrate by deriving an efficient circuit approximation to the ground state and implementing it on an IBM quantum processor.http://doi.org/10.1103/PhysRevResearch.6.013105 |
| spellingShingle | Cristian Voinea Songyang Pu Ammar Kirmani Pouyan Ghaemi Armin Rahmani Zlatko Papić Deformed Fredkin model for the ν=5/2 Moore-Read state on thin cylinders Physical Review Research |
| title | Deformed Fredkin model for the ν=5/2 Moore-Read state on thin cylinders |
| title_full | Deformed Fredkin model for the ν=5/2 Moore-Read state on thin cylinders |
| title_fullStr | Deformed Fredkin model for the ν=5/2 Moore-Read state on thin cylinders |
| title_full_unstemmed | Deformed Fredkin model for the ν=5/2 Moore-Read state on thin cylinders |
| title_short | Deformed Fredkin model for the ν=5/2 Moore-Read state on thin cylinders |
| title_sort | deformed fredkin model for the ν 5 2 moore read state on thin cylinders |
| url | http://doi.org/10.1103/PhysRevResearch.6.013105 |
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