Universality of Z_{3} parafermions via edge-mode interaction and quantum simulation of topological space evolution with Rydberg atoms
Parafermions are Z_{n} generalizations of Majorana quasiparticles, with fractional non-Abelian statistics. They can be used to encode topological qudits and perform Clifford operations by their braiding. Here we investigate the generation of quantum gates by allowing Z_{3} parafermions to interact i...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2023-05-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.5.023076 |
| _version_ | 1827285263790899200 |
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| author | Asmae Benhemou Toonyawat Angkhanawin Charles S. Adams Dan E. Browne Jiannis K. Pachos |
| author_facet | Asmae Benhemou Toonyawat Angkhanawin Charles S. Adams Dan E. Browne Jiannis K. Pachos |
| author_sort | Asmae Benhemou |
| collection | DOAJ |
| description | Parafermions are Z_{n} generalizations of Majorana quasiparticles, with fractional non-Abelian statistics. They can be used to encode topological qudits and perform Clifford operations by their braiding. Here we investigate the generation of quantum gates by allowing Z_{3} parafermions to interact in order to achieve universality. In particular, we study the form of the nontopological gate that arises through direct short-range interaction of the parafermion edge modes in a Z_{3} parafermion chain. We show that such an interaction gives rise to a dynamical phase gate on the encoded ground space, generating a non-Clifford gate which can be tuned to belong to even levels of the Clifford hierarchy. We illustrate how to access highly noncontextual states using this dynamical gate. Finally, we propose an experiment that simulates the braiding and dynamical evolutions of the Z_{3} topological states with Rydberg atom technology. |
| first_indexed | 2024-04-24T10:12:04Z |
| format | Article |
| id | doaj.art-b024ebe39f764d2e835dfc5ece2127ba |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:12:04Z |
| publishDate | 2023-05-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-b024ebe39f764d2e835dfc5ece2127ba2024-04-12T17:30:36ZengAmerican Physical SocietyPhysical Review Research2643-15642023-05-015202307610.1103/PhysRevResearch.5.023076Universality of Z_{3} parafermions via edge-mode interaction and quantum simulation of topological space evolution with Rydberg atomsAsmae BenhemouToonyawat AngkhanawinCharles S. AdamsDan E. BrowneJiannis K. PachosParafermions are Z_{n} generalizations of Majorana quasiparticles, with fractional non-Abelian statistics. They can be used to encode topological qudits and perform Clifford operations by their braiding. Here we investigate the generation of quantum gates by allowing Z_{3} parafermions to interact in order to achieve universality. In particular, we study the form of the nontopological gate that arises through direct short-range interaction of the parafermion edge modes in a Z_{3} parafermion chain. We show that such an interaction gives rise to a dynamical phase gate on the encoded ground space, generating a non-Clifford gate which can be tuned to belong to even levels of the Clifford hierarchy. We illustrate how to access highly noncontextual states using this dynamical gate. Finally, we propose an experiment that simulates the braiding and dynamical evolutions of the Z_{3} topological states with Rydberg atom technology.http://doi.org/10.1103/PhysRevResearch.5.023076 |
| spellingShingle | Asmae Benhemou Toonyawat Angkhanawin Charles S. Adams Dan E. Browne Jiannis K. Pachos Universality of Z_{3} parafermions via edge-mode interaction and quantum simulation of topological space evolution with Rydberg atoms Physical Review Research |
| title | Universality of Z_{3} parafermions via edge-mode interaction and quantum simulation of topological space evolution with Rydberg atoms |
| title_full | Universality of Z_{3} parafermions via edge-mode interaction and quantum simulation of topological space evolution with Rydberg atoms |
| title_fullStr | Universality of Z_{3} parafermions via edge-mode interaction and quantum simulation of topological space evolution with Rydberg atoms |
| title_full_unstemmed | Universality of Z_{3} parafermions via edge-mode interaction and quantum simulation of topological space evolution with Rydberg atoms |
| title_short | Universality of Z_{3} parafermions via edge-mode interaction and quantum simulation of topological space evolution with Rydberg atoms |
| title_sort | universality of z 3 parafermions via edge mode interaction and quantum simulation of topological space evolution with rydberg atoms |
| url | http://doi.org/10.1103/PhysRevResearch.5.023076 |
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