Topological quantum computation on supersymmetric spin chains
Abstract Quantum gates built out of braid group elements form the building blocks of topological quantum computation. They have been extensively studied in SU(2) k quantum group theories, a rich source of examples of non-Abelian anyons such as the Ising (k = 2), Fibonacci (k = 3) and Jones-Kauffman...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-02-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP02(2023)251 |
| _version_ | 1827900096933527552 |
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| author | Indrajit Jana Filippo Montorsi Pramod Padmanabhan Diego Trancanelli |
| author_facet | Indrajit Jana Filippo Montorsi Pramod Padmanabhan Diego Trancanelli |
| author_sort | Indrajit Jana |
| collection | DOAJ |
| description | Abstract Quantum gates built out of braid group elements form the building blocks of topological quantum computation. They have been extensively studied in SU(2) k quantum group theories, a rich source of examples of non-Abelian anyons such as the Ising (k = 2), Fibonacci (k = 3) and Jones-Kauffman (k = 4) anyons. We show that the fusion spaces of these anyonic systems can be precisely mapped to the product state zero modes of certain Nicolai-like supersymmetric spin chains. As a result, we can realize the braid group in terms of the product state zero modes of these supersymmetric systems. These operators kill all the other states in the Hilbert space, thus preventing the occurrence of errors while processing information, making them suitable for quantum computing. |
| first_indexed | 2024-03-12T23:26:24Z |
| format | Article |
| id | doaj.art-a57bdd3aafb94ba68bb5a72617f29ff8 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-12T23:26:24Z |
| publishDate | 2023-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-a57bdd3aafb94ba68bb5a72617f29ff82023-07-16T11:06:30ZengSpringerOpenJournal of High Energy Physics1029-84792023-02-012023214510.1007/JHEP02(2023)251Topological quantum computation on supersymmetric spin chainsIndrajit Jana0Filippo Montorsi1Pramod Padmanabhan2Diego Trancanelli3School of Basic Sciences, Indian Institute of TechnologyDipartimento di Scienze Fisiche, Informatiche e Matematiche, Università di Modena e Reggio EmiliaSchool of Basic Sciences, Indian Institute of TechnologyDipartimento di Scienze Fisiche, Informatiche e Matematiche, Università di Modena e Reggio EmiliaAbstract Quantum gates built out of braid group elements form the building blocks of topological quantum computation. They have been extensively studied in SU(2) k quantum group theories, a rich source of examples of non-Abelian anyons such as the Ising (k = 2), Fibonacci (k = 3) and Jones-Kauffman (k = 4) anyons. We show that the fusion spaces of these anyonic systems can be precisely mapped to the product state zero modes of certain Nicolai-like supersymmetric spin chains. As a result, we can realize the braid group in terms of the product state zero modes of these supersymmetric systems. These operators kill all the other states in the Hilbert space, thus preventing the occurrence of errors while processing information, making them suitable for quantum computing.https://doi.org/10.1007/JHEP02(2023)251AnyonsExtended SupersymmetryQuantum GroupsTopological States of Matter |
| spellingShingle | Indrajit Jana Filippo Montorsi Pramod Padmanabhan Diego Trancanelli Topological quantum computation on supersymmetric spin chains Journal of High Energy Physics Anyons Extended Supersymmetry Quantum Groups Topological States of Matter |
| title | Topological quantum computation on supersymmetric spin chains |
| title_full | Topological quantum computation on supersymmetric spin chains |
| title_fullStr | Topological quantum computation on supersymmetric spin chains |
| title_full_unstemmed | Topological quantum computation on supersymmetric spin chains |
| title_short | Topological quantum computation on supersymmetric spin chains |
| title_sort | topological quantum computation on supersymmetric spin chains |
| topic | Anyons Extended Supersymmetry Quantum Groups Topological States of Matter |
| url | https://doi.org/10.1007/JHEP02(2023)251 |
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