Measuring Chern–Simons level k by braiding $$SU(2)_k$$ S U ( 2 ) k anyons
Abstract Chern–Simons theory in application to the quantum computing is actively developing at the present. However, most discussed are the questions of using materials with known parameters and building corresponding quantum gates and algorithms. In this paper we discuss opposite problem of finding...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-01-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | https://doi.org/10.1140/epjc/s10052-024-13734-1 |
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| author | Artem Belov Andrey Morozov |
| author_facet | Artem Belov Andrey Morozov |
| author_sort | Artem Belov |
| collection | DOAJ |
| description | Abstract Chern–Simons theory in application to the quantum computing is actively developing at the present. However, most discussed are the questions of using materials with known parameters and building corresponding quantum gates and algorithms. In this paper we discuss opposite problem of finding Chern–Simons level k in the unknown material. For this purpose, we use the previously derived braiding rules for Chern–Simons $$SU(2)_k$$ S U ( 2 ) k anyons. Using certain operations (turnarounds) on three anyons, one can measure probabilities of annihilation of pairs of anyons, which depend on the parameter of the theory. Therefore, Chern–Simons level k can be found from such an experiment. It is implied that anyons additionally possess certain properties which are required for topological quantum computations. |
| format | Article |
| id | doaj-art-53647a77ccf7461fabbd40169afc47b9 |
| institution | Kabale University |
| issn | 1434-6052 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj-art-53647a77ccf7461fabbd40169afc47b92025-02-02T12:38:16ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60522025-01-0185111110.1140/epjc/s10052-024-13734-1Measuring Chern–Simons level k by braiding $$SU(2)_k$$ S U ( 2 ) k anyonsArtem Belov0Andrey Morozov1NRC “Kurchatov Institute”NRC “Kurchatov Institute”Abstract Chern–Simons theory in application to the quantum computing is actively developing at the present. However, most discussed are the questions of using materials with known parameters and building corresponding quantum gates and algorithms. In this paper we discuss opposite problem of finding Chern–Simons level k in the unknown material. For this purpose, we use the previously derived braiding rules for Chern–Simons $$SU(2)_k$$ S U ( 2 ) k anyons. Using certain operations (turnarounds) on three anyons, one can measure probabilities of annihilation of pairs of anyons, which depend on the parameter of the theory. Therefore, Chern–Simons level k can be found from such an experiment. It is implied that anyons additionally possess certain properties which are required for topological quantum computations.https://doi.org/10.1140/epjc/s10052-024-13734-1 |
| spellingShingle | Artem Belov Andrey Morozov Measuring Chern–Simons level k by braiding $$SU(2)_k$$ S U ( 2 ) k anyons European Physical Journal C: Particles and Fields |
| title | Measuring Chern–Simons level k by braiding $$SU(2)_k$$ S U ( 2 ) k anyons |
| title_full | Measuring Chern–Simons level k by braiding $$SU(2)_k$$ S U ( 2 ) k anyons |
| title_fullStr | Measuring Chern–Simons level k by braiding $$SU(2)_k$$ S U ( 2 ) k anyons |
| title_full_unstemmed | Measuring Chern–Simons level k by braiding $$SU(2)_k$$ S U ( 2 ) k anyons |
| title_short | Measuring Chern–Simons level k by braiding $$SU(2)_k$$ S U ( 2 ) k anyons |
| title_sort | measuring chern simons level k by braiding su 2 k s u 2 k anyons |
| url | https://doi.org/10.1140/epjc/s10052-024-13734-1 |
| work_keys_str_mv | AT artembelov measuringchernsimonslevelkbybraidingsu2ksu2kanyons AT andreymorozov measuringchernsimonslevelkbybraidingsu2ksu2kanyons |