Error Correction for Non-Abelian Topological Quantum Computation
The possibility of quantum computation using non-Abelian anyons has been considered for over a decade. However, the question of how to obtain and process information about what errors have occurred in order to negate their effects has not yet been considered. This is in stark contrast with quantum c...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2014-03-01
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| Series: | Physical Review X |
| Online Access: | http://doi.org/10.1103/PhysRevX.4.011051 |
| _version_ | 1818989887080103936 |
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| author | James R. Wootton Jan Burri Sofyan Iblisdir Daniel Loss |
| author_facet | James R. Wootton Jan Burri Sofyan Iblisdir Daniel Loss |
| author_sort | James R. Wootton |
| collection | DOAJ |
| description | The possibility of quantum computation using non-Abelian anyons has been considered for over a decade. However, the question of how to obtain and process information about what errors have occurred in order to negate their effects has not yet been considered. This is in stark contrast with quantum computation proposals for Abelian anyons, for which decoding algorithms have been tailor-made for many topological error-correcting codes and error models. Here, we address this issue by considering the properties of non-Abelian error correction, in general. We also choose a specific anyon model and error model to probe the problem in more detail. The anyon model is the charge submodel of D(S_{3}). This shares many properties with important models such as the Fibonacci anyons, making our method more generally applicable. The error model is a straightforward generalization of those used in the case of Abelian anyons for initial benchmarking of error correction methods. It is found that error correction is possible under a threshold value of 7% for the total probability of an error on each physical spin. This is remarkably comparable with the thresholds for Abelian models. |
| first_indexed | 2024-12-20T19:45:37Z |
| format | Article |
| id | doaj.art-17688524c11342b8b92e3cc80d299cf9 |
| institution | Directory Open Access Journal |
| issn | 2160-3308 |
| language | English |
| last_indexed | 2024-12-20T19:45:37Z |
| publishDate | 2014-03-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review X |
| spelling | doaj.art-17688524c11342b8b92e3cc80d299cf92022-12-21T19:28:26ZengAmerican Physical SocietyPhysical Review X2160-33082014-03-014101105110.1103/PhysRevX.4.011051Error Correction for Non-Abelian Topological Quantum ComputationJames R. WoottonJan BurriSofyan IblisdirDaniel LossThe possibility of quantum computation using non-Abelian anyons has been considered for over a decade. However, the question of how to obtain and process information about what errors have occurred in order to negate their effects has not yet been considered. This is in stark contrast with quantum computation proposals for Abelian anyons, for which decoding algorithms have been tailor-made for many topological error-correcting codes and error models. Here, we address this issue by considering the properties of non-Abelian error correction, in general. We also choose a specific anyon model and error model to probe the problem in more detail. The anyon model is the charge submodel of D(S_{3}). This shares many properties with important models such as the Fibonacci anyons, making our method more generally applicable. The error model is a straightforward generalization of those used in the case of Abelian anyons for initial benchmarking of error correction methods. It is found that error correction is possible under a threshold value of 7% for the total probability of an error on each physical spin. This is remarkably comparable with the thresholds for Abelian models.http://doi.org/10.1103/PhysRevX.4.011051 |
| spellingShingle | James R. Wootton Jan Burri Sofyan Iblisdir Daniel Loss Error Correction for Non-Abelian Topological Quantum Computation Physical Review X |
| title | Error Correction for Non-Abelian Topological Quantum Computation |
| title_full | Error Correction for Non-Abelian Topological Quantum Computation |
| title_fullStr | Error Correction for Non-Abelian Topological Quantum Computation |
| title_full_unstemmed | Error Correction for Non-Abelian Topological Quantum Computation |
| title_short | Error Correction for Non-Abelian Topological Quantum Computation |
| title_sort | error correction for non abelian topological quantum computation |
| url | http://doi.org/10.1103/PhysRevX.4.011051 |
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