Abelian Group Quantum Error Correction in Kitaev's Model
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914751196430336 |
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| author | Cui, Shawn X. Galindo, César Romero, Diego |
| author_facet | Cui, Shawn X. Galindo, César Romero, Diego |
| contents | In this paper, we present a detailed mathematical description of the error correction process for Kitaev's model for finite Abelian groups. The number of errors Kitaev's model can correct depends on the lattice and its topology. Although there is a theoretical maximum number of errors that can be corrected, we prove that correcting this number of errors, in general, is an NP-complete problem. Consequently, we introduce a polynomial-time correction algorithm that corrects a number of errors below the theoretical maximum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_08552 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Abelian Group Quantum Error Correction in Kitaev's Model Cui, Shawn X. Galindo, César Romero, Diego Quantum Algebra Mathematical Physics In this paper, we present a detailed mathematical description of the error correction process for Kitaev's model for finite Abelian groups. The number of errors Kitaev's model can correct depends on the lattice and its topology. Although there is a theoretical maximum number of errors that can be corrected, we prove that correcting this number of errors, in general, is an NP-complete problem. Consequently, we introduce a polynomial-time correction algorithm that corrects a number of errors below the theoretical maximum. |
| title | Abelian Group Quantum Error Correction in Kitaev's Model |
| topic | Quantum Algebra Mathematical Physics |
| url | https://arxiv.org/abs/2404.08552 |