Genons, Double Covers and Fault-tolerant Clifford Gates
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866916287237586944 |
|---|---|
| author | Burton, Simon Durso-Sabina, Elijah Brown, Natalie C. |
| author_facet | Burton, Simon Durso-Sabina, Elijah Brown, Natalie C. |
| contents | A great deal of work has been done developing quantum codes with varying overhead and connectivity constraints. However, given the such an abundance of codes, there is a surprising shortage of fault-tolerant logical gates supported therein. We define a construction, such that given an input $[[n,k,d]]$ code, yields a $[[2n,2k,\ge d]]$ symplectic double code with naturally occurring fault-tolerant logical Clifford gates. As applied to 2-dimensional $D(\mathbb{Z}_2)$-topological codes with genons (twists) and domain walls, we find the symplectic double is genon free, and of possibly higher genus. Braiding of genons on the original code becomes Dehn twists on the symplectic double. Such topological operations are particularly suited for architectures with all-to-all connectivity, and we demonstrate this experimentally on Quantinuum's H1-1 trapped-ion quantum computer. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_09951 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Genons, Double Covers and Fault-tolerant Clifford Gates Burton, Simon Durso-Sabina, Elijah Brown, Natalie C. Quantum Physics A great deal of work has been done developing quantum codes with varying overhead and connectivity constraints. However, given the such an abundance of codes, there is a surprising shortage of fault-tolerant logical gates supported therein. We define a construction, such that given an input $[[n,k,d]]$ code, yields a $[[2n,2k,\ge d]]$ symplectic double code with naturally occurring fault-tolerant logical Clifford gates. As applied to 2-dimensional $D(\mathbb{Z}_2)$-topological codes with genons (twists) and domain walls, we find the symplectic double is genon free, and of possibly higher genus. Braiding of genons on the original code becomes Dehn twists on the symplectic double. Such topological operations are particularly suited for architectures with all-to-all connectivity, and we demonstrate this experimentally on Quantinuum's H1-1 trapped-ion quantum computer. |
| title | Genons, Double Covers and Fault-tolerant Clifford Gates |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2406.09951 |