Embedding the $n$-Qubit Projective Clifford Group into a Symmetric Group
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866916456656011264 |
|---|---|
| author | Lee, Chin-Yen |
| author_facet | Lee, Chin-Yen |
| contents | In this paper, we construct a symmetric group ${\rm Sym}_{2(4^n-1)}$, which contains a subgroup isomorphic to the $n$-qubit projective Clifford group $\mathcal{C}_n$. To establish this result, we investigate the centralizers of the $z$ gate and the phase gate within the $n$-qubit projective Clifford group, utilizing the normal form of the Clifford operators. As a byproduct, we also provide a presentation of the inertia subgroup of $\mathcal{C}_n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_10590 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Embedding the $n$-Qubit Projective Clifford Group into a Symmetric Group Lee, Chin-Yen Group Theory In this paper, we construct a symmetric group ${\rm Sym}_{2(4^n-1)}$, which contains a subgroup isomorphic to the $n$-qubit projective Clifford group $\mathcal{C}_n$. To establish this result, we investigate the centralizers of the $z$ gate and the phase gate within the $n$-qubit projective Clifford group, utilizing the normal form of the Clifford operators. As a byproduct, we also provide a presentation of the inertia subgroup of $\mathcal{C}_n$. |
| title | Embedding the $n$-Qubit Projective Clifford Group into a Symmetric Group |
| topic | Group Theory |
| url | https://arxiv.org/abs/2410.10590 |