Generating non-Clifford gate operations through exact mapping between Majorana fermions and $\mathbb{Z}_4$ parafermions
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909769504129024 |
|---|---|
| author | Safwan, Ali Hamed Bomantara, Raditya Weda |
| author_facet | Safwan, Ali Hamed Bomantara, Raditya Weda |
| contents | Majorana fermions and their generalizations to $\mathbb{Z}_n$ parafermions are considered promising building blocks of fault-tolerant quantum computers for their ability to encode quantum information nonlocally. In such topological quantum computers, highly robust quantum gates are obtained by braiding pairs of these quasi-particles. However, it is well-known that braiding Majorana fermions or parafermions only leads to a Clifford gate, hindering quantum universality. This paper establishes an exact mapping between Majorana fermions to $\mathbb{Z}_4$ parafermions in systems under total parity non-conserving and total parity conserving setting. It is revealed that braiding of Majorana fermions may lead to non-Clifford quantum gates in the 4-dimensional qudit representation spanned by $\mathbb{Z}_4$ parafermions, whilst braiding of $\mathbb{Z}_4$ parafermions may similarly yield non-Clifford quantum gates in the qubit representation spanned by Majorana fermions. This finding suggests that topologically protected universal quantum computing may be possible with Majorana fermions ($\mathbb{Z}_4$ parafermions) by supplementing the usual braiding operations with the braiding of $\mathbb{Z}_4$ parafermions (Majorana fermions) that could be formed out of Majorana fermions ($\mathbb{Z}_4$ parafermions) via the mapping prescribed here. Finally, the paper discusses how braiding of Majorana fermions or $\mathbb{Z}_4$ parafermions could be obtained via a series of parity measurements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_18736 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generating non-Clifford gate operations through exact mapping between Majorana fermions and $\mathbb{Z}_4$ parafermions Safwan, Ali Hamed Bomantara, Raditya Weda Quantum Physics Mesoscale and Nanoscale Physics Majorana fermions and their generalizations to $\mathbb{Z}_n$ parafermions are considered promising building blocks of fault-tolerant quantum computers for their ability to encode quantum information nonlocally. In such topological quantum computers, highly robust quantum gates are obtained by braiding pairs of these quasi-particles. However, it is well-known that braiding Majorana fermions or parafermions only leads to a Clifford gate, hindering quantum universality. This paper establishes an exact mapping between Majorana fermions to $\mathbb{Z}_4$ parafermions in systems under total parity non-conserving and total parity conserving setting. It is revealed that braiding of Majorana fermions may lead to non-Clifford quantum gates in the 4-dimensional qudit representation spanned by $\mathbb{Z}_4$ parafermions, whilst braiding of $\mathbb{Z}_4$ parafermions may similarly yield non-Clifford quantum gates in the qubit representation spanned by Majorana fermions. This finding suggests that topologically protected universal quantum computing may be possible with Majorana fermions ($\mathbb{Z}_4$ parafermions) by supplementing the usual braiding operations with the braiding of $\mathbb{Z}_4$ parafermions (Majorana fermions) that could be formed out of Majorana fermions ($\mathbb{Z}_4$ parafermions) via the mapping prescribed here. Finally, the paper discusses how braiding of Majorana fermions or $\mathbb{Z}_4$ parafermions could be obtained via a series of parity measurements. |
| title | Generating non-Clifford gate operations through exact mapping between Majorana fermions and $\mathbb{Z}_4$ parafermions |
| topic | Quantum Physics Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2411.18736 |