A family of permutationally invariant quantum codes
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917653309816832 |
|---|---|
| author | Aydin, Arda Alekseyev, Max A. Barg, Alexander |
| author_facet | Aydin, Arda Alekseyev, Max A. Barg, Alexander |
| contents | We construct a new family of permutationally invariant codes that correct $t$ Pauli errors for any $t\ge 1$. We also show that codes in the new family correct quantum deletion errors as well as spontaneous decay errors. Our construction contains some of the previously known permutationally invariant quantum codes as particular cases, which also admit transversal gates. In many cases, the codes in the new family are shorter than the best previously known explicit permutationally invariant codes for Pauli errors and deletions. Furthermore, our new code family includes a new $((4,2,2))$ optimal single-deletion-correcting code. As a separate result, we generalize the conditions for permutationally invariant codes to correct $t$ Pauli errors from the previously known results for $t=1$ to any number of errors. For small $t$, these conditions can be used to construct new examples of codes by computer. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_05358 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A family of permutationally invariant quantum codes Aydin, Arda Alekseyev, Max A. Barg, Alexander Quantum Physics Information Theory We construct a new family of permutationally invariant codes that correct $t$ Pauli errors for any $t\ge 1$. We also show that codes in the new family correct quantum deletion errors as well as spontaneous decay errors. Our construction contains some of the previously known permutationally invariant quantum codes as particular cases, which also admit transversal gates. In many cases, the codes in the new family are shorter than the best previously known explicit permutationally invariant codes for Pauli errors and deletions. Furthermore, our new code family includes a new $((4,2,2))$ optimal single-deletion-correcting code. As a separate result, we generalize the conditions for permutationally invariant codes to correct $t$ Pauli errors from the previously known results for $t=1$ to any number of errors. For small $t$, these conditions can be used to construct new examples of codes by computer. |
| title | A family of permutationally invariant quantum codes |
| topic | Quantum Physics Information Theory |
| url | https://arxiv.org/abs/2310.05358 |