The equivalence of quantum deletion and insertion errors on permutation-invariant codes
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866912891059306496 |
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| author | Bulled, Lewis Ouyang, Yingkai |
| author_facet | Bulled, Lewis Ouyang, Yingkai |
| contents | Quantum synchronisation errors are a class of quantum errors that change the number of qubits in a quantum system. The classical error correction of synchronisation errors has been well-studied, including an insertion-deletion equivalence more than a half-century ago, but little progress has been made towards the quantum counterpart since the birth of quantum error correction. We address the longstanding problem of a quantum insertion-deletion equivalence on permutation-invariant codes, detailing the conditions under which such codes are $t$-insertion error-correctable. We extend these conditions to quantum insdel errors, formulating a more restrictive set of conditions under which permutation-invariant codes are $(t,s)$-insdel error-correctable. Our work resolves many of the outstanding questions regarding the quantum error correction of synchronisation errors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_08780 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The equivalence of quantum deletion and insertion errors on permutation-invariant codes Bulled, Lewis Ouyang, Yingkai Quantum Physics Quantum synchronisation errors are a class of quantum errors that change the number of qubits in a quantum system. The classical error correction of synchronisation errors has been well-studied, including an insertion-deletion equivalence more than a half-century ago, but little progress has been made towards the quantum counterpart since the birth of quantum error correction. We address the longstanding problem of a quantum insertion-deletion equivalence on permutation-invariant codes, detailing the conditions under which such codes are $t$-insertion error-correctable. We extend these conditions to quantum insdel errors, formulating a more restrictive set of conditions under which permutation-invariant codes are $(t,s)$-insdel error-correctable. Our work resolves many of the outstanding questions regarding the quantum error correction of synchronisation errors. |
| title | The equivalence of quantum deletion and insertion errors on permutation-invariant codes |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2602.08780 |