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Peer-reviewedCC BY 4.0npj Quantum Information

The equivalence of quantum deletion and insertion errors on permutation-invariant codes

  • Lewis Bulled
  • Yingkai Ouyang
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Abstract

Quantum synchronisation errors are a class of 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 insertion-deletion errors, formulating a more restrictive set of conditions under which permutation-invariant codes are ( t , s )-insdel error-correctable. For completeness, we extend our approach to qudit errors on qudit permutation-invariant codes. Our work resolves many of the outstanding questions regarding the quantum error correction of synchronisation errors.

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Cite

BibTeXRIS
BibTeX
@article{bulled2026equivalence,
  title = {{The equivalence of quantum deletion and insertion errors on permutation-invariant codes}},
  author = {Lewis Bulled and Yingkai Ouyang},
  journal = {npj Quantum Information},
  year = {2026},
  month = oct,
  doi = {10.1038/s41534-026-01371-3},
  url = {https://www.nature.com/articles/s41534-026-01371-3},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - The equivalence of quantum deletion and insertion errors on permutation-invariant codes
AU  - Lewis Bulled
AU  - Yingkai Ouyang
PY  - 2026
DA  - 2026/10/03
JO  - npj Quantum Information
DO  - 10.1038/s41534-026-01371-3
UR  - https://www.nature.com/articles/s41534-026-01371-3
AB  - Quantum synchronisation errors are a class of 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 insertion-deletion errors, formulating a more restrictive set of conditions under which permutation-invariant codes are ( t , s )-insdel error-correctable. For completeness, we extend our approach to qudit errors on qudit permutation-invariant codes. Our work resolves many of the outstanding questions regarding the quantum error correction of synchronisation errors.
SN  - 2056-6387
ER  -