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

• URL: http://arxiv.org/abs/2602.08780v1
• Date: Mon, 09 Feb 2026 15:23:26 GMT
• Title: The equivalence of quantum deletion and insertion errors on permutation-invariant codes
• Authors: Lewis Bulled, Yingkai Ouyang,
• Abstract summary: We address the longstanding problem of a quantum insertion-deletion equivalence on permutation-invariant codes.<n>We formulate a more restrictive set of conditions under which permutation-invariant codes are $(t,s)$-insdel error-correctable.
• Score: 3.437656066916039
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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