An angular momentum approach to quantum insertion errors

• URL: http://arxiv.org/abs/2509.03413v1
• Date: Wed, 03 Sep 2025 15:39:24 GMT
• Title: An angular momentum approach to quantum insertion errors
• Authors: Lewis Bulled, Yingkai Ouyang,
• Abstract summary: We detail a quantum error correction protocol that can correct single insertion errors on a class of gapped permutation-invariant codes.<n>We provide a simple two-stage syndrome extraction protocol that yields a two-bit syndrome.<n>We demonstrate that these measurements project the state onto a new codespace, and we detail a teleportation protocol to map the projected state back to a permutation-invariant code on the desired number of qubits.
• Score: 3.437656066916039
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum insertion errors are a class of errors that increase the number of qubits in a quantum system. Despite a wealth of research on classical insertion errors, there has been limited progress towards a general framework for correcting quantum insertion errors. We detail a quantum error correction protocol that can correct single insertion errors on a class of gapped permutation-invariant codes. We provide a simple two-stage syndrome extraction protocol that yields a two-bit syndrome, by measuring the total angular momentum and its projection along the $z$-axis (modulo the code gap) of the post-insertion state. We demonstrate that these measurements project the state onto a new codespace, and we detail a teleportation protocol to map the projected state back to a permutation-invariant code on the desired number of qubits.

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