Gottesman-Kitaev-Preskill error-correction with decohered resources
Abstract
Teleportation-based Gottesman-Kitaev-Preskill (GKP) error correction typically assumes a decoherence-free GKP ancilla Bell pair, an idealization that is difficult to reconcile with the ubiquitous environmental decoherence in bosonic systems. Here, we analyze the performance of the GKP protocol subject to pure-dephasing processes, ubiquitous in realistic situations. We show that, under this class of interactions, teleportation, instead of projecting the input onto the GKP subspace, transforms GKP error correction into a correlated Pauli-Gaussian noise process that can accumulate over successive correction rounds. Thus, unlike in previously studied noisy GKP scenarios, the code no longer self-corrects. Moreover, repeated noisy GKP teleportation drives the encoded modes out of the logical subspace, progressively degrading the encoded codewords. We show that the resulting leakage rapidly saturates with the number of correction rounds. Finally, we investigate the implications of our results for motional-oscillator-based GKP error-correction platforms.
Related
- Composable logical gate error in approximate quantum error correction: reexamining gate implementations in Gottesman-Kitaev-Preskill codes
- Modeling Logical Gates and Readout of Superconducting Gottesman-Kitaev-Preskill Qubits
- Gottesman-Kitaev-Preskill codes: A lattice perspective
- Remote Gottesman-Kitaev-Preskill Entanglement Generation between Trapped Ions
- Stellar Representation of Gottesman Kitaev Preskill States on the Double Discrete Cylinder
BibTeX
@misc{bhati2026gottesmankitaevpreskill,
title = {{Gottesman-Kitaev-Preskill error-correction with decohered resources}},
author = {Rajendra S. Bhati and T. Bazylewicz and Jarosław K. Korbicz},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.31462},
eprint = {2609.31462},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.31462},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Gottesman-Kitaev-Preskill error-correction with decohered resources
AU - Rajendra S. Bhati
AU - T. Bazylewicz
AU - Jarosław K. Korbicz
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.31462
UR - https://arxiv.org/abs/2609.31462
AB - Teleportation-based Gottesman-Kitaev-Preskill (GKP) error correction typically assumes a decoherence-free GKP ancilla Bell pair, an idealization that is difficult to reconcile with the ubiquitous environmental decoherence in bosonic systems. Here, we analyze the performance of the GKP protocol subject to pure-dephasing processes, ubiquitous in realistic situations. We show that, under this class of interactions, teleportation, instead of projecting the input onto the GKP subspace, transforms GKP error correction into a correlated Pauli-Gaussian noise process that can accumulate over successive correction rounds. Thus, unlike in previously studied noisy GKP scenarios, the code no longer self-corrects. Moreover, repeated noisy GKP teleportation drives the encoded modes out of the logical subspace, progressively degrading the encoded codewords. We show that the resulting leakage rapidly saturates with the number of correction rounds. Finally, we investigate the implications of our results for motional-oscillator-based GKP error-correction platforms.
ER -