Subsystem self-correction of the GKP qubit
Abstract
Passive quantum error correction, also known as self-correction, is a holy grail in quantum information science. Recent theoretical advances suggest that the Gottesman-Kitaev-Preskill (GKP) code can exhibit self-correction properties, positioning it as a candidate for the realization of self-correcting quantum memories. In this article, we provide a self-contained derivation of the self-correcting behavior of the ideal GKP Hamiltonian, manifested in the Arrhenius type scaling of the logical lifetime, from a quantum-information perspective based on the subsystem code decomposition. When coupling through the physical quadrature q and p, the detailed-balance jump operators decompose into a dominant part acting only on the gauge subsystem and a boundary term that acts non-trivially on the logical qubit. The boundary term is then exponentially suppressed by the Gibbs weights near the edge of the modular cells. In contrast to spin-based quantum memories such as the two-dimensional surface code, the GKP Hamiltonian realizes an effective string tension in modular phase space, whereby the energy cost increases as an error approaches the boundary of a logical sector.
Related
- Efficient Quantum Error Correction from Three Dimensional Qubit Control
- Epitaxial NbN-junction-based self-shunted superconducting flux qubit with high anharmonicity
- Exactness of Symmetry-Broken Self-Interaction Correction in the Strongly-Correlated or Classical Limit: Harmonium as a Demonstration
- Subsystem Spacetime Code
- Exact subsystem dynamics in the deterministic Floquet-PXP model
BibTeX
@misc{cheung2026subsystem,
title = {{Subsystem self-correction of the GKP qubit}},
author = {Brian Chung Hang Cheung and Lasse Bjørn Kristensen and Frederik Nathan and Michael Kastoryano},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.07702},
eprint = {2609.07702},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.07702},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Subsystem self-correction of the GKP qubit
AU - Brian Chung Hang Cheung
AU - Lasse Bjørn Kristensen
AU - Frederik Nathan
AU - Michael Kastoryano
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2609.07702
UR - https://arxiv.org/abs/2609.07702
AB - Passive quantum error correction, also known as self-correction, is a holy grail in quantum information science. Recent theoretical advances suggest that the Gottesman-Kitaev-Preskill (GKP) code can exhibit self-correction properties, positioning it as a candidate for the realization of self-correcting quantum memories. In this article, we provide a self-contained derivation of the self-correcting behavior of the ideal GKP Hamiltonian, manifested in the Arrhenius type scaling of the logical lifetime, from a quantum-information perspective based on the subsystem code decomposition. When coupling through the physical quadrature q and p, the detailed-balance jump operators decompose into a dominant part acting only on the gauge subsystem and a boundary term that acts non-trivially on the logical qubit. The boundary term is then exponentially suppressed by the Gibbs weights near the edge of the modular cells. In contrast to spin-based quantum memories such as the two-dimensional surface code, the GKP Hamiltonian realizes an effective string tension in modular phase space, whereby the energy cost increases as an error approaches the boundary of a logical sector.
ER -