Subsystem self-correction of the GKP qubit

• URL: http://arxiv.org/abs/2609.07702v1
• Date: Mon, 07 Sep 2026 16:18:23 GMT
• Title: Subsystem self-correction of the GKP qubit
• Abstract summary: Passive quantum error correction, also known as self-correction, is a holy grail in quantum information science.<n>Recent theoretical advances suggest that the Gottesman-Kitaev-Preskill code can exhibit self-correction properties.<n>In this article, we provide a self-contained derivation of the self-correcting behavior of the ideal GKP Hamiltonian.
• Score: 0.6999740786886536
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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