Stabilization of finite-energy grid states of a quantum harmonic oscillator by reservoir engineering with two dissipation channels

Quantum Physics [Submitted on 15 Apr 2026] Stabilization of finite-energy grid states of a quantum harmonic oscillator by reservoir engineering with two dissipation channels Rémi Robin, Pierre Rouchon, Lev-Arcady Sellem We propose and analyze an experimentally accessible Lindblad master equation for a quantum harmonic oscillator, simplifying a previous proposal to alleviate implementation constraints. It approximately stabilizes periodic grid states introduced in 2001 by Gottesman, Kitaev and Preskill (GKP), with applications for quantum error correction and quantum metrology. We obtain explicit estimates for the energy of the solutions of the Lindblad master equation. We estimate the convergence rate to the codespace when stabilizing a GKP qubit, and numerically study the effect of noise. We then present simulations illustrating how a modification of parameters allows preparing states of metrological interest in steady-state. Subjects: Quantum Physics (quant-ph); Optimization and Control (math.OC) Cite as: arXiv:2604.13529 [quant-ph]   (or arXiv:2604.13529v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.13529 Focus to learn more Submission history From: Rémi Robin [view email] [v1] Wed, 15 Apr 2026 06:24:28 UTC (985 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 Change to browse by: math math.OC References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)