Quantum Decoherence of the Surface Code: A Generalized Caldeira-Leggett Approach

Quantum Physics [Submitted on 21 Apr 2026] Quantum Decoherence of the Surface Code: A Generalized Caldeira-Leggett Approach E. Novais, A. H. Castro-Neto Standard quantum error correction (QEC) models typically assume discrete, Markovian noise, obscuring the continuous quantum nature of physical environments. In this manuscript, we investigate the fundamental limits of an actively corrected surface code coupled to a continuous, un-reset quantum environment at zero and finite temperature. Using the generalized Caldeira-Leggett framework, we map the long-time evolution of the logical qubit to a boundary conformal field theory, establishing an exact equivalence to the anisotropic Kondo model. We evaluate computational times for a finite code distance L for all spatial and temporal correlations. Our analysis reveals that a true thermodynamic threshold exists strictly for short-range environments (z>1/(s+1)). In critical or long-range regimes, the macroscopic footprint of the code weaponizes the continuous bath, hindering the topological protection. Comments: 18 pages, 5 figures, submitted to the special issue "Frontiers in Quantum Mechanics and the 45 Years of the Caldeira-Leggett Model" Subjects: Quantum Physics (quant-ph); Strongly Correlated Electrons (cond-mat.str-el) Cite as: arXiv:2604.18968 [quant-ph]   (or arXiv:2604.18968v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.18968 Focus to learn more Submission history From: Eduardo Novais [view email] [v1] Tue, 21 Apr 2026 01:32:59 UTC (38 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 Change to browse by: cond-mat cond-mat.str-el 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?)