Coherent error induced phase transition

[2506.00650] Coherent error induced phase transition Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Quantum Physics arXiv:2506.00650 (quant-ph) [Submitted on 31 May 2025 ( v1 ), last revised 15 Jul 2026 (this version, v3)] Title: Coherent error induced phase transition Authors: Hanchen Liu , Xiao Chen View a PDF of the paper titled Coherent error induced phase transition, by Hanchen Liu and Xiao Chen View PDF HTML (experimental) Abstract: We investigate the stability of logical information in quantum stabilizer codes subject to coherent unitary errors. Beginning with a logical state, we apply a random unitary error channel and subsequently measure stabilizer checks, resulting in a syndrome-dependent post-measurement state. By examining both this \emph{syndrome state} and the associated syndrome distribution, we identify a phase transition in the behavior of the logical information. In the Clifford/stabilizer setting, the change of logical stabilizer structure in a syndrome branch determines the state-level MAP Pauli-frame return probability for a chosen logical-basis input. We separately use quantum coherent information to diagnose recoverability of arbitrary encoded inputs at the channel level. Below a critical error threshold \(p_c\), the syndrome branches remain compatible with the original logical sector, enabling a high state-return probability. Above \(p_c\), the data are consistent with effective scrambling of the encoded subspace relative to the stabilizer checks, where the syndrome-resolved logical maps approach a global-Clifford-induced stabilizer instrument. This common post-threshold picture organizes both the toric-code and finite-rate random-stabilizer-code results within the same scrambling mechanism. The syndrome distribution supplies complementary local and global structural diagnostics whose scaling depends on the code family. We refer to this phenomenon as a \emph{coherent error induced phase transition}. To illustrate this transition, we study two classes of quantum error-correcting codes, the toric code and finite-rate random stabilizer codes, thereby shedding light on the design and performance limits of quantum error correction under coherent errors. Comments: Fixed notations and figures Subjects: Quantum Physics (quant-ph) ; Statistical Mechanics (cond-mat.stat-mech) Cite as: arXiv:2506.00650 [quant-ph] (or arXiv:2506.00650v3 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2506.00650 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Hanchen Liu [ view email ] [v1] Sat, 31 May 2025 17:37:57 UTC (2,127 KB) [v2] Thu, 9 Apr 2026 03:39:35 UTC (2,177 KB) [v3] Wed, 15 Jul 2026 02:56:42 UTC (2,080 KB) Full-text links: Access Paper: View a PDF of the paper titled Coherent error induced phase transition, by Hanchen Liu and Xiao Chen View PDF HTML (experimental) TeX Source view license Current browse context: quant-ph < prev | next > new | recent | 2025-06 Change to browse by: cond-mat cond-mat.stat-mech References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... 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