Insights into decohered critical states using an exact solution to matchgate circuits with Pauli noise

Quantum Physics [Submitted on 21 Apr 2026] Insights into decohered critical states using an exact solution to matchgate circuits with Pauli noise Andrew Pocklington, Aashish A. Clerk The fate of non-trivial many-body states subject to decoherence is of both fundamental and practical interest. Here, we demonstrate a new analytic technique that allows for an exact treatment of dynamics of observables in matchgate circuits subject to arbitrary Pauli noise. We use this to obtain new insights on how decoherence influences critical ground states, focusing on the 1D transverse field Ising model subject to local Markovian Pauli noise. While such noise cannot kill the critical behavior of spin correlation functions, we show that it does lead to a surprising non-equilibrium state, with experimental signatures that are measurable without requiring post-selection or multiple copies of the system. Despite the infinite-temperature nature of the dissipation, the decohered state is characterized by a thermal distribution of low-energy quasi-particles. This is the direct consequence of a noise-induced emergent length scale that manifests itself in fermionic correlators. We show how these phenomena are directly accessible in experiments using a single probe qubit, and that our results also hold for a different dephased critical state (that of an XX spin chain in the zero magnetization sector). Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.18996 [quant-ph]   (or arXiv:2604.18996v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.18996 Focus to learn more Submission history From: Andrew Pocklington [view email] [v1] Tue, 21 Apr 2026 02:28:33 UTC (410 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 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?)