Liouvillian Gap in Dissipative Haar-Doped Clifford Circuits
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Quantum Physics arXiv:2602.03234 (quant-ph) [Submitted on 3 Feb 2026] Title:Liouvillian Gap in Dissipative Haar-Doped Clifford Circuits Authors:Ha Eum Kim, Andrew D. Kim, Jong Yeon Lee View a PDF of the paper titled Liouvillian Gap in Dissipative Haar-Doped Clifford Circuits, by Ha Eum Kim and 2 other authors View PDF HTML (experimental) Abstract:Quantum chaos is commonly assessed through probe-dependent signatures such as spectral statistics, OTOCs, and entanglement growth, which need not coincide. Recently, a dissipative diagnostic of chaos has been proposed, in which an infinitesimal coupling to a bath yields a finite Liouvillian gap in chaotic systems, marking the onset of intrinsic relaxation. This raises a conceptual question: what is the minimal departure from Clifford dynamics needed for this intrinsically relaxing behavior to emerge? In this work, we investigate the dynamics under the Floquet two-qubit Clifford circuit interleaved with a finite density of Haar-random single-site gates, followed by a depolarizing channel with strength $\gamma$.
For Floquet Clifford circuits built from an \textit{i}SWAP-class two-qubit gate, our analysis identifies two distinct regimes for the Liouvillian gap in the thermodynamic limit, exemplified by the undoped and fully doped extreme cases. In both regimes, the dissipative diagnostic signals chaotic behavior, differing only in how the gap scales with system size. In the undoped circuit, the gap scales as $\Delta \sim \gamma N$, whereas in the fully doped circuit it remains finite as $N\to\infty$. We find that the doping density $p_h$ governs the crossover: as $p_h\to 0$, any spatial structure remains undoped-like, whereas for finite $p_h$ certain structures can enter a finite-gap regime. These results are analytically established in the strongly dissipative regime $\gamma\gg 1$ by deriving lower bounds on the gap as a function of $p_h$ and explicit finite-gap constructions, and their extension toward $\gamma\to 0$ is supported by numerics. Importantly, our analytic treatment depends only on the spatial doping structure, so the same gap scaling persists even when the Haar rotations are independently resampled each Floquet period. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2602.03234 [quant-ph] (or arXiv:2602.03234v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2602.03234 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Ha Eum Kim [view email] [v1] Tue, 3 Feb 2026 08:11:31 UTC (2,004 KB) Full-text links: Access Paper: View a PDF of the paper titled Liouvillian Gap in Dissipative Haar-Doped Clifford Circuits, by Ha Eum Kim and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-02 References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: 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 Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)