A Mean-Field Lindblad Master Equation Framework for Interaction-Driven Decoherence in Solid-State Qubit Ensembles
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Quantum Physics arXiv:2606.25261 (quant-ph) [Submitted on 24 Jun 2026] Title:A Mean-Field Lindblad Master Equation Framework for Interaction-Driven Decoherence in Solid-State Qubit Ensembles Authors:Dhiman Nandi, Sanghamitra Neogi View a PDF of the paper titled A Mean-Field Lindblad Master Equation Framework for Interaction-Driven Decoherence in Solid-State Qubit Ensembles, by Dhiman Nandi and Sanghamitra Neogi View PDF HTML (experimental) Abstract:Multi-qubit systems are essential for scalable quantum technologies, but their performance is often limited by decoherence from qubit--qubit interactions and environmental noise. Although environmental decoherence in single-qubit systems and gate fidelity in multi-qubit systems have been widely studied, a predictive framework connecting qubit interactions, concentration, spatial distribution, and bath occupation to relaxation and decoherence times remains lacking. Here, we develop a multi-qubit mean-field Lindblad master equation (MQMF-LME) framework for the population and coherence dynamics of a solid-state qubit in an interacting multi-qubit environment. The framework treats one qubit as the system of interest and the surrounding qubits as an effective bath, incorporating intrinsic relaxation and bidirectional excitation transfer between the system and the bath. Analytical solutions provide closed-form expressions for density-matrix dynamics, steady-state populations, relaxation time $T_1$, and decoherence time $T_2$, while numerical simulations extend the framework to concentration-dependent dynamics, $1/f$-noise-induced dephasing, and material-specific excitation-transfer mechanisms. For a model system with Förster resonance energy transfer (FRET)-mediated excitation exchange, higher qubit concentrations reduce both $T_1$ and $T_2$, whereas $1/f$ noise reduces $T_2$ without changing $T_1$. Applied to Er$^{3+}$-doped CeO$_2$, the framework shows that long-range FRET-mediated excitation transfer reproduces the experimental decrease in relaxation time with dopant concentration, whereas short-range Dexter-type exchange does not, identifying FRET-mediated excitation transfer as the dominant mechanism. The MQMF-LME framework provides a modular route for linking microscopic interactions and environmental noise sources to measurable decoherence times in solid-state multi-qubit systems. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2606.25261 [quant-ph] (or arXiv:2606.25261v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.25261 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Sanghamitra Neogi [view email] [v1] Wed, 24 Jun 2026 00:49:23 UTC (4,771 KB) Full-text links: Access Paper: View a PDF of the paper titled A Mean-Field Lindblad Master Equation Framework for Interaction-Driven Decoherence in Solid-State Qubit Ensembles, by Dhiman Nandi and Sanghamitra NeogiView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-06 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?) 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?)