Non-Stationary Decoherence in Superconducting Qubits: Memory Multi-Fractional Brownian Motion and a Time-Dependent Quantum Brownian Motion Extension
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Quantum Physics arXiv:2605.18914 (quant-ph) [Submitted on 18 May 2026] Title:Non-Stationary Decoherence in Superconducting Qubits: Memory Multi-Fractional Brownian Motion and a Time-Dependent Quantum Brownian Motion Extension Authors:Mahboob Ul Haq View a PDF of the paper titled Non-Stationary Decoherence in Superconducting Qubits: Memory Multi-Fractional Brownian Motion and a Time-Dependent Quantum Brownian Motion Extension, by Mahboob Ul Haq View PDF HTML (experimental) Abstract:Building upon our prior work [1], we present a unified stochastic drift model (SdM) for superconducting charge qubits based on memory multi-fractional Brownian motion (mmFBM). The classical sector employs a time-dependent Hurst exponent H(t) and adaptive memory kernel K(t,s), capturing non-stationary 1/f^beta noise and long-range temporal correlations inaccessible to conventional models. The quantum extension is formulated via a time-dependent Caldeira--Leggett environment with spectral density J(omega;t) = eta(t) omega_c^{1-s(t)} omega^{s(t)} exp(-omega/omega_c), where s(t) = 2H(t)-1, consistently reproducing beta(t) = 2H(t)-1. Four central results emerge: (1) relaxation and noise amplitudes act independently on energy decay; (2) time-varying H(t) matches experimental 1/f spectra more accurately than any constant exponent; (3) adaptive kernel dynamics preserve correlations without artificial damping; and (4) simulations predict coherence times (T1 ~ 5.00 x 10^6 ns, T2 ~ 4.18 x 10^5 ns) consistent with theory when charge noise dominates. The qubit exhibits stretched-exponential Ramsey and echo decay, non-Markovian dephasing, and a temperature-driven quantum-to-classical crossover. We derive the effective time-local Lindblad master equation, establish the classical mmFBM limit at high temperatures, and provide experimentally testable scaling relations. The non-exponential decay patterns reveal fundamental limitations of Markovian approaches, and the framework guides the design of noise-resilient qubit architectures. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2605.18914 [quant-ph] (or arXiv:2605.18914v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.18914 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Mahboob Ul Haq [view email] [v1] Mon, 18 May 2026 01:33:32 UTC (165 KB) Full-text links: Access Paper: View a PDF of the paper titled Non-Stationary Decoherence in Superconducting Qubits: Memory Multi-Fractional Brownian Motion and a Time-Dependent Quantum Brownian Motion Extension, by Mahboob Ul HaqView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-05 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?)