Non-Stationary Decoherence in Superconducting Qubits:Memory Multi-Fractional Brownian Motion and a Time-Dependent Quantum Brownian Motion Extension
Abstract
Abstract Building upon our prior work [1], we present a unified stochastic drift model (SdM) for su-perconducting 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 β 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(ω; t) = η(t) ω 1−s(t) c ω s(t) e −ω/ωc , where s(t) = 2H(t) − 1, consistently reproducing β(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 (T 1 ∼ 5.00 × 10 6 ns, T 2 ∼ 4.18 × 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 Lind-blad 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…
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