Quantum Decoherence Spectroscopy as a Dark Matter Detection Channel: A Non-Markovian Fluxonium Array with Graph Neural Network Signal Extraction

We propose a novel dark matter detection scheme based on non-Markovian qubit decoherence spectroscopy using a fluxonium array coupled to a structured ¹³C spin bath. The detector exploits memory-kernel dynamics at millikelvin temperatures to coherently accumulate a dark matter signal while suppressing thermal noise via CPMG dynamical decoupling. A spatio-temporal Graph Attention Network processes cross-correlated decoherence data from a two-node array to extract the DM fringe-shift signal. We derive the Fisher-matrix sensitivity forecast and Cramér–Rao bound, projecting sensitivity to the scalar-EM coupling d_e ≲ 5×10⁻¹¹ at m_DM ~ 10⁻¹⁸ eV and d_e ≲ 5×10⁻¹⁵ at m_DM ~ 10⁻²² eV for a one-year integration with N = 10⁶ measurement runs. Note: The GNN architecture and classification results presented in Section VI are subject to ongoing refinement. An updated version will be deposited upon completion.