Elucidating many-body effects in molecular core spectra through real-time approaches: Efficient classical approximations and a quantum perspective.

Accurately resolving many-body satellite features in molecular core-level spectra requires theoretical approaches that capture electron correlation both efficiently and systematically. The recently developed time-dependent double coupled-cluster (TD-dCC) Ansatz achieves this by combining correlation effects from the N- and (N - 1)-electron sectors, but its exact formulation remains computationally demanding. Here, we introduce a hierarchy of cost-effective approximate TD-dCC-truncated Baker-Campbell-Hausdorff (BCH) expansions, which preserve a single-similarity-transformation structure while retaining the essential correlation diagrams responsible for satellite formation. We further develop a detailed component analysis that isolates hole-mediated excitation pathways-correlated processes arising from the coupling between ground-state and ionized-state amplitudes-and use it to interpret quasiparticle and satellite features across the hierarchy. Applications to the single-impurity Anderson model and molecular systems (H2O and CH4) demonstrate that the approximate TD-dCC methods closely and efficiently reproduce exact many-body spectral features and quasiparticle weights. In parallel, we construct a fault-tolerant quantum signal processing algorithm for the core-hole Green's function, providing a scalable quantum route for simulating correlated core-level dynamics. Together, these developments establish complementary classical and quantum methodologies for quantitative, many-body-accurate core spectroscopy.