  In the $0+1$ dimensional imaginary-time path integral formulation of quantum
impurity problems, the retarded action encodes the hybridization of the
impurity with the bath. In this Article, we explore the computational power of
representing the retarded action as matrix product state (RAMPS). We focus on
the challenging Kondo regime of the single-impurity Anderson model, where
non-perturbative strong-correlation effects arise at very low energy scales. We
demonstrate that the RAMPS approach reliably reaches the Kondo regime for a
range of interaction strengths $U$, with a numerical error scaling as a weak
power law with inverse temperature. We investigate the convergence behavior of
the method with respect to bond dimension and time discretization by analyzing
the error of local observables in the full interacting problem and find
polynomial scaling in both parameters. Our results show that the RAMPS approach
offers promise as an alternative tool for studying quantum impurity problems in
regimes that challenge established methods, such as multi-orbital systems.
Overall, our study contributes to the development of efficient and accurate
non-wavefunction-based tensor-network methods for quantum impurity problems.
