The interaction between a single impurity and a superconductor leads to intra-gap localized and almost polarized bound states. Controlling and functionalizing these quantum bound states is a route actively followed for topological superconductivity but also to realize qubits. However, most of the theoretical descriptions of the magnetic impurities rely on a classical spin model which simply describes the excitation spectrum but however artificially breaks time-reversal symmetry and fails to reproduce correctly the ground state degeneracy. Despite a lot of experimental and theoretical works that have been devoted to the interplay between magnetism and superconductivity, the many-body dynamics of these bound states have hardly been studied. Since external driving is important for experimental probing of the dynamics, as well as a tool for manipulating the topological phase of the system, a non-equilibrium theory would be highly valuable. In this internship, we propose to study the dynamics of a simple model of a quantum spin impurity interacting with a superconducting substrate in the zero-band limit [4] and subject to a time-dependent magnetic field. This proposal is part of a collaboration we have with experimentalists on the Saclay Plateau studying atomic-scale spin dynamics.