Recent progress in superconducting-circuit experiments has demonstrated access to the ultrastrong light–matter coupling regime, where the rotating-wave approximation breaks down, excitation number is not conserved, and pronounced nonlinear phenomena can emerge. These effects are central both to prospective quantum-technology applications and to investigations of fundamental quantum electrodynamics in strongly interacting systems. Our project focuses on a model comprising a single-mode resonator ultrastrongly coupled to an effective two-level system. We aim to perform time-domain simulations of the interaction between this hybrid system and externally injected photon pulses building on the work of Kiilerich et al (PRA 102, 023717). High-fidelity numerical modeling in this regime is computationally demanding due to the enlarged Hilbert space and the need for accurate propagation of highly nonclassical states. The proposed simulations will enable us to characterize pulse-driven dynamics, quantify the generation of nonclassical states of light, and identify operating conditions relevant for experimental implementations.