Effective modelling and simulation for a coupled qubit-cavity system with off-resonant multitone drives

Microwave cavities coupled to transmon qubits are key components for continuous-variable quantum computing using superconducting circuits. When driven by off-resonant tones, the system undergoes precise time evolution, enabling effects such as selective photon addition. In this work, we derive an effective Hamiltonian for a qubit-cavity system driven by off-resonant multitone drives. Our model demonstrates improved agreement with experimental data compared to previous theoretical models. We explore the implications of this effective model and show how it can be used to efficiently simulate the dynamics of qubit-cavity interactions. Our results lay the groundwork for more accurate simulation and optimal control of qubit-cavity systems.