Efficiently simulating high-dimensional entangled qubit-resonator quantum trajectories

We numerically simulate the monitored evolution of a readout resonator coupled to a driven qubit in a superconducting circuit. Traditional dispersive readout of superconducting devices uses driven microwave resonators to indirectly read out the states of neighboring qubits by examining the induced dispersive frequency shift, assuming steady state resonator response. However, continuously monitoring the leaked resonator field induces stochastic time evolution of the entangled qubit-resonator state with nontrivial transient behavior. We develop an efficient method for simulating such transient evolution for both heterodyne and homodyne readout of the leaked field using a stochastic non-Hermitian Hamiltonian approach in a polaron frame. Our simulations highlight the subtle dynamical effects that can affect the readout process in certain parameter regimes, including tilting of the effective measurement axis due to concurrent qubit control, and deformation of the conditioned, dressed resonator states at higher resonator pump powers.