Reconstructing Transmon State Trajectories Outside the Bad-Cavity Regime using a Neural Network Filter

Superconducting transmon qubits are measured by coupling them to a resonator and monitoring the leaked microwave field continuously in time. In the bad-cavity regime, we can treat the resonator as a steady-state bath that produces Markovian quantum trajectories of the qubit. However, outside the bad-cavity regime, the entangled qubit-resonator state can nontrivially evolve in time. The resulting time-varying measurement strength significantly complicates theoretical models for tracking reduced qubit dynamics, which can become non-Markovian due to information back-flow from the resonator. Modern quantum processors regularly operate outside the bad-cavity regime, motivating the need for more sophisticated state tracking that handles these time-dependent effects. In this work, we experimentally investigate driven qubit dynamics outside the steady-state and bad-cavity regime and demonstrate that a recurrent neural network (RNN) accurately reconstruct the reduced qubit-state trajectories with time-dependent parameters. We reconstruct and verify trajectories involving Rabi frequencies comparable to the resonator linewidth, and find that the RNN correctly identifies drive-hybridization corrections to the measurement axis and strength.