Tracking non-Markovian quantum dynamics of a superconducting qubit with a recurrent neural network filter*

Determining the time-dependent Hamiltonian for control pulses of superconducting quantum circuits is critical for their use in reliable quantum information processing; however, interactions between coupled qubits and nearby resonators can cause transient dynamics to become non-Markovian. We use quantum state tracking with continuous weak measurement to experimentally investigate non-Markovianity in a transmon superconducting qubit coupled to a readout resonator. By weakly measuring the state of the transmon qubit undergoing tunable Rabi oscillations comparable to the cavity linewidth, we isolate dynamics that are difficult to describe with single-qubit trajectory theory. We address this difficulty by training a recurrent neural network to reconstruct the quantum trajectories, motivated by such a network's demonstrated ability to learn long-time correlations in sequential data. Here we detail the experimental protocol and present preliminary data.