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

Precise quantum control of superconducting qubits necessitates determining the time-dependent Hamiltonian of control pulses with high fidelity. While continuous state tracking has proved effective for determining qubit time-evolution in regimes with Markovian dynamics, fast control pulses used for native quantum gates and entanglement generation can result in non-Markovian transient dynamics. 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 qubit state during a Rabi oscillation sequence on a timescale comparable to the cavity decay rate, we isolate dynamics that are difficult to describe with single-qubit trajectory theory. We train 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, and estimate parameters of the stochastic master equation.