Machine learning approaches to predictive qubit-state estimation under dephasing

Decoherence remains a major challenge in quantum computing hardware and a variety of physical-layer controls provide opportunities to mitigate the impact of this phenomenon. In particular, laboratory-based systems typically suffer from the presence of non-Markovian noise processes and this opens an opportunity for using feedback and feedforward correction strategies exploiting underlying noise correlations. In this work, we use a numerical record of projective qubit measurements to investigate the performance of various machine learning algorithms in performing state estimation (retrodiction) and forward prediction of future qubit state evolution. Our approaches involve the construction of a dynamical model capturing qubit dynamics via autoregressive or Fourier-type protocols. A comparison of achievable prediction horizons, model robustness, and noise filtering capabilities for Kalman Filters (KF) and a Gaussian Process Regression (GPR) algorithm is provided. We demonstrate superior performance from the autoregressive KF relative to Fourier-based KF approaches. Further, a GPR algorithm with an infinite basis of oscillators permits only retrodiction based on the data but not forward prediction.