  Closed-loop control algorithms for real-time calibration of quantum
processors require efficient filters that can estimate physical error
parameters based on streams of measured quantum circuit outcomes. Development
of such filters is complicated by the highly nonlinear relationship
relationship between observed circuit outcomes and the magnitudes of elementary
errors. In this work, we apply the extended Kalman filter to data from quantum
gate set tomography to provide a streaming estimator of the both the system
error model and its uncertainties. Our numerical examples indicate extended
Kalman filtering can achieve similar performance to maximum likelihood
estimation, but with dramatically lower computational cost. With our method, a
standard laptop can process one- and two-qubit circuit outcomes and update gate
set error model at rates comparable with current experimental execution.
