Online estimation of quantum errors with the extended Kalman filter

The extended Kalman filter is one of the most widely used nonlinear control techniques in the world. We demonstrate how this celebrated filter can be used to provide streaming estimates of the error processes inside a quantum processor, enabling a wide range of new techniques for quantum control and calibration. Our filter uses the measurement distributions of individual quantum circuits to update an error estimate that replaces the large-batch processing required by standard Maximum Likelihood Estimation. We detail how to initialize the Kalman filter algorithm using prior information and randomized benchmarking results. Our method links the extended Kalman filter with the formalism of gate set tomography to provide online estimates of coherent and stochastic error rates inside a quantum computing device as well as robust error bars.