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We study an implementation of the open GRAPE (Gradient Ascent PulseEngineering) algorithm well suited for large open quantum systems. Whiletypical implementations of optimal control algorithms for open quantum systemsrely on explicit matrix exponential calculations, our implementation avoidsthese operations leading to a polynomial speed-up of the open GRAPE algorithmin cases of interest. This speed-up, as well as the reduced memory requirementsof our implementation, are illustrated by comparison to a standardimplementation of open GRAPE. As a practical example, we apply this open-systemoptimization method to active reset of a readout resonator in circuit QED. Inthis problem, the shape of a microwave pulse is optimized such as to empty thecavity from measurement photons as fast as possible. Using our open GRAPEimplementation, we obtain pulse shapes leading to a reset time over four timesfaster than passive reset.

Resonator reset in circuit QED by optimal control for large open quantum systems