  We study an implementation of the open GRAPE (Gradient Ascent Pulse
Engineering) algorithm well suited for large open quantum systems. While
typical implementations of optimal control algorithms for open quantum systems
rely on explicit matrix exponential calculations, our implementation avoids
these operations leading to a polynomial speed-up of the open GRAPE algorithm
in cases of interest. This speed-up, as well as the reduced memory requirements
of our implementation, are illustrated by comparison to a standard
implementation of open GRAPE. As a practical example, we apply this open-system
optimization method to active reset of a readout resonator in circuit QED. In
this problem, the shape of a microwave pulse is optimized such as to empty the
cavity from measurement photons as fast as possible. Using our open GRAPE
implementation, we obtain pulse shapes leading to a reset time over four times
faster than passive reset.
