  We implement a quantum optimal control algorithm based on automatic
differentiation and harness the acceleration afforded by graphics processing
units (GPUs). Automatic differentiation allows us to specify advanced
optimization criteria and incorporate them in the optimization process with
ease. We show that the use of GPUs can speed up calculations by more than an
order of magnitude. Our strategy facilitates efficient numerical simulations on
affordable desktop computers, and exploration of a host of optimization
constraints and system parameters relevant to real-life experiments. We
demonstrate optimization of quantum evolution based on fine-grained evaluation
of performance at each intermediate time step, thus enabling more intricate
control on the evolution path, suppression of departures from the truncated
model subspace, as well as minimization of the physical time needed to perform
high-fidelity state preparation and unitary gates.
