  Optimal control techniques provide a means to tailor the control pulse
sequence necessary for the generation of customized quantum gates, which help
enhancing the resilience of quantum simulations to gate errors and device
noise. However, the substantial amount of (classical) computing time required
for the generation of a gate might in most cases strongly reduce the efficiency
of this customized gates can quickly spoil the effectiveness of such an
approach, especially when the pulse optimization needs to be iterated. We
report the results of a device-level quantum simulations of the unitary (real)
time evolution of the hydrogen atom, based on superconducting qubit, and
propose a method to improve the efficiency of reduce the computing time
required for the generation of the control pulses. We use a simple
interpolation scheme to accurately reconstructed the real time-propagator for a
given time interval step starting from pulses obtained for a discrete set of
pre-determined time intervals. We also explore an analogous treatment has been
explored for the case in which the hydrogen atom Hamiltonian is parameterized
by the mass of the electron. In both cases the results show that it is possible
to we obtain a reconstruction with very high fidelity and a substantial
reduction of the computational effort.
