  Compressed sensing is a method that allows a significant reduction in the
number of samples required for accurate measurements in many applications in
experimental sciences and engineering. In this work, we show that compressed
sensing can also be used to speed up numerical simulations. We apply compressed
sensing to extract information from the real-time simulation of atomic and
molecular systems, including electronic and nuclear dynamics. We find that for
the calculation of vibrational and optical spectra the total propagation time,
and hence the computational cost, can be reduced by approximately a factor of
five.
