  We propose a hybrid approach to simulate quantum many body dynamics by
combining Trotter based quantum algorithm with classical dynamic mode
decomposition. The interest often lies in estimating observables rather than
explicitly obtaining the wave function's form. Our method predicts observables
of a quantum state in the long time by using data from a set of short time
measurements from a quantum computer. The upper bound for the global error of
our method scales as $O(t^{3/2})$ with a fixed set of the measurement. We apply
our method to quench dynamics in Hubbard model and nearest neighbor spin
systems and show that the observable properties can be predicted up to a
reasonable error by controlling the number of data points obtained from the
quantum measurements.
