We propose a hybrid approach to simulate quantum many-body dynamics by combining the Trotter-based quantum algorithm with classical dynamic mode decomposition. In quantum simulation, the interest often lies in estimating observables rather than explicitly obtaining the wave function. Instead of characterizing a quantum state, our method predicts observables of the 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 $O\left(t^{3/2}\right)$ with a fixed set of the measurement. We apply our method to quench dynamics in the 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.

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• Quantum algorithms & computation
• Quantum simulation
• Quantum many-body systems
• Approximation methods for many-body systems
• Hubbard model