Abstract
The simulation of non-Markovian quantum dynamics plays an important role in the understanding of charge and exciton dynamics in the condensed phase environment, yet such a simulation remains computationally expensive on classical computers. In this work, we develop a variational quantum algorithm that is capable of simulating non-Markovian quantum dynamics on quantum computers. The algorithm captures the non-Markovian effect by employing the Ehrenfest trajectories and Monte Carlo sampling of their thermal distribution. We test the algorithm with the spin-boson model on the quantum simulator, and the results match quantitatively with the exact ones. The algorithm naturally fits into the parallel computing platform of the NISQ devices and can be extended to anharmonic system-bath interactions and multistate systems.