  Quantum computers have the potential to simulate chemical systems beyond the
capability of classical computers. Recent developments in hybrid
quantum-classical approaches enable the determinations of the ground or low
energy states of molecular systems. Here, we extend near-term quantum
simulations of chemistry to time-dependent processes by simulating energy
transfer in organic semiconducting molecules. We developed a multi-scale
modeling workflow that combines conventional molecular dynamics and quantum
chemistry simulations with hybrid variational quantum algorithm to compute the
exciton dynamics in both the single excitation subspace (i.e. Frenkel
Hamiltonian) and the full-Hilbert space (i.e. multi-exciton) regimes. Our
numerical examples demonstrate the feasibility of our approach, and simulations
on IBM Q devices capture the qualitative behaviors of exciton dynamics, but
with considerable errors. We present an error mitigation technique that
combines experimental results from the variational and Trotter algorithms, and
obtain significantly improved quantum dynamics. Our approach opens up new
opportunities for modeling quantum dynamics in chemical, biological and
material systems with quantum computers.
