  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 semi-conducting molecules. We adopt an ab-initio exciton
model built from the atomistic simulation of an N-molecule system. The exciton
Hamiltonian is efficiently encoded in log2(N) qubits, and the dynamics is
evolved using a time-dependent variational quantum algorithm. Our numerical
examples demonstrate the feasibility of this approach, and simulations on IBM Q
devices capture the qualitative behaviors of exciton dynamics but with
considerable errors. We propose an error mitigation technique by combining
experimental results from the variational and Trotter algorithms, and obtain
significantly improved quantum dynamics. Our approach opens up new
opportunities for modeling energy transfer in technologically relevant systems
with quantum computers.
