  Open quantum system approaches are widely used in the description of
physical, chemical and biological systems. A famous example is electronic
excitation transfer in the initial stage of photosynthesis, where harvested
energy is transferred with remarkably high efficiency to a reaction center.
This transport is affected by the motion of a structured vibrational
environment, which makes simulations on a classical computer very demanding.
Here we propose an analog quantum simulator of complex open system dynamics
with a precisely engineered quantum environment. Our setup is based on
superconducting circuits, a well established technology. As an example, we
demonstrate that it is feasible to simulate exciton transport in the
Fenna-Matthews-Olson photosynthetic complex. Our approach allows for a
controllable single-molecule simulation and the investigation of energy
transfer pathways as well as non-Markovian noise-correlation effects.
