  Biomolecular light-harvesting antennas operate as nanoscale devices in a
regime where the coherent interactions of individual light, matter and
vibrational quanta are non-perturbatively strong. The complex behaviour arising
from this could, if fully understood, be exploited for myriad energy
applications. However, non-perturbative dynamics are computationally
challenging to simulate, and experiments on biomaterials explore very limited
regions of the non-perturbative parameter space. So-called `quantum simulators'
of light-harvesting models could provide a solution to this problem, and here
we employ the hierarchical equations of motion technique to investigate recent
superconducting experiments of Poto{\v{c}}nik $\it{et}$ $\it{al.}$ (Nat. Com.
9, 904 (2018)) used to explore excitonic energy capture. By explicitly
including the role of optical driving fields, non-perturbative dephasing noise
and the full multi-excitation Hilbert space of a three-qubit quantum circuit,
we predict the measureable impact of these factors on transfer efficiency. By
analysis of the eigenspectrum of the network, we uncover a structure of energy
levels that allows the network to exploit optical `dark' states and excited
state absorption for energy transfer. We also confirm that time-resolvable
coherent oscillations could be experimentally observed, even under strong,
non-additive action of the driving and optical fields.
