  Engineering and harnessing coherent excitonic transport in organic
nanostructures has recently been suggested as a promising way towards improving
man-made light harvesting materials. However, realising and testing the
dissipative system-environment models underlying these proposals is presently
very challenging in supramolecular materials. A promising alternative is to use
simpler and highly tunable quantum simulators built from programmable qubits,
as recently achieved in a superconducting circuit by Potocnik et al. In this
article, we simulate the real-time dynamics of an exciton coupled to a quantum
bath as it moves through a network based on the quantum circuit of Potocnik et
al. Using the numerically exact hierarchical equations of motion to capture the
open quantum system dynamics, we find that an ultrafast but completely
incoherent relaxation from a high-lying bright exciton into a doublet of
closely spaced dark excitons can spontaneously generate electronic coherences
and oscillatory real-space motion across the network (quantum beats).
Importantly, we show that this behaviour also survives when the environmental
noise is classically stochastic (effectively high temperature), as in present
experiments, and also leads to a novel, transient violation of detailed balance
in the population relaxation. These predictions highlight the possibilities of
designing matched electronic and spectral noise structures for robust coherence
generation that does not require coherent excitation or cold environments.
