  The unraveling of open quantum system dynamics in terms of stochastic quantum
trajectories offers a picture of open system dynamics that consistently
considers memory effects stemming from the finite correlation time of
environment fluctuations. These fluctuations significantly influence the
coherence and energy transport properties of excitonic systems. When their
correlation time is comparable to the timescale of the Hamiltonian evolution,
it leads to the departure of open system dynamics from the Markovian limit. In
this work, we leverage the unraveling of exciton dynamics through stochastic
Hamiltonian propagators to design quantum circuits that simulate exciton
transport, capturing finite memory effects. In addition to enabling the
synthesis of parametrizable quantum circuits, stochastic unitary propagators
provide a transparent framework for investigating non-Markovian effects on
exciton transport. Our analysis reveals a nuanced relationship between
environment correlation time and transport efficiency, identifying a regime of
"memory-assisted" quantum transport where time-correlated fluctuations allow
the system to reach higher efficiency. However, this property is not universal
and can only be realized in conjunction with specific features of the system
Hamiltonian.
