  The Fenna-Mathews-Olson (FMO) complex present in green sulphur bacteria is
known to mediate the transfer of excitation energy between light-harvesting
chlorosomes and membrane-embedded bacterial reaction centres. Due to the high
efficiency of such transport process, it is an extensively studied
pigment-protein complex system with the eventual aim of modelling and
engineering similar dynamics in other systems and use it for real-time
application. Some studies have attributed the enhancement of transport
efficiency to wave-like behaviour and non-Markovian quantum jumps resulting in
long-lived and revival of quantum coherence, respectively. Since dynamics in
these systems reside in the quantum-classical regime, quantum simulation of
such dynamics will help in exploring the subtle role of quantum features in
enhancing the transport efficiency, which has remained unsettled. Discrete
simulation of the dynamics in the FMO complex can help in efficient engineering
of the heat bath and controlling the environment with the system. In this work,
using the discrete quantum jump model we show and quantify the presence of
higher non-Markovian memory effects in specific site-pairs when internal
structures and environmental effects are in favour of faster transport. As a
consequence, our study leans towards the connection between non-Markovianity in
quantum jumps with the enhancement of transport efficiency.
