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In this paper, we propose a quantum algorithm for the simulation of the excitonic transport of energy, occurring in the first stage of the process of photosynthesis. The algorithm takes in account the quantum and environmental effects (pure dephasing), influencing the quantum transport. We performed quantum simulations of such phenomena, for a proof of concept scenario, in an actual quantum computer, IBM <jats:italic>Q<\/jats:italic>, of 5 qubits. 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