  Quantum effects such as the environment assisted quantum transport (ENAQT)
displayed in photosynthetic Fenna-Mathews-Olson (FMO) complex has been
simulated on analog quantum simulators. Digital quantum simulations offer
greater universality and flexibility over analog simulations. However, digital
quantum simulations of open quantum systems face a theoretical challenge; one
does not know the solutions of the continuous time master equation for
developing quantum gate operators. We give a theoretical framework for digital
quantum simulation of ENAQT by introducing new quantum evolution operators. We
develop the dynamical equation for the operators and prove that it is an
analytical solution of the master equation. As an example, using the dynamical
equations, we simulate the FMO complex in the digital setting, reproducing
theoretical and experimental evidence of the dynamics. The framework gives an
optimal method for {quantum circuit} implementation, giving a log reduction in
complexity over known methods. The generic framework can be extrapolated to
study other open quantum systems.
