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We apply a new formalism to derive the higher-order quantum kinetic expansion(QKE) for studying dissipative dynamics in a general quantum network coupledwith an arbitrary thermal bath. The dynamics of system population is describedby a time-convoluted kinetic equation, where the time-nonlocal rate kernel issystematically expanded on the order of off-diagonal elements of the systemHamiltonian. In the second order, the rate kernel recovers the expression ofthe noninteracting-blip approximation (NIBA) method. The higher-ordercorrections in the rate kernel account for the effects of the multi-sitequantum coherence and the bath relaxation. In a quantum harmonic bath, the ratekernels of different orders are analytically derived. As demonstrated by fourexamples, the higher-order QKE can reliably predict quantum dissipativedynamics, comparing well with the hierarchic equation approach. Moreimportantly, the higher-order rate kernels can distinguish and quantifydistinct nontrivial quantum coherent effects, such as long-range energytransfer from quantum tunneling and quantum interference arising from the phaseaccumulation of interactions.

Higher-Order Kinetic Expansion of Quantum Dissipative Dynamics: Mapping Quantum Networks to Kinetic Networks