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We present a quantum algorithm for the dynamical simulation of time-dependent Hamiltonians. Our method involves expanding the interaction-picture Hamiltonian as a sum of generalized permutations, which leads to an integral-free Dyson series of the time-evolution operator. Under this representation, we perform a quantum simulation for the time-evolution operator by means of the linear combination of unitaries technique. We optimize the time steps of the evolution based on the Hamiltonian'sdoi:10.1103/prxquantum.2.030342 fatcat:dgvrlxps2jaejhurh6bxvbid2y