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Trotter and linear-combination-of-unitary (LCU) are two popular Hamiltoniansimulation methods. We propose Hamiltonian simulation algorithms using LCU tocompensate Trotter error, which enjoy both of their advantages. By adding fewgates after the Kth-order Trotter, we realize a better time scaling than2Kth-order Trotter. Our first algorithm exponentially improves the accuracyscaling of the Kth-order Trotter formula. In the second algorithm, we considerthe detailed structure of Hamiltonians and construct LCU for Trotter errorswith commutator scaling. Consequently, for lattice Hamiltonians, the algorithmenjoys almost linear system-size dependence and quadratically improves theaccuracy of the Kth-order Trotter.

Simple and high-precision Hamiltonian simulation by compensating Trotter error with linear combination of unitary operations