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We present a quantum algorithm for simulating the dynamics of a first-quantized Hamiltonian in real space based on the truncated Taylor series algorithm. We avoid the possibility of singularities by applying various cutoffs to the system and using a high-order finite difference approximation to the kinetic energy operator. We find that our algorithm can simulate $\eta$ interacting particles using a number of calculations of the pairwise interactions that scales, for a fixed spatial griddoi:10.1088/1751-8121/aa77b8 fatcat:jmhghu7mgnd6nf7smivk77zdpm