We explore the applicability of a stochastic time-evolution algorithm based on probabilistic angle interpolation. To simplify the pre-processing of the algorithm, we take the continuous-time limit, thereby explicitly eliminating Trotter errors and streamlining the resource analysis. We also introduce a noise-mitigation method tailored to it. As demonstrations, we apply the algorithm to two representative problems: estimating the ground-state energy of the H3+ molecular Hamiltonian and computing out-of-time-ordered correlators in the sparse Sachdev-Ye-Kitaev model. We evaluate the protocol’’s performance through numerical simulations and experiments on a trapped-ion quantum computer, Quantinuum Reimei.