We study the computation of the zero set of the Bargmann transform of a signal contaminated with complex white noise, or, equivalently, the computation of the zeros of its short-time Fourier transform with Gaussian window. We introduce the adaptive minimal grid neighbors algorithm (AMN), a variant of a method that has recently appeared in the signal processing literature, and prove that with high probability it computes the desired zero set. More precisely, given samples of the Bargmann transform of a signal on a finite grid with spacing $δ$, AMN is shown to compute the desired zero set up to a factor of $δ$ in the Wasserstein error metric, with failure probability $O(δ^4 \log^2(1/δ))$. We also provide numerical tests and comparison with other algorithms.