We establish the convergences (with respect to the simulation time $t$; the number of particles $N$; the timestep $γ$) of a Moran/Fleming-Viot type particle scheme toward the quasi-stationary distribution of a diffusion on the $d$-dimensional torus, killed at a smooth rate. In these conditions, quantitative bounds are obtained that, for each parameter ($t\rightarrow \infty$, $N\rightarrow \infty$ or $γ\rightarrow 0$) are independent from the two others.