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Analysis of large galaxy surveys requires confidence in the robustness ofnumerical simulation methods. The simulations are used to construct mock galaxycatalogs to validate data analysis pipelines and identify potentialsystematics. We compare three $N$-body simulation codes, ABACUS, GADGET, andSWIFT, to investigate the regimes in which their results agree. We run $N$-bodysimulations at three different mass resolutions, $6.25\times10^{8}$,$2.11\times10^{9}$, and $5.00\times10^{9}~h^{-1}$M$_{\odot}$, matching phasesto reduce the noise within the comparisons. We find systematic errors in thehalo clustering between different codes are smaller than the DESI statisticalerror for $s > 20\, h^{-1}$Mpc in the correlation function in redshift space.Through the resolution comparison we find that simulations run with a massresolution of $2.1\times10^{9}~h^{-1}$M$_{\odot}$ are sufficiently convergedfor systematic effects in the halo clustering to be smaller than the DESIstatistical error at scales larger than $20 \, h^{-1}$Mpc. These findings showthat the simulations are robust for extracting cosmological information fromlarge scales which is the key goal of the DESI survey. Comparing matter powerspectra, we find the codes agree to within 1% for $k \leq 10~h$Mpc$^{-1}$. Wealso run a comparison of three initial condition generation codes and find goodagreement. In addition, we include a quasi-$N$-body code, FastPM, since we planuse it for certain DESI analyses. The impact of the halo definition andgalaxy-halo relation will be presented in a follow up study.

The DESI $N$-body Simulation Project I: Testing the Robustness of Simulations for the DESI Dark Time Survey