A High-Fidelity Realization of the Euclid Code Comparison $N$-body
  Simulation with Abacus
  We present a high-fidelity realization of the cosmological $N$-body
simulation from the Schneider et al. (2016) code comparison project. The
simulation was performed with our Abacus $N$-body code, which offers high force
accuracy, high performance, and minimal particle integration errors. The
simulation consists of $2048^3$ particles in a $500\ h^{-1}\mathrm{Mpc}$ box,
for a particle mass of $1.2\times 10^9\ h^{-1}\mathrm{M}_\odot$ with $10\
h^{-1}\mathrm{kpc}$ spline softening. Abacus executed 1052 global time steps to
$z=0$ in 107 hours on one dual-Xeon, dual-GPU node, for a mean rate of 23
million particles per second per step. We find Abacus is in good agreement with
Ramses and Pkdgrav3 and less so with Gadget3. We validate our choice of time
step by halving the step size and find sub-percent differences in the power
spectrum and 2PCF at nearly all measured scales, with $<0.3\%$ errors at $k<10\
\mathrm{Mpc}^{-1}h$. On large scales, Abacus reproduces linear theory better
than $0.01\%$. Simulation snapshots are available at
http://nbody.rc.fas.harvard.edu/public/S2016 .
