  Large-scale digital quantum simulations require thousands of fundamental
entangling gates to construct the simulated dynamics. Despite success in a
variety of small-scale simulations, quantum information processing platforms
have hitherto failed to demonstrate the combination of precise control and
scalability required to systematically outmatch classical simulators. We
analyse how fast gates could enable trapped-ion quantum processors to achieve
the requisite scalability to outperform classical computers without error
correction. We analyze the performance of a large-scale digital simulator, and
find that fidelity of around 70% is realizable for pi-pulse infidelities below
$10^{-5}$ in traps subject to realistic rates of heating and dephasing. This
scalability relies on fast gates: entangling gates faster than the trap period.
