Quantum simulation promises the ability to study the dynamics of highly complex quantum systems using more easily accessible and controllable systems1–3. Digital quantum simulation schemes, using quantum computing resources, enable versatile simulations of a collection of systems - indeed, a universal set of quantum gates is sufficient to compose any desired unitary arising from a local Hamiltonian4 . In contrast, analogue quantum simulation schemes require precise engineering of a Hamiltonian to reproduce the desired dynamics of the simulated system3 , such that they are necessarily less versatile. Moreover, digital simulators may allow for error correction due to their similarities with gate-based quantum computing schemes. Many systems are considered as potential quantum simulators: cold atoms in optical lattices5 , superconducting circuits6 , and nuclear spin systems7,8, in addition to trapped ions9,10. Each simulator platform has its own advantages and challenges - cold atoms scale well but are difficult to control individually, whereas trapped ions and superconducting circuits face scaling difficulties but have experimentally-demonstrated individual control and readout techniques11. Both trapped ions12–17 and superconducting circuits18–20 have demonstrated great potential for implementing digital quantum simulations, using to date up to nine qubits. Here we investigate the feasibility of a digital simulation scheme with trapped ions. This scheme17 proposes a digital simulation of fermionic Hamiltonians using Mølmer-Sørensen gates in an ion trap. In this work, we show that a simpler gate, equally capable of efficiently implementing the fermionic simulation, may be constructed using faster resonant two-qubit gates21. We also show that Mølmer-Sørensen gates are incapable of implementing the simulation at a sufficient scale to outperform classical computers within the coherence time of current ion traps, and that fast gates could enable this level of performance using near-future laser technology. Our results motivate the pursuit of fast gates as a critical scaling tool for trapped-ion computing architectures.