  Quantum computers offer the potential to efficiently simulate the dynamics of
quantum systems, a task whose difficulty scales exponentially with system size
on classical devices. To assess the potential for near-term quantum computers
to simulate many-body systems we develop a formalism to straightforwardly
compute bounds on the number of Trotter steps needed to accurately simulate the
time evolution of fermionic lattice models based on the first-order commutator
scaling. We apply this formalism to two closely related many-body models
prominent in condensed matter physics, the Hubbard and t-J models. We find
that, while a naive comparison of the Trotter depth first seems to favor the
Hubbard model, careful consideration of the model parameters and the allowable
error for accurate simulation leads to a substantial advantage in favor of the
t-J model. These results and formalism set the stage for significant
improvements in quantum simulation costs.
