  The utility of near-term quantum computers and simulators is likely to rely
upon software-hardware co-design, with error-aware algorithms and protocols
optimized for the platforms they are run on. Here, we show how knowledge of
noise in a system can be exploited to improve the design of gate-based quantum
simulation algorithms. We concretely demonstrate this co-design in the context
of a trapped ion quantum simulation of the dynamics of a Heisenberg spin model.
Specifically, we derive a theoretical noise model describing unitary gate
errors due to heating of the ions' collective motion, finding that the temporal
correlations in the noise induce an optimal gate depth. We then illustrate how
tailored feedforward control can be used to mitigate unitary gate errors and
improve the simulation outcome. Our results provide a practical guide to the
co-design of gate-based quantum simulation algorithms.
