  As noisy intermediate-scale quantum (NISQ) processors increase in size and
complexity, their use as general purpose quantum simulators will rely on
algorithms based on the Trotter-Suzuki expansion. We run quantum simulations on
a small, highly accurate quantum processor, and show how one can optimize
simulation accuracy by balancing algorithmic (Trotter) errors against native
errors specific to the quantum hardware at hand. We further study the interplay
between native errors, Trotter errors, and the emergence of chaos as seen in
measurements of a time averaged fidelity-out-of-time-ordered-correlator
