  Although the simulation of quantum chemistry is one of the most anticipated
applications of quantum computing, the scaling of known upper bounds on the
complexity of these algorithms is daunting. Prior work has bounded errors due
to Trotterization in terms of the norm of the error operator and analyzed
scaling with respect to the number of spin-orbitals. However, we find that
these error bounds can be loose by up to sixteen orders of magnitude for some
molecules. Furthermore, numerical results for small systems fail to reveal any
clear correlation between ground state error and number of spin-orbitals. We
instead argue that chemical properties, such as the maximum nuclear charge in a
molecule and the filling fraction of orbitals, can be decisive for determining
the cost of a quantum simulation. Our analysis motivates several strategies to
use classical processing to further reduce the required Trotter step size and
to estimate the necessary number of steps, without requiring additional quantum
resources. Finally, we demonstrate improved methods for state preparation
techniques which are asymptotically superior to proposals in the simulation
literature.
