  This paper improves and demonstrates the usefulness of the first quantized
plane-wave algorithms for the quantum simulation of electronic structure,
developed by Babbush et al. and Su et al. We describe the first quantum
algorithm for first quantized simulation that accurately includes
pseudopotentials. We focus on the Goedecker-Tetter-Hutter (GTH)
pseudopotential, which is among the most accurate and widely used
norm-conserving pseudopotentials enabling the removal of core electrons from
the simulation. The resultant screened nuclear potential regularizes cusps in
the electronic wavefunction so that orders of magnitude fewer plane waves are
required for a chemically accurate basis. Despite the complicated form of the
GTH pseudopotential, we are able to block encode the associated operator
without significantly increasing the overall cost of quantum simulation. This
is surprising since simulating the nuclear potential is much simpler without
pseudopotentials, yet is still the bottleneck. We also generalize prior methods
to enable the simulation of materials with non-cubic unit cells, which requires
nontrivial modifications. Finally, we combine these techniques to estimate the
block-encoding costs for commercially relevant instances of heterogeneous
catalysis (e.g. carbon monoxide adsorption on transition metals) and compare to
the quantum resources needed to simulate materials in second quantization. We
conclude that for computational cells with many particles, first quantization
often requires meaningfully less spacetime volume.
