  The abundant demand for deep learning compute resources has created a
renaissance in low precision hardware. Going forward, it will be essential for
simulation software to run on this new generation of machines without
sacrificing scientific fidelity. In this paper, we examine the precision
requirements of a representative kernel from quantum chemistry calculations:
calculation of the single particle density matrix from a given mean field
Hamiltonian (i.e. Hartree-Fock or Density Functional Theory) represented in an
LCAO basis. We find that double precision affords an unnecessarily high level
of precision, leading to optimization opportunities. We show how an
approximation built from an error-free matrix multiplication transformation can
be used to potentially accelerate this kernel on future hardware. Our results
provide a road map for adapting quantum chemistry software for the next
generation of High Performance Computing platforms.
