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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: the 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 roadmap for adapting quantum chemistry software for the next generation of high-performance computing platforms.
Dawson et al. (Sat,) studied this question.