Reducing Numerical Precision Requirements in Quantum Chemistry Calculations

TL;DR

This paper investigates the precision needs of quantum chemistry calculations, demonstrating that lower precision can be used without losing accuracy, thus enabling faster computations on emerging low-precision hardware.

Contribution

It introduces an approximation method that reduces precision requirements in quantum chemistry kernels, facilitating optimized performance on future hardware.

Findings

Double precision is more than necessary for the kernel studied.

An error-free matrix multiplication transformation can accelerate calculations.

The results guide adaptation of quantum chemistry software for new HPC platforms.

Abstract

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.