Quantum perturbation theory using Tensor cores and a deep neural network

TL;DR

This paper introduces a novel approach to quantum response calculations by leveraging Tensor cores and deep neural network structures, achieving high performance and efficient convergence in mixed precision computations.

Contribution

It maps density matrix perturbation theory onto neural network-like structures and demonstrates near-peak GPU performance for quantum calculations.

Findings

Achieves close to 200 Tflops performance on Nvidia A100 GPUs.

Introduces a parameter-free convergence criterion for noisy low-precision calculations.

Successfully applies the method to quantum response theories like DFTB and Hartree-Fock.

Abstract

Time-independent quantum response calculations are performed using Tensor cores. This is achieved by mapping density matrix perturbation theory onto the computational structure of a deep neural network. The main computational cost of each deep layer is dominated by tensor contractions, i.e. dense matrix-matrix multiplications, in mixed precision arithmetics which achieves close to peak performance. Quantum response calculations are demonstrated and analyzed using self-consistent charge density-functional tight-binding theory as well as coupled-perturbed Hartree-Fock theory. For linear response calculations, a novel parameter-free convergence criterion is presented that is well-suited for numerically noisy low precision floating point operations and we demonstrate a peak performance of almost 200 Tflops using the Tensor cores of two Nvidia A100 GPUs.