# Using Graph Partitioning for Scalable Distributed Quantum Molecular Dynamics

## TL;DR

This paper presents a graph partitioning approach to efficiently parallelize quantum molecular dynamics simulations by dividing the structure of the density matrix into components for scalable computation.

## Contribution

It introduces a novel graph partitioning method tailored for parallelizing matrix polynomial evaluations in quantum molecular dynamics simulations.

## Key findings

- Partitioning improves computational efficiency and scalability.
- Evaluation of different partitioning algorithms shows trade-offs between quality and runtime.
- The method enables more efficient large-scale quantum simulations.

## Abstract

The simulation of the physical movement of multi-body systems at an atomistic level, with forces calculated from a quantum mechanical description of the electrons, motivates a graph partitioning problem studied in this article. Several advanced algorithms relying on evaluations of matrix polynomials have been published in the literature for such simulations. We aim to use a special type of graph partitioning in order to efficiently parallelize these computations. For this, we create a graph representing the zero-nonzero structure of a thresholded density matrix, and partition that graph into several components. Each separate submatrix (corresponding to each subgraph) is then substituted into the matrix polynomial, and the result for the full matrix polynomial is reassembled at the end from the individual polynomials. This paper starts by introducing a rigorous definition as well as a mathematical justification of this partitioning problem. We assess the performance of several methods to compute graph partitions with respect to both the quality of the partitioning and their runtime.