Distributed-Memory DMRG via Sparse and Dense Parallel Tensor Contractions

TL;DR

This paper introduces two new parallel tensor contraction methods for DMRG, significantly improving performance and scalability on supercomputers, enabling more accurate quantum system modeling.

Contribution

It presents novel parallel approaches handling tensor sparsity in DMRG using Cyclops, enhancing efficiency and scalability over existing methods.

Findings

Up to 5.9X faster runtime compared to ITensor

99X higher processing rate

Weak scalability of DMRG with efficient tensor contractions

Abstract

The Density Matrix Renormalization Group (DMRG) algorithm is a powerful tool for solving eigenvalue problems to model quantum systems. DMRG relies on tensor contractions and dense linear algebra to compute properties of condensed matter physics systems. However, its efficient parallel implementation is challenging due to limited concurrency, large memory footprint, and tensor sparsity. We mitigate these problems by implementing two new parallel approaches that handle block sparsity arising in DMRG, via Cyclops, a distributed memory tensor contraction library. We benchmark their performance on two physical systems using the Blue Waters and Stampede2 supercomputers. Our DMRG performance is improved by up to 5.9X in runtime and 99X in processing rate over ITensor, at roughly comparable computational resource use. This enables higher accuracy calculations via larger tensors for quantum state approximation. We demonstrate that despite having limited concurrency, DMRG is weakly scalable with the use of efficient parallel tensor contraction mechanisms.