Distributed-memory DMRG via sparse and dense parallel tensor contractions

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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.

Original languageEnglish (US)
Title of host publicationProceedings of SC 2020
Subtitle of host publicationInternational Conference for High Performance Computing, Networking, Storage and Analysis
PublisherIEEE Computer Society
ISBN (Electronic)9781728199986
DOIs
StatePublished - Nov 2020
Event2020 International Conference for High Performance Computing, Networking, Storage and Analysis, SC 2020 - Virtual, Atlanta, United States
Duration: Nov 9 2020Nov 19 2020

Publication series

NameInternational Conference for High Performance Computing, Networking, Storage and Analysis, SC
Volume2020-November
ISSN (Print)2167-4329
ISSN (Electronic)2167-4337

Conference

Conference2020 International Conference for High Performance Computing, Networking, Storage and Analysis, SC 2020
CountryUnited States
CityVirtual, Atlanta
Period11/9/2011/19/20

Keywords

  • Cyclops Tensor Framework
  • DMRG
  • quantum systems
  • sparse tensors
  • tensor contractions
  • tensor networks

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Computer Science Applications
  • Hardware and Architecture
  • Software

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