Efficient 2d tensor network simulation of quantum systems

Yuchen Pang, Tianyi Hao, Annika Dugad, Yiqing Zhou, Edgar Solomonik

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

Abstract

Simulation of quantum systems is challenging due to the exponential size of the state space. Tensor networks provide a systematically improvable approximation for quantum states. 2D tensor networks such as Projected Entangled Pair States (PEPS) are well-suited for key classes of physical systems and quantum circuits. However, direct contraction of PEPS networks has exponential cost, while approximate algorithms require computations with large tensors. We propose new scalable algorithms and software abstractions for PEPS-based methods, accelerating the bottleneck operation of contraction and refactorization of a tensor subnetwork. We employ randomized SVD with an implicit matrix to reduce cost and memory footprint asymptotically. Further, we develop a distributed-memory PEPS library and study accuracy and efficiency of alternative algorithms for PEPS contraction and evolution on the Stampede2 supercomputer. We also simulate a popular near-term quantum algorithm, the Variational Quantum Eigensolver (VQE), and benchmark Imaginary Time Evolution (ITE), which compute ground states of Hamiltonians.

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
Externally publishedYes
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
Country/TerritoryUnited States
CityVirtual, Atlanta
Period11/9/2011/19/20

Keywords

  • Numerical simulation
  • Parallel algorithms
  • Quantum computing
  • Quantum mechanics

ASJC Scopus subject areas

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

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