Quantum algorithms for predicting the properties of complex materials

Grady Schofield, Yousef Saad, James R. Chelikowsky

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

Abstract

A central goal in computational materials science is to find efficient methods for solving the Kohn-Sham equation. The realization of this goal would allow one to predict properties such as phase stability, structure and optical and dielectric properties for a wide variety of materials. Typically, a solution of the Kohn-Sham equation requires computing a set of low-lying eigenpairs. Standard methods for computing such eigenpairs require two procedures: (a) maintaining the orthogonality of an approximation space, and (b) forming approximate eigenpairs with the Rayleigh-Ritz method. These two procedures scale cubically with the number of desired eigenpairs. Recently, we presented a method, applicable to any large Hermitian eigenproblem, by which the spectrum is partitioned among distinct groups of processors. This "divide and conquer" approach serves as a parallelization scheme at the level of the solver, making it compatible with existing schemes that parallelize at a physical level and at the level of primitive operations, e.g., matrix-vector multiplication. In addition, among all processor sets, the size of any approximation subspace is reduced, thereby reducing the cost of orthogonalization and the Rayleigh-Ritz method. We will address the key aspects of the algorithm, its implementation in real space, and demonstrate the nature of the algorithm by computing the electronic structure of a metal-semiconductor interface.

Original languageEnglish (US)
Title of host publicationProceedings of the XSEDE12 Conference
Subtitle of host publicationBridging from the eXtreme to the Campus and Beyond
DOIs
StatePublished - Aug 29 2012
Event1st Conference of the Extreme Science and Engineering Discovery Environment: Bridging from the eXtreme to the Campus and Beyond, XSEDE12 - Chicago, IL, United States
Duration: Jul 16 2012Jul 19 2012

Publication series

NameACM International Conference Proceeding Series

Other

Other1st Conference of the Extreme Science and Engineering Discovery Environment: Bridging from the eXtreme to the Campus and Beyond, XSEDE12
CountryUnited States
CityChicago, IL
Period7/16/127/19/12

Keywords

  • Kohn-Sham equation
  • complex materials
  • pseudopotentials
  • spectrum slicing

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