TY - GEN

T1 - Quantum algorithms for predicting the properties of complex materials

AU - Schofield, Grady

AU - Saad, Yousef

AU - Chelikowsky, James R.

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

KW - Kohn-Sham equation

KW - complex materials

KW - pseudopotentials

KW - spectrum slicing

UR - http://www.scopus.com/inward/record.url?scp=84865332625&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84865332625&partnerID=8YFLogxK

U2 - 10.1145/2335755.2335820

DO - 10.1145/2335755.2335820

M3 - Conference contribution

AN - SCOPUS:84865332625

SN - 9781450316026

T3 - ACM International Conference Proceeding Series

BT - Proceedings of the XSEDE12 Conference

T2 - 1st Conference of the Extreme Science and Engineering Discovery Environment: Bridging from the eXtreme to the Campus and Beyond, XSEDE12

Y2 - 16 July 2012 through 19 July 2012

ER -