Quantum Monte Carlo on graphical processing units

doi:10.1016/j.cpc.2007.03.004

2007-08-01

PRE

Amos G. Anderson *

William A. Goddard

Peter Schröder

DOI：10.1016/j.cpc.2007.03.004

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摘要

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Quantum Monte Carlo (QMC) is among the most accurate methods for solving the time independent Schrodinger equation. Unfortunately, the method is very expensive and requires a vast array of computing resources in order to obtain results of a reasonable convergence level. On the other hand, the method is not only easily parallelizable across CPU clusters, but as we report here, it also has a high degree of data parallelism. This facilitates the use of recent technological advances in Graphical Processing Units (GPUs), a powerful type of processor well known to computer gamers. In this paper we report on an end-to-end QMC application with core elements of the algorithm running on a GPU. With individual kernels achieving as much as 30x speed up, the overall application performs at up to 6x faster relative to an optimized CPU implementation, yet requires only a modest increase in hardware cost. This demonstrates the speedup improvements possible for QMC in running on advanced hardware, thus exploring a path toward providing QMC level accuracy as a more standard tool. The major current challenge in running codes of this type on the GPU arises from the lack of fully compliant IEEE floating point implementations. To achieve better accuracy we propose the use of the Kahan summation formula in matrix multiplications. While this drops overall performance, we demonstrate that the proposed new algorithm can match CPU single precision. (c) 2007 Elsevier B.V. All rights reserved.

Keyword:

graphical processing units

quantum Monte Carlo

matrix multiplication

floating point error

Kahan summation formula

de-normals