Tensor contractions are ubiquitous in computational chemistry andphysics, where tensors generally represent states or operators andcontractions express the algebra of these quantities. In this context,the states and operators often preserve physical conservation laws,which are manifested as group symmetries in the tensors. These groupsymmetries imply that each tensor has block sparsity and can be storedin a reduced form. For nontrivial contractions, the memory footprint andcost are lowered, respectively, by a linear and a quadratic factor inthe number of symmetry sectors. Stateoftheart tensor contractionsoftware libraries exploit this opportunity by iterating over blocks orusing general blocksparse tensor representations. Both approachesentail overhead in performance and code complexity. With intuition aidedby tensor diagrams, we present a technique, irreducible representationalignment, which enables efficient handling of Abelian group symmetriesvia only dense tensors, by using contractionspecific reduced forms.This technique yields a general algorithm for arbitrary group symmetriccontractions, which we implement in Python and apply to a variety ofrepresentative contractions from quantum chemistry and tensor networkmethods. As a consequence of relying on only dense tensor contractions,we can easily make use of efficient batched matrix multiplication viaIntelâ€™s MKL and distributed tensor contraction via the Cyclops library,achieving good efficiency and parallel scalability on up to 4096 KnightsLanding cores of a supercomputer.
more » « less Award ID(s):
 1931258
 NSFPAR ID:
 10477296
 Publisher / Repository:
 SciPost Physics Codebases
 Date Published:
 Journal Name:
 SciPost Physics Codebases
 ISSN:
 2949804X
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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