Effective Utilization of Tensor Symmetry in Operation Optimization of Tensor Contraction Expressions

The optimization of tensor expressions with hundreds of terms is required for the development of accurate quantum chemistry models such as the coupled cluster method. In this paper, we address the effective exploitation of symmetry properties of tensors in performing algebraic transformations for minimizing operation count of tensor expressions. We develop rules to detect symmetries in intermediate tensors, cost models for tensor contractions with symmetries, and a canonical representation to facilitate effective common subexpression elimination. We demonstrate significant improvements to the operation counts for the coupled cluster method when compared to several state-of-the-art im-plementations. Furthermore, we show that tensor expressions optimized for a few input parameter combinations can be used to achieve operation counts within 3% of the optimal, for the entire parameter space of interest.