# Automated Operation Minimization of Tensor Contraction Expressions in Electronic Structure Calculations

@inproceedings{Hartono2005AutomatedOM, title={Automated Operation Minimization of Tensor Contraction Expressions in Electronic Structure Calculations}, author={Albert Hartono and Alexander Sibiryakov and Marcel Nooijen and Gerald Baumgartner and David E. Bernholdt and So Hirata and Chi-Chung Lam and Russell M. Pitzer and J. Ramanujam and P. Sadayappan}, booktitle={International Conference on Computational Science}, year={2005} }

Complex tensor contraction expressions arise in accurate electronic structure models in quantum chemistry, such as the Coupled Cluster method. Transformations using algebraic properties of commutativity and associativity can be used to significantly decrease the number of arithmetic operations required for evaluation of these expressions, but the optimization problem is NP-hard. Operation minimization is an important optimization step for the Tensor Contraction Engine, a tool being developed…

## 31 Citations

### Identifying Cost-Effective Common Subexpressions to Reduce Operation Count in Tensor Contraction Evaluations

- Computer ScienceInternational Conference on Computational Science
- 2006

An effective algorithm for common subexpression identification is developed and its effectiveness on tensor contraction expressions for coupled cluster equations is demonstrated.

### Performance optimization of tensor contraction expressions for many-body methods in quantum chemistry.

- Computer ScienceThe journal of physical chemistry. A
- 2009

An effective algorithm for operation minimization with common subexpression identification is described and its effectiveness on tensor contraction expressions for coupled cluster equations is demonstrated and a library for efficient index permutation of multidimensional tensors is described.

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

- Computer Science
- 2012

### Framework for Distributed Contractions of Tensors with Symmetry

- Computer Science
- 2013

A novel approach is introduced that avoids data redistribution in contracting symmetric tensors while avoiding redundant storage and maintaining load balance and is presented on two parallel supercomputers.

### CAST: Contraction Algorithm for Symmetric Tensors

- Computer Science2014 43rd International Conference on Parallel Processing
- 2014

A novel approach that avoids data redistribution during contraction of symmetric tensors while also bypassing redundant storage and maintaining load balance is introduced, and a novel approach to tensor redistribution that can take advantage of parallel hyperplanes when the initial distribution has replicated dimensions is presented.

### Towards an efficient use of the BLAS library for multilinear tensor contractions

- Computer ScienceAppl. Math. Comput.
- 2014

### Faster identification of optimal contraction sequences for arbitrary tensor networks

- Computer Science
- 2014

This talk presents a novel approach to the search for an optimal gate application sequence which performs several orders of magnitude faster than existing search algorithms, while still guaranteeing identification of an optimal evaluation sequence for a given quantum circuit.

### Integrated compiler optimizations for tensor contractions

- Computer Science
- 2008

This dissertation addresses several performance optimization issues in the context of the Tensor Contraction Engine (TCE), a domain-specific compiler to synthesize parallel, out-of-core programs for…

### A Communication-Optimal Framework for Contracting Distributed Tensors

- Computer ScienceSC14: International Conference for High Performance Computing, Networking, Storage and Analysis
- 2014

A framework with three fundamental communication operators to generate communication-efficient contraction algorithms for arbitrary tensor contractions is developed and it is shown that for a given amount of memory per processor, the framework is communication optimal for all tensorcontractions.

### AutoHOOT: Automatic High-Order Optimization for Tensors

- Computer SciencePACT
- 2020

This work introduces AutoHOOT, the first automatic differentiation framework targeting at high-order optimization for tensor computations, which contains a new explicit Jacobian / Hessian expression generation kernel whose outputs maintain the input tensors' granularity and are easy to optimize.

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