Benchmarking treewidth as a practical component of tensor network simulations

Dumitrescu, Eugene F.; Fisher, Allison L.; Goodrich, Timothy D.; Humble, Travis S.; Sullivan, Blair D.; Wright, Andrew L.

doi:10.1371/journal.pone.0207827

Title: Benchmarking treewidth as a practical component of tensor network simulations

Journal Article · 18 December 2018 · PLoS ONE

DOI: https://doi.org/10.1371/journal.pone.0207827 · OSTI ID:1490605

^[1]; Fisher, Allison L. ^[2];

^[2];

^[1];

^[2]; Wright, Andrew L. ^[2]

Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
North Carolina State Univ., Raleigh, NC (United States)

Tensor networks are powerful factorization techniques which reduce resource requirements for numerically simulating principal quantum many-body systems and algorithms. The computational complexity of a tensor network simulation depends on the tensor ranks and the order in which they are contracted. Unfortunately, computing optimal contraction sequences (orderings) in general is known to be a computationally difficult (NP-complete) task. In 2005, Markov and Shi showed that optimal contraction sequences correspond to optimal (minimum width) tree decompositions of a tensor network’s line graph, relating the contraction sequence problem to a rich literature in structural graph theory. While treewidth-based methods have largely been ignored in favor of dataset-specific algorithms in the prior tensor networks literature, we demonstrate their practical relevance for problems arising from two distinct methods used in quantum simulation: multi-scale entanglement renormalization ansatz (MERA) datasets and quantum circuits generated by the quantum approximate optimization algorithm (QAOA). We exhibit multiple regimes where treewidth-based algorithms outperform domain-specific algorithms, while demonstrating that the optimal choice of algorithm has a complex dependence on the network density, expected contraction complexity, and user run time requirements. We further provide an open source software framework designed with an emphasis on accessibility and extendability, enabling replicable experimental evaluations and future exploration of competing methods by practitioners.

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Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 1490605

Journal Information:: PLoS ONE, Vol. 13, Issue 12; ISSN 1932-6203

Publisher:: Public Library of ScienceCopyright Statement

Country of Publication:: United States

Language:: English

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