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arXiv · 1908.11034

Carving-width and contraction trees for tensor networks

J. Jakes-Schauer·D. Anekstein·P. Wocjan
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Abstract

We study the problem of finding contraction orderings on tensor networks for physical simulations using a syncretic abstract data type, the $\textit{contraction-tree}$, and explain its connection to temporal and spatial measures of tensor contraction computational complexity (nodes express time; arcs express space). We have implemented the Ratcatcher of Seymour and Thomas for determining the carving-width of planar networks, in order to offer experimental evidence that this measure of spatial complexity makes a generally effective heuristic for limiting their total contraction time.

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J. Jakes-Schauer, D. Anekstein, P. Wocjan. 2019-08-29. Carving-width and contraction trees for tensor networks. https://arxiv.org/abs/1908.11034

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