Quantum annealing algorithms for Boolean tensor networks

Pelofske, Elijah; Hahn, Georg; O’Malley, Daniel; Djidjev, Hristo N.; Alexandrov, Boian S.

doi:10.1038/s41598-022-12611-9

Quantum annealing algorithms for Boolean tensor networks

Journal Article · Fri May 20 00:00:00 EDT 2022 · Scientific Reports

DOI:https://doi.org/10.1038/s41598-022-12611-9· OSTI ID:1869036

Pelofske, Elijah; Hahn, Georg; O’Malley, Daniel; Djidjev, Hristo N.; Alexandrov, Boian S.

Abstract

Quantum annealers manufactured by D-Wave Systems, Inc., are computational devices capable of finding high-quality heuristic solutions of NP-hard problems. In this contribution, we explore the potential and effectiveness of such quantum annealers for computing Boolean tensor networks. Tensors offer a natural way to model high-dimensional data commonplace in many scientific fields, and representing a binary tensor as a Boolean tensor network is the task of expressing a tensor containing categorical (i.e., $$$$\{0, 1\}$$$$ ${0, 1}$ ) values as a product of low dimensional binary tensors. A Boolean tensor network is computed by Boolean tensor decomposition, and it is usually not exact. The aim of such decomposition is to minimize the given distance measure between the high-dimensional input tensor and the product of lower-dimensional (usually three-dimensional) tensors and matrices representing the tensor network. In this paper, we introduce and analyze three general algorithms for Boolean tensor networks: Tucker, Tensor Train, and Hierarchical Tucker networks. The computation of a Boolean tensor network is reduced to a sequence of Boolean matrix factorizations, which we show can be expressed as a quadratic unconstrained binary optimization problem suitable for solving on a quantum annealer. By using a novel method we introduce called parallel quantum annealing, we demonstrate that Boolean tensor’s with up to millions of elements can be decomposed efficiently using a DWave 2000Q quantum annealer.

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Sponsoring Organization:: USDOE

OSTI ID:: 1869036

Alternate ID(s):: OSTI ID: 1870634

Journal Information:: Scientific Reports, Journal Name: Scientific Reports Journal Issue: 1 Vol. 12; ISSN 2045-2322

Publisher:: Nature Publishing GroupCopyright Statement

Country of Publication:: United Kingdom

Language:: English

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