Quantum annealing algorithms for Boolean tensor networks

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...

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Veröffentlicht in:Scientific reports Jg. 12; H. 1; S. 8539 - 19
Hauptverfasser: Pelofske, Elijah, Hahn, Georg, O’Malley, Daniel, Djidjev, Hristo N., Alexandrov, Boian S.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: London Nature Publishing Group UK 20.05.2022
Nature Publishing Group
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Algorithms
Boolean
Computer applications
Computer science
D-Wave
Decomposition
Humanities and Social Sciences
MATHEMATICS AND COMPUTING
multidisciplinary
Parallel quantum annealing
Quantum annealing
Quantum information
Qubits
Science
Science (multidisciplinary)
Software
Tensor networks
Tensor train
Tucker
Tucker decomposition
ISSN:2045-2322, 2045-2322
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Zusammenfassung: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 } ) 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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LA-UR-21-27414
USDOE Laboratory Directed Research and Development (LDRD) Program
89233218CNA000001; 20190020DR; BG05M2OP001-1.001-0003
ISSN:2045-2322
2045-2322
DOI:10.1038/s41598-022-12611-9