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Minor Embedding in Broken Chimera and Pegasus Graphs is NP-complete

Lobe, Elisabeth and Lutz, Annette (2022) Minor Embedding in Broken Chimera and Pegasus Graphs is NP-complete. Theoretical Computer Science. Elsevier. ISSN 0304-3975. (Submitted)

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Abstract

The embedding is an essential step when calculating on the D-Wave machine. In this work we show the hardness of the embedding problem for both types of existing hardware, represented by the Chimera and the Pegasus graphs, containing unavailable qubits. We construct certain broken Chimera graphs, where it is hard to find a Hamiltonian cycle. As the Hamiltonian cycle problem is a special case of the embedding problem, this proves the general complexity result for the Chimera graphs. By exploiting the subgraph relation between the Chimera and the Pegasus graphs, the proof is then further extended to the Pegasus graphs.

Item URL in elib:https://elib.dlr.de/146749/
Document Type:Article
Title:Minor Embedding in Broken Chimera and Pegasus Graphs is NP-complete
Authors:
AuthorsInstitution or Email of AuthorsAuthor's ORCID iD
Lobe, ElisabethElisabeth.Lobe (at) dlr.dehttps://orcid.org/0000-0002-3473-8906
Lutz, AnnetteAnnette.Lutz (at) dlr.deUNSPECIFIED
Date:2022
Journal or Publication Title:Theoretical Computer Science
Refereed publication:Yes
Open Access:Yes
Gold Open Access:No
In SCOPUS:Yes
In ISI Web of Science:Yes
Publisher:Elsevier
Series Name:TCS-C
ISSN:0304-3975
Status:Submitted
Keywords:Graph minor, embedding, Hamiltonian cycle problem, NP-complete, quantum annealing, Chimera graph, Pegasus graph
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Space
HGF - Program Themes:Space System Technology
DLR - Research area:Raumfahrt
DLR - Program:R SY - Space System Technology
DLR - Research theme (Project):R - Quantum computing
Location: Braunschweig
Institutes and Institutions:Institute for Software Technology > High-Performance Computing
Institute for Software Technology
Deposited By: Lobe, Elisabeth
Deposited On:07 Dec 2021 11:52
Last Modified:07 Dec 2021 11:52

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