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Minor embedding in broken chimera and derived graphs is NP-complete.

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Title: Minor embedding in broken chimera and derived graphs is NP-complete.
Authors: Lobe, Elisabeth1 (AUTHOR) elisabeth.lobe@dlr.de, Lutz, Annette2 (AUTHOR)
Source: Theoretical Computer Science. Mar2024, Vol. 989, pN.PAG-N.PAG. 1p.
Subjects: Hamiltonian graph theory, Quantum annealing, Qubits
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 all types of currently existing hardware, represented by the Chimera and the derived Pegasus and Zephyr 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 derived graphs, the proof is then further extended to the Pegasus graphs and to the Zephyr graphs. [ABSTRACT FROM AUTHOR]
Copyright of Theoretical Computer Science is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 175297824
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PubType: Academic Journal
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  Data: Minor embedding in broken chimera and derived graphs is NP-complete.
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  Data: <searchLink fieldCode="AR" term="%22Lobe%2C+Elisabeth%22">Lobe, Elisabeth</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> elisabeth.lobe@dlr.de</i><br /><searchLink fieldCode="AR" term="%22Lutz%2C+Annette%22">Lutz, Annette</searchLink><relatesTo>2</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Theoretical+Computer+Science%22">Theoretical Computer Science</searchLink>. Mar2024, Vol. 989, pN.PAG-N.PAG. 1p.
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  Data: <searchLink fieldCode="DE" term="%22Hamiltonian+graph+theory%22">Hamiltonian graph theory</searchLink><br /><searchLink fieldCode="DE" term="%22Quantum+annealing%22">Quantum annealing</searchLink><br /><searchLink fieldCode="DE" term="%22Qubits%22">Qubits</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: 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 all types of currently existing hardware, represented by the Chimera and the derived Pegasus and Zephyr 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 derived graphs, the proof is then further extended to the Pegasus graphs and to the Zephyr graphs. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Theoretical Computer Science is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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    Identifiers:
      – Type: doi
        Value: 10.1016/j.tcs.2023.114369
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      – Code: eng
        Text: English
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      – SubjectFull: Hamiltonian graph theory
        Type: general
      – SubjectFull: Quantum annealing
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      – SubjectFull: Qubits
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      – TitleFull: Minor embedding in broken chimera and derived graphs is NP-complete.
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              M: 03
              Text: Mar2024
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              Y: 2024
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