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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/ | |||||||||
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| Document Type: | Article | |||||||||
| Title: | Minor Embedding in Broken Chimera and Pegasus Graphs is NP-complete | |||||||||
| Authors: |
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| 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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