Minor Embedding in Broken Chimera and Pegasus Graphs is NP-complete
| Autor: | Lobe, Elisabeth, Lutz, Annette |
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| Rok vydání: | 2021 |
| Předmět: |
FOS: Computer and information sciences
F.2.2 G.2.2 Quantum Physics Graph minor quantum annealing FOS: Physical sciences Pegasus graph 68Q17 05C83 Computational Complexity (cs.CC) Nonlinear Sciences::Cellular Automata and Lattice Gases Hamiltonian cycle problem embedding Computer Science - Computational Complexity Nonlinear Sciences::Adaptation and Self-Organizing Systems Chimera graph Quantum Physics (quant-ph) NP-complete MathematicsofComputing_DISCRETEMATHEMATICS |
| DOI: | 10.48550/arxiv.2110.08325 |
| Popis: | 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. Comment: 36 pages, 21 figures |
| Databáze: | OpenAIRE |
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