Quantum walk on a chimera graph
We analyse a continuous-time quantum walk on a chimera graph, which is a graph of choice for designing quantum annealers, and we discover beautiful quantum walk features such as localization that starkly distinguishes classical from quantum behaviour. Motivated by technological thrusts, we study con...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2018-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/aab701 |
| _version_ | 1797750787226468352 |
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| author | Shu Xu Xiangxiang Sun Jizhou Wu Wei-Wei Zhang Nigum Arshed Barry C Sanders |
| author_facet | Shu Xu Xiangxiang Sun Jizhou Wu Wei-Wei Zhang Nigum Arshed Barry C Sanders |
| author_sort | Shu Xu |
| collection | DOAJ |
| description | We analyse a continuous-time quantum walk on a chimera graph, which is a graph of choice for designing quantum annealers, and we discover beautiful quantum walk features such as localization that starkly distinguishes classical from quantum behaviour. Motivated by technological thrusts, we study continuous-time quantum walk on enhanced variants of the chimera graph and on diminished chimera graph with a random removal of vertices. We explain the quantum walk by constructing a generating set for a suitable subgroup of graph isomorphisms and corresponding symmetry operators that commute with the quantum walk Hamiltonian; the Hamiltonian and these symmetry operators provide a complete set of labels for the spectrum and the stationary states. Our quantum walk characterization of the chimera graph and its variants yields valuable insights into graphs used for designing quantum-annealers. |
| first_indexed | 2024-03-12T16:37:52Z |
| format | Article |
| id | doaj.art-c85d82f3300b41faaa2bae1f67ca6b57 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:37:52Z |
| publishDate | 2018-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-c85d82f3300b41faaa2bae1f67ca6b572023-08-08T14:48:22ZengIOP PublishingNew Journal of Physics1367-26302018-01-0120505303910.1088/1367-2630/aab701Quantum walk on a chimera graphShu Xu0https://orcid.org/0000-0003-1062-9075Xiangxiang Sun1https://orcid.org/0000-0001-9248-5188Jizhou Wu2https://orcid.org/0000-0003-4732-1437Wei-Wei Zhang3https://orcid.org/0000-0002-8164-9527Nigum Arshed4https://orcid.org/0000-0002-7631-4431Barry C Sanders5https://orcid.org/0000-0002-8326-8912Shanghai Branch, National Laboratory for Physical Sciences at Microscale, University of Science and Technology of China , Shanghai 201315, People's Republic of ChinaDepartment of Modern Physics, University of Science and Technology of China , Hefei, Anhui 230026, People's Republic of ChinaShanghai Branch, National Laboratory for Physical Sciences at Microscale, University of Science and Technology of China , Shanghai 201315, People's Republic of ChinaShanghai Branch, National Laboratory for Physical Sciences at Microscale, University of Science and Technology of China , Shanghai 201315, People's Republic of ChinaShanghai Branch, National Laboratory for Physical Sciences at Microscale, University of Science and Technology of China , Shanghai 201315, People's Republic of ChinaShanghai Branch, National Laboratory for Physical Sciences at Microscale, University of Science and Technology of China , Shanghai 201315, People's Republic of China; Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China , Hefei, Anhui 230026, People's Republic of China; Institute for Quantum Science and Technology, University of Calgary , Alberta T2N 1N4, Canada; Program in Quantum Information Science, Canadian Institute for Advanced Research , Toronto, Ontario M5G 1Z8, CanadaWe analyse a continuous-time quantum walk on a chimera graph, which is a graph of choice for designing quantum annealers, and we discover beautiful quantum walk features such as localization that starkly distinguishes classical from quantum behaviour. Motivated by technological thrusts, we study continuous-time quantum walk on enhanced variants of the chimera graph and on diminished chimera graph with a random removal of vertices. We explain the quantum walk by constructing a generating set for a suitable subgroup of graph isomorphisms and corresponding symmetry operators that commute with the quantum walk Hamiltonian; the Hamiltonian and these symmetry operators provide a complete set of labels for the spectrum and the stationary states. Our quantum walk characterization of the chimera graph and its variants yields valuable insights into graphs used for designing quantum-annealers.https://doi.org/10.1088/1367-2630/aab701quantum walkquantum computationquantum simulation03.67.Ac |
| spellingShingle | Shu Xu Xiangxiang Sun Jizhou Wu Wei-Wei Zhang Nigum Arshed Barry C Sanders Quantum walk on a chimera graph New Journal of Physics quantum walk quantum computation quantum simulation 03.67.Ac |
| title | Quantum walk on a chimera graph |
| title_full | Quantum walk on a chimera graph |
| title_fullStr | Quantum walk on a chimera graph |
| title_full_unstemmed | Quantum walk on a chimera graph |
| title_short | Quantum walk on a chimera graph |
| title_sort | quantum walk on a chimera graph |
| topic | quantum walk quantum computation quantum simulation 03.67.Ac |
| url | https://doi.org/10.1088/1367-2630/aab701 |
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