Quantum Algorithm for Approximating Maximum Independent Sets
<jats:p>We present a quantum algorithm for approximating maximum independent sets of a graph based on quantum non-Abelian adiabatic mixing in the sub-Hilbert space of degenerate ground states, which generates quantum annealing in a secondary Hamiltonian. For both sparse and dense random graphs...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
IOP Publishing
2022
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| Online Access: | https://hdl.handle.net/1721.1/142336 |
| _version_ | 1826205725179772928 |
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| author | Yu, Hongye Wilczek, Frank Wu, Biao |
| author2 | Massachusetts Institute of Technology. Center for Theoretical Physics |
| author_facet | Massachusetts Institute of Technology. Center for Theoretical Physics Yu, Hongye Wilczek, Frank Wu, Biao |
| author_sort | Yu, Hongye |
| collection | MIT |
| description | <jats:p>We present a quantum algorithm for approximating maximum independent sets of a graph based on quantum non-Abelian adiabatic mixing in the sub-Hilbert space of degenerate ground states, which generates quantum annealing in a secondary Hamiltonian. For both sparse and dense random graphs <jats:italic>G</jats:italic>, numerical simulation suggests that our algorithm on average finds an independent set of size close to the maximum size <jats:italic>α</jats:italic>(<jats:italic>G</jats:italic>) in low polynomial time. The best classical algorithms, by contrast, produce independent sets of size about half of <jats:italic>α</jats:italic>(<jats:italic>G</jats:italic>) in polynomial time.</jats:p> |
| first_indexed | 2024-09-23T13:17:36Z |
| format | Article |
| id | mit-1721.1/142336 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T13:17:36Z |
| publishDate | 2022 |
| publisher | IOP Publishing |
| record_format | dspace |
| spelling | mit-1721.1/1423362023-01-20T18:09:18Z Quantum Algorithm for Approximating Maximum Independent Sets Yu, Hongye Wilczek, Frank Wu, Biao Massachusetts Institute of Technology. Center for Theoretical Physics <jats:p>We present a quantum algorithm for approximating maximum independent sets of a graph based on quantum non-Abelian adiabatic mixing in the sub-Hilbert space of degenerate ground states, which generates quantum annealing in a secondary Hamiltonian. For both sparse and dense random graphs <jats:italic>G</jats:italic>, numerical simulation suggests that our algorithm on average finds an independent set of size close to the maximum size <jats:italic>α</jats:italic>(<jats:italic>G</jats:italic>) in low polynomial time. The best classical algorithms, by contrast, produce independent sets of size about half of <jats:italic>α</jats:italic>(<jats:italic>G</jats:italic>) in polynomial time.</jats:p> 2022-05-04T17:56:25Z 2022-05-04T17:56:25Z 2021 2022-05-04T17:12:30Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/142336 Yu, Hongye, Wilczek, Frank and Wu, Biao. 2021. "Quantum Algorithm for Approximating Maximum Independent Sets." Chinese Physics Letters, 38 (3). en 10.1088/0256-307X/38/3/030304 Chinese Physics Letters Attribution-NonCommercial-ShareAlike 4.0 International https://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf IOP Publishing arXiv |
| spellingShingle | Yu, Hongye Wilczek, Frank Wu, Biao Quantum Algorithm for Approximating Maximum Independent Sets |
| title | Quantum Algorithm for Approximating Maximum Independent Sets |
| title_full | Quantum Algorithm for Approximating Maximum Independent Sets |
| title_fullStr | Quantum Algorithm for Approximating Maximum Independent Sets |
| title_full_unstemmed | Quantum Algorithm for Approximating Maximum Independent Sets |
| title_short | Quantum Algorithm for Approximating Maximum Independent Sets |
| title_sort | quantum algorithm for approximating maximum independent sets |
| url | https://hdl.handle.net/1721.1/142336 |
| work_keys_str_mv | AT yuhongye quantumalgorithmforapproximatingmaximumindependentsets AT wilczekfrank quantumalgorithmforapproximatingmaximumindependentsets AT wubiao quantumalgorithmforapproximatingmaximumindependentsets |