Efficient quantum algorithm for dissipative nonlinear differential equations
<jats:title>Significance</jats:title> <jats:p>Nonlinear differential equations appear in many domains and are notoriously difficult to solve. Whereas previous quantum algorithms for general nonlinear differential equations have complexity exponential in the evolution tim...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Proceedings of the National Academy of Sciences
2023
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| Online Access: | https://hdl.handle.net/1721.1/147143 |
| _version_ | 1826207238005456896 |
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| author | Liu, Jin-Peng Kolden, Herman Øie Krovi, Hari K Loureiro, Nuno F Trivisa, Konstantina Childs, Andrew M |
| author2 | Massachusetts Institute of Technology. Department of Nuclear Science and Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Nuclear Science and Engineering Liu, Jin-Peng Kolden, Herman Øie Krovi, Hari K Loureiro, Nuno F Trivisa, Konstantina Childs, Andrew M |
| author_sort | Liu, Jin-Peng |
| collection | MIT |
| description | <jats:title>Significance</jats:title>
<jats:p>Nonlinear differential equations appear in many domains and are notoriously difficult to solve. Whereas previous quantum algorithms for general nonlinear differential equations have complexity exponential in the evolution time, we give the first quantum algorithm for dissipative nonlinear differential equations that is efficient provided the dissipation is sufficiently strong relative to nonlinear and forcing terms and the solution does not decay too rapidly. We also establish a lower bound showing that differential equations with sufficiently weak dissipation have worst-case complexity exponential in time, giving an almost tight classification of the quantum complexity of simulating nonlinear dynamics. Furthermore, numerical results for the Burgers equation suggest that our algorithm may potentially address complex nonlinear phenomena even in regimes with weaker dissipation.</jats:p> |
| first_indexed | 2024-09-23T13:46:12Z |
| format | Article |
| id | mit-1721.1/147143 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T13:46:12Z |
| publishDate | 2023 |
| publisher | Proceedings of the National Academy of Sciences |
| record_format | dspace |
| spelling | mit-1721.1/1471432023-01-18T03:22:22Z Efficient quantum algorithm for dissipative nonlinear differential equations Liu, Jin-Peng Kolden, Herman Øie Krovi, Hari K Loureiro, Nuno F Trivisa, Konstantina Childs, Andrew M Massachusetts Institute of Technology. Department of Nuclear Science and Engineering <jats:title>Significance</jats:title> <jats:p>Nonlinear differential equations appear in many domains and are notoriously difficult to solve. Whereas previous quantum algorithms for general nonlinear differential equations have complexity exponential in the evolution time, we give the first quantum algorithm for dissipative nonlinear differential equations that is efficient provided the dissipation is sufficiently strong relative to nonlinear and forcing terms and the solution does not decay too rapidly. We also establish a lower bound showing that differential equations with sufficiently weak dissipation have worst-case complexity exponential in time, giving an almost tight classification of the quantum complexity of simulating nonlinear dynamics. Furthermore, numerical results for the Burgers equation suggest that our algorithm may potentially address complex nonlinear phenomena even in regimes with weaker dissipation.</jats:p> 2023-01-17T18:25:06Z 2023-01-17T18:25:06Z 2021 2023-01-17T18:10:56Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/147143 Liu, Jin-Peng, Kolden, Herman Øie, Krovi, Hari K, Loureiro, Nuno F, Trivisa, Konstantina et al. 2021. "Efficient quantum algorithm for dissipative nonlinear differential equations." Proceedings of the National Academy of Sciences of the United States of America, 118 (35). en 10.1073/PNAS.2026805118 Proceedings of the National Academy of Sciences of the United States of America Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Proceedings of the National Academy of Sciences PNAS |
| spellingShingle | Liu, Jin-Peng Kolden, Herman Øie Krovi, Hari K Loureiro, Nuno F Trivisa, Konstantina Childs, Andrew M Efficient quantum algorithm for dissipative nonlinear differential equations |
| title | Efficient quantum algorithm for dissipative nonlinear differential equations |
| title_full | Efficient quantum algorithm for dissipative nonlinear differential equations |
| title_fullStr | Efficient quantum algorithm for dissipative nonlinear differential equations |
| title_full_unstemmed | Efficient quantum algorithm for dissipative nonlinear differential equations |
| title_short | Efficient quantum algorithm for dissipative nonlinear differential equations |
| title_sort | efficient quantum algorithm for dissipative nonlinear differential equations |
| url | https://hdl.handle.net/1721.1/147143 |
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